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Read the passage and answer the following questions:
To better understand how the brain underlies selfhood, we need to understand its complex form; its intricate structure at the level of connections between neurons. After all, understanding biological structure has revealed the nature of many diverse life forms. Plants thrive because their typically broad leaves are perfect for transducing light energy into vital chemical energy. Similarly, eyes, whether human or insect, enable the transduction of light from one’s surroundings into electrical signals within the nervous system. These impulses carry information that represents features of the surrounding environment. But when it comes to the relationship between structure and function, brains have remained an enigma. There’s a lot more to them than to other organs that have specific functions, such as eyes, hearts or even hands. These organs can now be surgically replaced. Yet, even if a brain transplant were possible, you couldn’t just switch your brain with another person’s and maintain the same mind. Upon birth, a person’s brain structure is largely prescribed by experience in the womb and their unique genetic code. As we age, experience continues to imprint unique changes on the brain’s neural connectivity, increasing connections in some areas while decreasing them in others, accumulating reroutes upon reroutes as a person ages and learns, gaining knowledge and experience. Additionally, there are alterations in the strength of existing connections. These processes are especially evident in twins, whose brains are strikingly similar when born. However, as they grow, learn and experience the world, their brains diverge, and their essential selves become increasingly unique.
Although there are indeed anatomical regions that appear to serve relatively specific functions, one’s memory is not formed, stored or recalled within the activity of any single brain region. Certain structures, such as the amygdala and the hippocampus, play key roles but trying to find memory in one specific area is simply impossible. It would be like trying to listen to Beethoven’s Fifth but hearing only the strings. Instead, memory, in its broadest sense, lies in the uniqueness of a brain’s entire connective structure, known as the connectome. The connectome consists of its complete network of neurons and all the connections between them, called synapses. It is argued that, fundamentally, ‘you are your connectome’.
Mapping a connectome at the level of single neurons, however, is currently impossible in a living animal. Instead, animal brains must be extracted, perfused with a fixative such as formaldehyde and sliced up as many times as possible before being analysed structurally in order to painstakingly find individual neurons and trace their paths. To achieve this, the properties of each new slice are recorded using various microscopy techniques. Once that’s been done, patterns of electrical flow can be estimated from different neuron types and from connections that excite or inhibit other neurons. What’s crucial is that the extracted brain is preserved accurately enough to maintain its intricate, complex connectome before it’s sliced up.
Currently, it’s unlikely that any human brain has been preserved with its entire connectome perfectly intact as our brains degrade too quickly after death.
Which of the following can be inferred from the passage?
"...Yet, even if a brain transplant were possible, you couldn’t just switch your brain with another person’s and maintain the same mind..." From the above lines, it is evident that the idea being conveyed by the author does not match the claim being made in Option A. The statement in A distorts the purpose of the comment made by the author and hence, can be eliminated as the correct answer.
"...Upon birth, a person’s brain structure is largely prescribed by experience in the womb and their unique genetic code..." From the above lines, it is evident that an individual's experience inside his/her mother's womb is not solely responsible for the formulation of his/her brain structure. We can reject Option B since it presents us with an extreme (not implied in the passage).
Option C is out of scope since there is no comparison about the growth of plants based on the broadness of their leaves.
Option D can clearly be inferred from the following lines: "...What’s crucial is that the extracted brain is preserved accurately enough to maintain its intricate, complex connectome before it’s sliced up..."
Hence, Option D is the correct answer.
Read the passage and answer the following questions:
To better understand how the brain underlies selfhood, we need to understand its complex form; its intricate structure at the level of connections between neurons. After all, understanding biological structure has revealed the nature of many diverse life forms. Plants thrive because their typically broad leaves are perfect for transducing light energy into vital chemical energy. Similarly, eyes, whether human or insect, enable the transduction of light from one’s surroundings into electrical signals within the nervous system. These impulses carry information that represents features of the surrounding environment. But when it comes to the relationship between structure and function, brains have remained an enigma. There’s a lot more to them than to other organs that have specific functions, such as eyes, hearts or even hands. These organs can now be surgically replaced. Yet, even if a brain transplant were possible, you couldn’t just switch your brain with another person’s and maintain the same mind. Upon birth, a person’s brain structure is largely prescribed by experience in the womb and their unique genetic code. As we age, experience continues to imprint unique changes on the brain’s neural connectivity, increasing connections in some areas while decreasing them in others, accumulating reroutes upon reroutes as a person ages and learns, gaining knowledge and experience. Additionally, there are alterations in the strength of existing connections. These processes are especially evident in twins, whose brains are strikingly similar when born. However, as they grow, learn and experience the world, their brains diverge, and their essential selves become increasingly unique.
Although there are indeed anatomical regions that appear to serve relatively specific functions, one’s memory is not formed, stored or recalled within the activity of any single brain region. Certain structures, such as the amygdala and the hippocampus, play key roles but trying to find memory in one specific area is simply impossible. It would be like trying to listen to Beethoven’s Fifth but hearing only the strings. Instead, memory, in its broadest sense, lies in the uniqueness of a brain’s entire connective structure, known as the connectome. The connectome consists of its complete network of neurons and all the connections between them, called synapses. It is argued that, fundamentally, ‘you are your connectome’.
Mapping a connectome at the level of single neurons, however, is currently impossible in a living animal. Instead, animal brains must be extracted, perfused with a fixative such as formaldehyde and sliced up as many times as possible before being analysed structurally in order to painstakingly find individual neurons and trace their paths. To achieve this, the properties of each new slice are recorded using various microscopy techniques. Once that’s been done, patterns of electrical flow can be estimated from different neuron types and from connections that excite or inhibit other neurons. What’s crucial is that the extracted brain is preserved accurately enough to maintain its intricate, complex connectome before it’s sliced up.
Currently, it’s unlikely that any human brain has been preserved with its entire connectome perfectly intact as our brains degrade too quickly after death.
The author mentions the example of plants and eyes at the beginning to...
Let us pay heed to the introduction: "To better understand how the brain underlies selfhood, we need to understand its complex form; its intricate structure at the level of connections between neurons. After all, understanding biological structure has revealed the nature of many diverse life forms. Plants thrive because their typically broad leaves are perfect for transducing light energy into vital chemical energy. Similarly, eyes, whether human or insect, enable the transduction of light from one’s surroundings into electrical signals within the nervous system. These impulses carry information that represents features of the surrounding environment. But when it comes to the relationship between structure and function, brains have remained an enigma..."
The author begins with the claim that a better grasp of the underlying structure or the complex form of the brain might aid in understanding its role in selfhood. He furthers his claim by mentioning that this has been the case with many diverse life forms  gaining a deeper awareness of their biological structure enabled a better understanding of their function. The example of plants and the eyes have been mentioned in this regard: to supplement this assertion. However, at the same time, the author hints at how the brain does not completely adhere to this relation (of structure and function), and there are unknown elements present associated with the brain functioning (associated cognitive processes). Option C captures this correctly.
Option A: The author's focus is not on making the readers understand the structure of plants or the eyes; instead, the biological structure is tied up to a corresponding function Option A does not capture the author's intention and hence, can be eliminated.
Option B: The statement here appears to be far fetched. The author doesn't assert that understanding the biological structure "always" reveals the nature of life forms; he specifies that this is the case in some situations and with certain entities. Thus, we can reject Option B.
Option D: The author clearly states that extending the same idea (as is the case with plants and the eyes) to the brain would be inappropriate due to the inherent complexity). Option D deviates from this idea and is, therefore, incorrect.
Hence, Option C is the correct answer.
Read the passage and answer the following questions:
To better understand how the brain underlies selfhood, we need to understand its complex form; its intricate structure at the level of connections between neurons. After all, understanding biological structure has revealed the nature of many diverse life forms. Plants thrive because their typically broad leaves are perfect for transducing light energy into vital chemical energy. Similarly, eyes, whether human or insect, enable the transduction of light from one’s surroundings into electrical signals within the nervous system. These impulses carry information that represents features of the surrounding environment. But when it comes to the relationship between structure and function, brains have remained an enigma. There’s a lot more to them than to other organs that have specific functions, such as eyes, hearts or even hands. These organs can now be surgically replaced. Yet, even if a brain transplant were possible, you couldn’t just switch your brain with another person’s and maintain the same mind. Upon birth, a person’s brain structure is largely prescribed by experience in the womb and their unique genetic code. As we age, experience continues to imprint unique changes on the brain’s neural connectivity, increasing connections in some areas while decreasing them in others, accumulating reroutes upon reroutes as a person ages and learns, gaining knowledge and experience. Additionally, there are alterations in the strength of existing connections. These processes are especially evident in twins, whose brains are strikingly similar when born. However, as they grow, learn and experience the world, their brains diverge, and their essential selves become increasingly unique.
Although there are indeed anatomical regions that appear to serve relatively specific functions, one’s memory is not formed, stored or recalled within the activity of any single brain region. Certain structures, such as the amygdala and the hippocampus, play key roles but trying to find memory in one specific area is simply impossible. It would be like trying to listen to Beethoven’s Fifth but hearing only the strings. Instead, memory, in its broadest sense, lies in the uniqueness of a brain’s entire connective structure, known as the connectome. The connectome consists of its complete network of neurons and all the connections between them, called synapses. It is argued that, fundamentally, ‘you are your connectome’.
Mapping a connectome at the level of single neurons, however, is currently impossible in a living animal. Instead, animal brains must be extracted, perfused with a fixative such as formaldehyde and sliced up as many times as possible before being analysed structurally in order to painstakingly find individual neurons and trace their paths. To achieve this, the properties of each new slice are recorded using various microscopy techniques. Once that’s been done, patterns of electrical flow can be estimated from different neuron types and from connections that excite or inhibit other neurons. What’s crucial is that the extracted brain is preserved accurately enough to maintain its intricate, complex connectome before it’s sliced up.
Currently, it’s unlikely that any human brain has been preserved with its entire connectome perfectly intact as our brains degrade too quickly after death.
Why does the author cite the example of Beethoven’s Fifth?
Option A is incorrect since the author does not discuss the relative difficulty of understanding Beethoven's Fifth and the working of the brain at the neural level. ("as challenging as")
It is true that the amygdala and the hippocampus play a crucial role in the brain. But the phrase 'equally important' used in B makes the option incorrect because no comparison is made between them on the basis of the magnitude of their importance. Additionally, the statement here misses out on the core point being conveyed.
"...Certain structures, such as the amygdala and the hippocampus, play key roles but trying to find memory in one specific area is simply impossible. It would be like trying to listen to Beethoven’s Fifth but hearing only the strings..."
Option C is incorrect because we are not trying to separate the string part out of the entire symphony when listening, but we are trying to listen to Beethoven’s Fifth just by hearing the strings. So, option C conveys a different meaning.
From the following lines in the passage  "...Certain structures, such as the amygdala and the hippocampus, play key roles but trying to find memory in one specific area is simply impossible. It would be like trying to listen to Beethoven’s Fifth but hearing only the strings..." we can understand that if we focus on a particular part of the brain, we won't be able to understand the whole. As is said in the passage, it would be like trying to listen to Beethoven’s Fifth by only hearing the strings. Option D captures this aptly.
Read the passage and answer the following questions:
To better understand how the brain underlies selfhood, we need to understand its complex form; its intricate structure at the level of connections between neurons. After all, understanding biological structure has revealed the nature of many diverse life forms. Plants thrive because their typically broad leaves are perfect for transducing light energy into vital chemical energy. Similarly, eyes, whether human or insect, enable the transduction of light from one’s surroundings into electrical signals within the nervous system. These impulses carry information that represents features of the surrounding environment. But when it comes to the relationship between structure and function, brains have remained an enigma. There’s a lot more to them than to other organs that have specific functions, such as eyes, hearts or even hands. These organs can now be surgically replaced. Yet, even if a brain transplant were possible, you couldn’t just switch your brain with another person’s and maintain the same mind. Upon birth, a person’s brain structure is largely prescribed by experience in the womb and their unique genetic code. As we age, experience continues to imprint unique changes on the brain’s neural connectivity, increasing connections in some areas while decreasing them in others, accumulating reroutes upon reroutes as a person ages and learns, gaining knowledge and experience. Additionally, there are alterations in the strength of existing connections. These processes are especially evident in twins, whose brains are strikingly similar when born. However, as they grow, learn and experience the world, their brains diverge, and their essential selves become increasingly unique.
Although there are indeed anatomical regions that appear to serve relatively specific functions, one’s memory is not formed, stored or recalled within the activity of any single brain region. Certain structures, such as the amygdala and the hippocampus, play key roles but trying to find memory in one specific area is simply impossible. It would be like trying to listen to Beethoven’s Fifth but hearing only the strings. Instead, memory, in its broadest sense, lies in the uniqueness of a brain’s entire connective structure, known as the connectome. The connectome consists of its complete network of neurons and all the connections between them, called synapses. It is argued that, fundamentally, ‘you are your connectome’.
Mapping a connectome at the level of single neurons, however, is currently impossible in a living animal. Instead, animal brains must be extracted, perfused with a fixative such as formaldehyde and sliced up as many times as possible before being analysed structurally in order to painstakingly find individual neurons and trace their paths. To achieve this, the properties of each new slice are recorded using various microscopy techniques. Once that’s been done, patterns of electrical flow can be estimated from different neuron types and from connections that excite or inhibit other neurons. What’s crucial is that the extracted brain is preserved accurately enough to maintain its intricate, complex connectome before it’s sliced up.
Currently, it’s unlikely that any human brain has been preserved with its entire connectome perfectly intact as our brains degrade too quickly after death.
Which of the following sentences is/are true as per the passage?
"...There’s a lot more to them than to other organs that have specific functions, such as eyes, hearts or even hands. These organs can now be surgically replaced..." Although the author does render us with examples highlighting that this might be the case, there is more to the picture that needs to be considered. The author introduces an additional constraint: "...Yet, even if a brain transplant were possible, you couldn’t just switch your brain with another person’s and maintain the same mind...". Hence, we cannot definitively state that Option A is true (inadequate information).
We can consider Option B to be true from the following lines "These processes are especially evident in twins, whose brains are strikingly similar when born. However, as they grow, learn and experience the world, their brains diverge, and their essential selves become increasingly unique."
"...Currently, it’s unlikely that any human brain has been preserved with its entire connectome perfectly intact as our brains degrade too quickly after death..." Although the author makes this assertion, the future of the preservation of the human brain is not a subject that is touched upon. Hence, Option C is out of scope.
"...Mapping a connectome at the level of single neurons, however, is currently impossible in a living animal..." Although this comment is made, we can eliminate Option D on the same grounds as Option C (out of scope).
Hence, Option B is the correct answer.
Read the passage carefully and answer the following questions:
We must dispense with the idea that democracy is like a torch that gets passed from one leading society to another. The core feature of democracy  that those who rule can do so only with the consent of the people  wasn’t invented in one place at one time: it evolved independently in a great many human societies. Over several millennia and across multiple continents, early democracy was an institution in which rulers governed jointly with councils and assemblies of the people. Classical Greece provided particularly important instances of this democratic practice, and it’s true that the Greeks gave us a language for thinking about democracy, including the word demokratia itself. But they didn’t invent the practice. The core feature of early democracy was that the people had power, even if multiparty elections didn’t happen. The people, or at least some significant fraction of them, exercised this power in many different ways. In some cases, a ruler was chosen by a council or assembly, and was limited to being first among equals. In other instances, a ruler inherited their position, but faced constraints to seek consent from the people before taking actions both large and small.
The first difference between early democracy and our democracies today is that this earlier form of rule was a smallscale phenomenon. In Classical Athens those who had the right to participate in politics tended to do so in a very direct and intensive way, particularly in local assemblies. In modern democracy, participation is very broad, but it’s also not deep; for most of us, it’s limited to voting in elections every few years, and in between these moments others make the decisions. The potential risk of this arrangement, as has been noted by astute observers since the birth of modern republics, is that citizens might grow distrustful of the people who are actually running government on a daily basis and of the special influences to which they might be subject. One way to address the problem of scale is to delegate much more power to states, provinces and localities. But on crucial issues of foreign trade, diplomacy or pressing constitutional questions, it’s impractical for individual states, regions or provinces to set their own policy. If large scale has the potential to lead to distrust and disengagement in a democracy, then a closely related problem is that of polarisation, which can take many forms, such as that involving tensions between different classes of people in the same location, or a difference of opinions between people living in different locations.
The absence of a state bureaucracy was a chief reason why early democracy proved to be such a stable form of rule for so many societies. With little autonomous power  apart from the ability to persuade  those who would have liked to rule as autocrats found themselves without the means to do so. The flipside of this was that, in many early democracies, those who were unhappy with a central decision could simply refuse to participate or even decamp to a new locality. Modern democracy lacks the same protections from central power that early democracies enjoyed. At the same time, having a powerful central state can allow a society to achieve goals such as universal education and prosperity, to name but a few. The question then is how to live with a state while preserving democracy.
Which of the following can be inferred from the passage?
Option A: "...If large scale has the potential to lead to distrust and disengagement in a democracy, then a closely related problem is that of polarisation..." It is not implied in the passage that large scale democracy can solve the problem of polarization. Hence, Option A cannot be inferred.
Option B: "...One way to address the problem of scale is to delegate much more power to states, provinces and localities..." The word "majority" in B distorts the point conveyed by the author. It is stated that more powers should be delegated to the state.
Option C: "...At the same time, having a powerful central state can allow a society to achieve goals such as universal education and prosperity, to name but a few..." From the passage, we cannot infer that universal education and prosperity are the most important goals of society. This makes option C incorrect as well.
Option D: "...In modern democracy, participation is very broad, but it’s also not deep; for most of us, it’s limited to voting in elections every few years, and in between these moments others make the decisions. The potential risk of this arrangement (...) is that citizens might grow distrustful of the people who are actually running the government..." From the abovementioned lines, we can infer that the reason behind citizens growing distrustful of the government would be the lack of depth in their participation. Being restricted to voting every few years and not having a say in government policies is an issue for the general masses.
Hence, Option D can be inferred from the passage.
Read the passage carefully and answer the following questions:
We must dispense with the idea that democracy is like a torch that gets passed from one leading society to another. The core feature of democracy  that those who rule can do so only with the consent of the people  wasn’t invented in one place at one time: it evolved independently in a great many human societies. Over several millennia and across multiple continents, early democracy was an institution in which rulers governed jointly with councils and assemblies of the people. Classical Greece provided particularly important instances of this democratic practice, and it’s true that the Greeks gave us a language for thinking about democracy, including the word demokratia itself. But they didn’t invent the practice. The core feature of early democracy was that the people had power, even if multiparty elections didn’t happen. The people, or at least some significant fraction of them, exercised this power in many different ways. In some cases, a ruler was chosen by a council or assembly, and was limited to being first among equals. In other instances, a ruler inherited their position, but faced constraints to seek consent from the people before taking actions both large and small.
The first difference between early democracy and our democracies today is that this earlier form of rule was a smallscale phenomenon. In Classical Athens those who had the right to participate in politics tended to do so in a very direct and intensive way, particularly in local assemblies. In modern democracy, participation is very broad, but it’s also not deep; for most of us, it’s limited to voting in elections every few years, and in between these moments others make the decisions. The potential risk of this arrangement, as has been noted by astute observers since the birth of modern republics, is that citizens might grow distrustful of the people who are actually running government on a daily basis and of the special influences to which they might be subject. One way to address the problem of scale is to delegate much more power to states, provinces and localities. But on crucial issues of foreign trade, diplomacy or pressing constitutional questions, it’s impractical for individual states, regions or provinces to set their own policy. If large scale has the potential to lead to distrust and disengagement in a democracy, then a closely related problem is that of polarisation, which can take many forms, such as that involving tensions between different classes of people in the same location, or a difference of opinions between people living in different locations.
The absence of a state bureaucracy was a chief reason why early democracy proved to be such a stable form of rule for so many societies. With little autonomous power  apart from the ability to persuade  those who would have liked to rule as autocrats found themselves without the means to do so. The flipside of this was that, in many early democracies, those who were unhappy with a central decision could simply refuse to participate or even decamp to a new locality. Modern democracy lacks the same protections from central power that early democracies enjoyed. At the same time, having a powerful central state can allow a society to achieve goals such as universal education and prosperity, to name but a few. The question then is how to live with a state while preserving democracy.
Why does the author mention the local assemblies of Classical Athens?
The author states the following at the beginning of the second paragraph: "...The first difference between early democracy and our democracies today is that this earlier form of rule was a smallscale phenomenon. In Classical Athens, those who had the right to participate in politics tended to do so in a very direct and intensive way, particularly in local assemblies. In modern democracies, participation is very broad, but it’s also not deep; for most of us, it’s limited to voting in elections every few years, and in between these moments others make the decisions...."
From the excerpt above, we can understand that the author is trying to highlight the differences between earlier and modern democracies regarding how much and how many citizens were involved in the running of the government. Option C correctly captures this point.
The author is not trying to prove that earlier democracies were better than the modern ones in any respect. An objective comparison highlighting the difference in scale is being undertaken here. Hence, Option A can be eliminated.
The intention is not to persuade the readers in any manner. Additionally, the author does not emphasize the need for intensive and direct participation in modern democracies (not implied). Hence Option B can be rejected.
It is not conveyed that the direct participation that used to happen in earlier democracies cannot happen in modern ones. Hence, Option D is incorrect.
Option C accurately clarifies the reason behind the author mentioning the local assemblies of Classical Athens.
Read the passage carefully and answer the following questions:
We must dispense with the idea that democracy is like a torch that gets passed from one leading society to another. The core feature of democracy  that those who rule can do so only with the consent of the people  wasn’t invented in one place at one time: it evolved independently in a great many human societies. Over several millennia and across multiple continents, early democracy was an institution in which rulers governed jointly with councils and assemblies of the people. Classical Greece provided particularly important instances of this democratic practice, and it’s true that the Greeks gave us a language for thinking about democracy, including the word demokratia itself. But they didn’t invent the practice. The core feature of early democracy was that the people had power, even if multiparty elections didn’t happen. The people, or at least some significant fraction of them, exercised this power in many different ways. In some cases, a ruler was chosen by a council or assembly, and was limited to being first among equals. In other instances, a ruler inherited their position, but faced constraints to seek consent from the people before taking actions both large and small.
The first difference between early democracy and our democracies today is that this earlier form of rule was a smallscale phenomenon. In Classical Athens those who had the right to participate in politics tended to do so in a very direct and intensive way, particularly in local assemblies. In modern democracy, participation is very broad, but it’s also not deep; for most of us, it’s limited to voting in elections every few years, and in between these moments others make the decisions. The potential risk of this arrangement, as has been noted by astute observers since the birth of modern republics, is that citizens might grow distrustful of the people who are actually running government on a daily basis and of the special influences to which they might be subject. One way to address the problem of scale is to delegate much more power to states, provinces and localities. But on crucial issues of foreign trade, diplomacy or pressing constitutional questions, it’s impractical for individual states, regions or provinces to set their own policy. If large scale has the potential to lead to distrust and disengagement in a democracy, then a closely related problem is that of polarisation, which can take many forms, such as that involving tensions between different classes of people in the same location, or a difference of opinions between people living in different locations.
The absence of a state bureaucracy was a chief reason why early democracy proved to be such a stable form of rule for so many societies. With little autonomous power  apart from the ability to persuade  those who would have liked to rule as autocrats found themselves without the means to do so. The flipside of this was that, in many early democracies, those who were unhappy with a central decision could simply refuse to participate or even decamp to a new locality. Modern democracy lacks the same protections from central power that early democracies enjoyed. At the same time, having a powerful central state can allow a society to achieve goals such as universal education and prosperity, to name but a few. The question then is how to live with a state while preserving democracy.
Which of the following is the author of the passage most likely to agree with?
" In modern democracy, participation is very broad, but it’s also not deep; for most of us, it’s limited to voting in elections every few years, and in between these moments others make the decisions. The potential risk of this arrangement, as has been noted by astute observers since the birth of modern republics, is that citizens might grow distrustful of the people who are actually running government on a daily basis..."
From the above lines, it is clear that when people don't participate or engage in decision making, they begin to lose trust in the government. So, if people participate sporadically, as mentioned in option A, there will be little trust between the government and the public. Hence, the author will not agree with sentence A.
On the other hand, option D proposes transparency and openness. The author is propublic participation as can be seen from the passage. Option D, if implemented, could foster trust and improve participation and thus would be something the author agrees with.
" At the same time, having a powerful central state can allow a society to achieve goals such as universal education and prosperity, to name but a few."
Even though the passage says that the presence of state bureaucracy allows the centre to be more powerful, it also mentions some of the important goals that can be achieved only with a powerful central state. So, option B is incorrect.
The author never implies something that is mentioned in option C as it is not feasible since modern democracies are largescale and would disrupt the working of the government.
Read the passage carefully and answer the following questions:
We must dispense with the idea that democracy is like a torch that gets passed from one leading society to another. The core feature of democracy  that those who rule can do so only with the consent of the people  wasn’t invented in one place at one time: it evolved independently in a great many human societies. Over several millennia and across multiple continents, early democracy was an institution in which rulers governed jointly with councils and assemblies of the people. Classical Greece provided particularly important instances of this democratic practice, and it’s true that the Greeks gave us a language for thinking about democracy, including the word demokratia itself. But they didn’t invent the practice. The core feature of early democracy was that the people had power, even if multiparty elections didn’t happen. The people, or at least some significant fraction of them, exercised this power in many different ways. In some cases, a ruler was chosen by a council or assembly, and was limited to being first among equals. In other instances, a ruler inherited their position, but faced constraints to seek consent from the people before taking actions both large and small.
The first difference between early democracy and our democracies today is that this earlier form of rule was a smallscale phenomenon. In Classical Athens those who had the right to participate in politics tended to do so in a very direct and intensive way, particularly in local assemblies. In modern democracy, participation is very broad, but it’s also not deep; for most of us, it’s limited to voting in elections every few years, and in between these moments others make the decisions. The potential risk of this arrangement, as has been noted by astute observers since the birth of modern republics, is that citizens might grow distrustful of the people who are actually running government on a daily basis and of the special influences to which they might be subject. One way to address the problem of scale is to delegate much more power to states, provinces and localities. But on crucial issues of foreign trade, diplomacy or pressing constitutional questions, it’s impractical for individual states, regions or provinces to set their own policy. If large scale has the potential to lead to distrust and disengagement in a democracy, then a closely related problem is that of polarisation, which can take many forms, such as that involving tensions between different classes of people in the same location, or a difference of opinions between people living in different locations.
The absence of a state bureaucracy was a chief reason why early democracy proved to be such a stable form of rule for so many societies. With little autonomous power  apart from the ability to persuade  those who would have liked to rule as autocrats found themselves without the means to do so. The flipside of this was that, in many early democracies, those who were unhappy with a central decision could simply refuse to participate or even decamp to a new locality. Modern democracy lacks the same protections from central power that early democracies enjoyed. At the same time, having a powerful central state can allow a society to achieve goals such as universal education and prosperity, to name but a few. The question then is how to live with a state while preserving democracy.
Which of the following cannot be inferred from the passage?
I. Classical Greece did not just invent the practice of democracy, but also gave us the word 'demokratia'.
II. The advantage of early democracies over modern ones is the very direct and intensive participation of the people in local assemblies.
III. The presence or absence of state bureaucracy is a vital factor affecting the stability of a democratic rule.
Statement I: In the introductory paragraph of the passage, it is mentioned that "it’s true that the Greeks gave us a language for thinking about democracy, including the word demokratia itself. But they didn’t invent the practice." So, statement I cannot be inferred.
Statement II: The passage does differentiate between early and modern democracies on the basis of depth and extent of participation of the people in the process of decision making but does not tell us that this makes one advantageous over the other. Statement II cannot be inferred.
Statement III: "The absence of a state bureaucracy was a chief reason why early democracy proved to be such a stable form of rule for so many societies. With little autonomous power  apart from the ability to persuade  those who would have liked to rule as autocrats found themselves without the means to do so." makes statement III inferrable as it states that it is a 'chief' reason and there was no scope for an autocratic rule.
Hence, Statements I and II
cannot be inferred from the passage. Option A is the correct answer.
Read the passage carefully and answer the following questions:
Green energy investment is hot again in the U.S. To some, the new boom will raise the specter of the cleantech bust that followed a streak of exuberance a decade ago. But there are reasons to believe that this time the trend is no bubble or mirage.
The most basic reason is that the fundamental underlying technology has matured in a way it simply hadn’t a decade ago. In 2009, the levelized cost of solar photovoltaic electricity was $359 per megawatthour — more than four times as expensive as electricity from a natural gas plant. By 2019, solar PV had fallen in price to $40 per megawatthour, 28% cheaper than gas. That’s an 89% decline in 10 years, with more cost drops yet to come. Meanwhile, lithiumion batteries have experienced a similar drop in prices.
That orderofmagnitude drop in costs makes all the difference. First of all, it means that solar and wind aren’t risky new technologies. Solyndra, a solar manufacturer, failed in 2011 because it was trying to market an innovative new kind of solar cell, which ended up being too expensive when the triedandtrue design came down in cost. Future investments in solar won’t have to bet on any difficult technological breakthroughs. Batteries might be a different story — lots of money is being thrown at startups trying to create solidstate batteries, which would be a true breakthrough. But Tesla Inc. is doing just fine with the old kind, so that sector is probably going to do OK as well. Venture investing does well when it doesn’t have to bet on “hard tech”, and much of clean tech is no longer hard.
Second, cost drops in clean energy mean that success doesn’t depend on government intervention. In the earlier boom, fickle government subsidies were often necessary for capitalintensive energy companies to succeed. Now, even though President Joe Biden is planning a big push into cleanenergy investment, the market is investing quite a lot in renewables all on its own.
Finally, investors have probably learned their lesson. Clean energy itself was never a good fit for venture. It’s capital intensive, since buying solar panels and wind turbines entails a lot of money up front; venture capital tends to focus on cheap, small investments that scale. And instead of companies creating highly differentiated products and new markets, as in software, clean electricity companies are basically all trying to provide the same commodified product.
This time around, venture capitalists are letting bigger investors handle the build out of solar and wind, and finding other niches where lowcost, differentiated startups can add value — such as solar services and financing, labgrown meat and electric vehicles. Some of those bets are certainly going to fail, but that’s always the case in private equity. The success of Tesla — now with a market cap of almost $700 billion, or 28 times the amount that was lost in the cleantech bust — demonstrates the timehonored principle that a few big hits can compensate for a lot of little failures.
In other words, clean tech is entering the final stage of the famous Gartner Hype Cycle — a pattern that describes the progression of emerging technologies and business models, starting with an innovation that sees expectations climb and then crash, before they finally rise again to sustained productivity. The cleantech bust, like the dotcom bust in 2000, was a case of investor enthusiasm for a new technology outstripping the technology itself. But just as few today would question the value of companies like Google and Facebook that came into their own during a trough in investor enthusiasm, eventually the value of clean technology won’t be in question.
The central idea of the passage is that
In the passage, the author opines that the cleantech industry is witnessing a surge in investments, and unlike the last time, which ended in a cleantech bust, this time, it may well be the start of a sustainable phase for the industry. He also provides several reasons to justify his stance. Additionally, he believes that the investors have learned their lessons from the cleantech bust and are ready to make mature investment decisions.
Option B conveys the above inference and is the answer. The other options are either extreme or tangential to the discussion.
Option A is true, but it is not the central idea of the passage.
Option C fails to capture all the relevant points. In the fifth paragraph, the author states "Clean energy itself was never a good fit for venture. It’s capital intensive, since buying solar panels and wind turbines entails a lot of money up front; venture capital tends to focus on cheap, small investments that scale." Hence, clean energy was never a good fit for venture capitalists, according to the author. The dearth of differentiated products cannot be quoted as the sole reason for this hypothesis. The capitalintensive nature of the industry is equally important, if not more. Hence, option C can be eliminated.
Option D can be eliminated as well. It is tangential to the discussion. Furthermore, in the second paragraph, the author mentions that the cleantech industry has evolved, which is a major reason why there might not be another cleantech bust. So, it is not possible to say that investor overenthusiasm alone leads to bubbles and economic crises.
Read the passage carefully and answer the following questions:
Green energy investment is hot again in the U.S. To some, the new boom will raise the specter of the cleantech bust that followed a streak of exuberance a decade ago. But there are reasons to believe that this time the trend is no bubble or mirage.
The most basic reason is that the fundamental underlying technology has matured in a way it simply hadn’t a decade ago. In 2009, the levelized cost of solar photovoltaic electricity was $359 per megawatthour — more than four times as expensive as electricity from a natural gas plant. By 2019, solar PV had fallen in price to $40 per megawatthour, 28% cheaper than gas. That’s an 89% decline in 10 years, with more cost drops yet to come. Meanwhile, lithiumion batteries have experienced a similar drop in prices.
That orderofmagnitude drop in costs makes all the difference. First of all, it means that solar and wind aren’t risky new technologies. Solyndra, a solar manufacturer, failed in 2011 because it was trying to market an innovative new kind of solar cell, which ended up being too expensive when the triedandtrue design came down in cost. Future investments in solar won’t have to bet on any difficult technological breakthroughs. Batteries might be a different story — lots of money is being thrown at startups trying to create solidstate batteries, which would be a true breakthrough. But Tesla Inc. is doing just fine with the old kind, so that sector is probably going to do OK as well. Venture investing does well when it doesn’t have to bet on “hard tech”, and much of clean tech is no longer hard.
Second, cost drops in clean energy mean that success doesn’t depend on government intervention. In the earlier boom, fickle government subsidies were often necessary for capitalintensive energy companies to succeed. Now, even though President Joe Biden is planning a big push into cleanenergy investment, the market is investing quite a lot in renewables all on its own.
Finally, investors have probably learned their lesson. Clean energy itself was never a good fit for venture. It’s capital intensive, since buying solar panels and wind turbines entails a lot of money up front; venture capital tends to focus on cheap, small investments that scale. And instead of companies creating highly differentiated products and new markets, as in software, clean electricity companies are basically all trying to provide the same commodified product.
This time around, venture capitalists are letting bigger investors handle the build out of solar and wind, and finding other niches where lowcost, differentiated startups can add value — such as solar services and financing, labgrown meat and electric vehicles. Some of those bets are certainly going to fail, but that’s always the case in private equity. The success of Tesla — now with a market cap of almost $700 billion, or 28 times the amount that was lost in the cleantech bust — demonstrates the timehonored principle that a few big hits can compensate for a lot of little failures.
In other words, clean tech is entering the final stage of the famous Gartner Hype Cycle — a pattern that describes the progression of emerging technologies and business models, starting with an innovation that sees expectations climb and then crash, before they finally rise again to sustained productivity. The cleantech bust, like the dotcom bust in 2000, was a case of investor enthusiasm for a new technology outstripping the technology itself. But just as few today would question the value of companies like Google and Facebook that came into their own during a trough in investor enthusiasm, eventually the value of clean technology won’t be in question.
The author compares the cleantech bust to the dotcom bust because
In the last paragraph, the author states that "...The cleantech bust, like the dotcom bust in 2000, was a case of investor enthusiasm for a new technology outstripping the technology itself...." So, the rate of increase in investment and the number of investors onboarded was incongruent with the pace at which the technology was developing. Comparing the options, Option C conveys this inference in the best way.
Option A talks about investor enthusiasm stalling technological progress, which cannot be inferred.
Option B, too, is out of context. The author does not discuss the investors' knowledge of the technology's limitations.
Option D is incorrect. The author does not make such an assertion.
Hence, Option C is the correct answer.
Read the passage carefully and answer the following questions:
Green energy investment is hot again in the U.S. To some, the new boom will raise the specter of the cleantech bust that followed a streak of exuberance a decade ago. But there are reasons to believe that this time the trend is no bubble or mirage.
The most basic reason is that the fundamental underlying technology has matured in a way it simply hadn’t a decade ago. In 2009, the levelized cost of solar photovoltaic electricity was $359 per megawatthour — more than four times as expensive as electricity from a natural gas plant. By 2019, solar PV had fallen in price to $40 per megawatthour, 28% cheaper than gas. That’s an 89% decline in 10 years, with more cost drops yet to come. Meanwhile, lithiumion batteries have experienced a similar drop in prices.
That orderofmagnitude drop in costs makes all the difference. First of all, it means that solar and wind aren’t risky new technologies. Solyndra, a solar manufacturer, failed in 2011 because it was trying to market an innovative new kind of solar cell, which ended up being too expensive when the triedandtrue design came down in cost. Future investments in solar won’t have to bet on any difficult technological breakthroughs. Batteries might be a different story — lots of money is being thrown at startups trying to create solidstate batteries, which would be a true breakthrough. But Tesla Inc. is doing just fine with the old kind, so that sector is probably going to do OK as well. Venture investing does well when it doesn’t have to bet on “hard tech”, and much of clean tech is no longer hard.
Second, cost drops in clean energy mean that success doesn’t depend on government intervention. In the earlier boom, fickle government subsidies were often necessary for capitalintensive energy companies to succeed. Now, even though President Joe Biden is planning a big push into cleanenergy investment, the market is investing quite a lot in renewables all on its own.
Finally, investors have probably learned their lesson. Clean energy itself was never a good fit for venture. It’s capital intensive, since buying solar panels and wind turbines entails a lot of money up front; venture capital tends to focus on cheap, small investments that scale. And instead of companies creating highly differentiated products and new markets, as in software, clean electricity companies are basically all trying to provide the same commodified product.
This time around, venture capitalists are letting bigger investors handle the build out of solar and wind, and finding other niches where lowcost, differentiated startups can add value — such as solar services and financing, labgrown meat and electric vehicles. Some of those bets are certainly going to fail, but that’s always the case in private equity. The success of Tesla — now with a market cap of almost $700 billion, or 28 times the amount that was lost in the cleantech bust — demonstrates the timehonored principle that a few big hits can compensate for a lot of little failures.
In other words, clean tech is entering the final stage of the famous Gartner Hype Cycle — a pattern that describes the progression of emerging technologies and business models, starting with an innovation that sees expectations climb and then crash, before they finally rise again to sustained productivity. The cleantech bust, like the dotcom bust in 2000, was a case of investor enthusiasm for a new technology outstripping the technology itself. But just as few today would question the value of companies like Google and Facebook that came into their own during a trough in investor enthusiasm, eventually the value of clean technology won’t be in question.
According to the passage, which of the following is NOT a reason why the increase in green energy investments may not be a bubble this time?
In the second paragraph, the author states that the underlying technology has matured, and many forms of energy, including solar and lithium batteries, have become cheaper. This significant decrease in costs has lowered the risks associated with the investments in these areas. Hence, Option A can be inferred.
"Second, cost drops in clean energy mean that success doesn’t depend on government intervention......the market is investing quite a lot in renewables all on its own." Option B can be inferred from these lines.
In the fifth and the sixth paragraphs, the author discusses why clean energy was never a good fit for venture capitalists and how they have moved away from capital intensive sectors to niche areas that are lowcost and differentiated. Hence, Option D can be inferred too.
Option C is a distortion. In the passage, the author comments that "Future investments in solar won’t have to bet on any difficult technological breakthroughs." However, this observation cannot be generalised. Furthermore, the author also discusses the importance of solidstate batteries, opining that it would be a major breakthrough in the future. Hence, Option C is the answer.
Read the passage carefully and answer the following questions:
Green energy investment is hot again in the U.S. To some, the new boom will raise the specter of the cleantech bust that followed a streak of exuberance a decade ago. But there are reasons to believe that this time the trend is no bubble or mirage.
The most basic reason is that the fundamental underlying technology has matured in a way it simply hadn’t a decade ago. In 2009, the levelized cost of solar photovoltaic electricity was $359 per megawatthour — more than four times as expensive as electricity from a natural gas plant. By 2019, solar PV had fallen in price to $40 per megawatthour, 28% cheaper than gas. That’s an 89% decline in 10 years, with more cost drops yet to come. Meanwhile, lithiumion batteries have experienced a similar drop in prices.
That orderofmagnitude drop in costs makes all the difference. First of all, it means that solar and wind aren’t risky new technologies. Solyndra, a solar manufacturer, failed in 2011 because it was trying to market an innovative new kind of solar cell, which ended up being too expensive when the triedandtrue design came down in cost. Future investments in solar won’t have to bet on any difficult technological breakthroughs. Batteries might be a different story — lots of money is being thrown at startups trying to create solidstate batteries, which would be a true breakthrough. But Tesla Inc. is doing just fine with the old kind, so that sector is probably going to do OK as well. Venture investing does well when it doesn’t have to bet on “hard tech”, and much of clean tech is no longer hard.
Second, cost drops in clean energy mean that success doesn’t depend on government intervention. In the earlier boom, fickle government subsidies were often necessary for capitalintensive energy companies to succeed. Now, even though President Joe Biden is planning a big push into cleanenergy investment, the market is investing quite a lot in renewables all on its own.
Finally, investors have probably learned their lesson. Clean energy itself was never a good fit for venture. It’s capital intensive, since buying solar panels and wind turbines entails a lot of money up front; venture capital tends to focus on cheap, small investments that scale. And instead of companies creating highly differentiated products and new markets, as in software, clean electricity companies are basically all trying to provide the same commodified product.
This time around, venture capitalists are letting bigger investors handle the build out of solar and wind, and finding other niches where lowcost, differentiated startups can add value — such as solar services and financing, labgrown meat and electric vehicles. Some of those bets are certainly going to fail, but that’s always the case in private equity. The success of Tesla — now with a market cap of almost $700 billion, or 28 times the amount that was lost in the cleantech bust — demonstrates the timehonored principle that a few big hits can compensate for a lot of little failures.
In other words, clean tech is entering the final stage of the famous Gartner Hype Cycle — a pattern that describes the progression of emerging technologies and business models, starting with an innovation that sees expectations climb and then crash, before they finally rise again to sustained productivity. The cleantech bust, like the dotcom bust in 2000, was a case of investor enthusiasm for a new technology outstripping the technology itself. But just as few today would question the value of companies like Google and Facebook that came into their own during a trough in investor enthusiasm, eventually the value of clean technology won’t be in question.
According to the author, which of the following is NOT a feature of venture investing?
I. Venture investing generally thrives when the decisions are not contingent on technological breakthroughs.
II. Venture capitalists largely invest in lowrisk endeavours.
III. Venture capitalists focus on cheap, small investments that are scalable.
IV. Venture capitalists do not invest in established technology companies that have achieved economies of scale.
{"Venture investing does well when it doesn’t have to bet on hard tech"}. Statement I can be inferred from this line.
Statement II has not been implied in the passage. In fact, venture investing entails an element of risk. For example, in the penultimate paragraph, the author mentions that {"Some of those bets are certainly going to fail, but that’s always the case in private equity."} Hence, venture investments can often be risky.
{"venture capital tends to focus on cheap, small investments that scale."} Statement III is a nearverbatim inference from this line.
Statement IV has not been implied in the passage. Though venture capitalists focus on startups and small investments that can be scaled, it does not transitively rule out VC investment in established technological companies. Hence, statement IV cannot be inferred.
Statements II and IV cannot be inferred. Option A is the answer.
Read the passage carefully and answer the following questions:
Green energy investment is hot again in the U.S. To some, the new boom will raise the specter of the cleantech bust that followed a streak of exuberance a decade ago. But there are reasons to believe that this time the trend is no bubble or mirage.
The most basic reason is that the fundamental underlying technology has matured in a way it simply hadn’t a decade ago. In 2009, the levelized cost of solar photovoltaic electricity was $359 per megawatthour — more than four times as expensive as electricity from a natural gas plant. By 2019, solar PV had fallen in price to $40 per megawatthour, 28% cheaper than gas. That’s an 89% decline in 10 years, with more cost drops yet to come. Meanwhile, lithiumion batteries have experienced a similar drop in prices.
That orderofmagnitude drop in costs makes all the difference. First of all, it means that solar and wind aren’t risky new technologies. Solyndra, a solar manufacturer, failed in 2011 because it was trying to market an innovative new kind of solar cell, which ended up being too expensive when the triedandtrue design came down in cost. Future investments in solar won’t have to bet on any difficult technological breakthroughs. Batteries might be a different story — lots of money is being thrown at startups trying to create solidstate batteries, which would be a true breakthrough. But Tesla Inc. is doing just fine with the old kind, so that sector is probably going to do OK as well. Venture investing does well when it doesn’t have to bet on “hard tech”, and much of clean tech is no longer hard.
Second, cost drops in clean energy mean that success doesn’t depend on government intervention. In the earlier boom, fickle government subsidies were often necessary for capitalintensive energy companies to succeed. Now, even though President Joe Biden is planning a big push into cleanenergy investment, the market is investing quite a lot in renewables all on its own.
Finally, investors have probably learned their lesson. Clean energy itself was never a good fit for venture. It’s capital intensive, since buying solar panels and wind turbines entails a lot of money up front; venture capital tends to focus on cheap, small investments that scale. And instead of companies creating highly differentiated products and new markets, as in software, clean electricity companies are basically all trying to provide the same commodified product.
This time around, venture capitalists are letting bigger investors handle the build out of solar and wind, and finding other niches where lowcost, differentiated startups can add value — such as solar services and financing, labgrown meat and electric vehicles. Some of those bets are certainly going to fail, but that’s always the case in private equity. The success of Tesla — now with a market cap of almost $700 billion, or 28 times the amount that was lost in the cleantech bust — demonstrates the timehonored principle that a few big hits can compensate for a lot of little failures.
In other words, clean tech is entering the final stage of the famous Gartner Hype Cycle — a pattern that describes the progression of emerging technologies and business models, starting with an innovation that sees expectations climb and then crash, before they finally rise again to sustained productivity. The cleantech bust, like the dotcom bust in 2000, was a case of investor enthusiasm for a new technology outstripping the technology itself. But just as few today would question the value of companies like Google and Facebook that came into their own during a trough in investor enthusiasm, eventually the value of clean technology won’t be in question.
The author is least likely to agree with which of the following statements?
In the penultimate paragraph, the author cites the example of Tesla, which recovered its losses incurred during the cleantech bust, a period of investor disillusionment, and has since increased its market cap severalfold. So, the author would agree with the statement in Option A.
According to the Gartner Hype Cycle, emerging technology or business model first piques investor interest and then sees a dip in that enthusiasm, followed by a recovery that eventually leads to sustained productivity. So, a technology that traverses this path would eventually enjoy consistent growth and productivity. Hence, the chances of a second bubble are slim to none. The author would agree with Option B.
In the sixth paragraph, the author comments on the strategic tweak made by venture capitals, focussing on startups in niche areas working on differentiated products. He further cites this as one of the reasons why there may not be another bubble. Hence, he agrees with this strategy. Option C is implied.
The author is least likely to agree with the statement in option D. The author particularly endorses the strategy adopted by venture capitals, who focus on startups that seek to innovate and come up with differentiated products while letting bigger investors handle the buildout of solar and wind. Hence, the author is not likely to propose a onesizefitsall strategy for investors, which Option D suggests.
Hence, Option D is the correct answer.
Read the passage carefully and answer the following questions:
Over the last decade, an increasingly confident right wing has presented disillusioned voters with a simple choice: elitist, neoliberal hyperglobalisation or popular, patriotic nationalism. This new faultline pits economic and social liberalism against social conservatism and the promise of muscular economic intervention. Despite the defeat of Donald Trump in 2020, progressives have yet to find a strategy to combat this potent—if false—divide.
The traditional rightleft dividing line—economic liberalism and social conservatism on the right, economic interventionism and social liberalism on the left—forced workingclass nationalists to choose between their socially conservative instincts (including hostility to immigration) and their support for state intervention in the economy. In essence, they had to decide which liberalism—social or economic—to reject.
The 2016 Brexit referendum freed such voters from this restraint—and it certainly set back the old liberal order. But despite many jumping to the conclusion that fervent nationalism explained the whole Brexit phenomenon, it was not clear which liberalism was being rejected. Many of the towns that repudiated the EU were voting just as much against the deindustrialisation that took place during the years Britain was in the EU as they were voting to restore a supposedly Edenic 1950s. Back in the conventional world of parliamentary elections, in 2017 Labour’s antineoliberal economic programme under Jeremy Corbyn added 3.5m votes to its 2015 general election tally. But by 2019, identity trumped economics—on which the Tories, Labour's opponents, had anyway begun to change their tune under Boris Johnson—and the red wall crumbled.
The British right was not alone in affecting to spurn both liberalisms. From Warsaw via Workington to Wisconsin, workingclass voters received promises from rightwing populists that their economic interests would not be sacrificed on the altar of neoliberalism. Poland’s Law and Justice Party adopted an economic and social programme that would win over “leftbehind” Poles. Marine Le Pen’s National Front professed to abandon its fascist past and moved the spotlight onto protecting French industry. Johnson committed his party to an interventionist “levellingup” agenda. And Trump promised industrial protection against overseas competition, as well as the biggest programme of public works since the New Deal.
This new faultline not only redrew the political map: it fractured the old consensus around core democratic values—stretching from right to left—that had existed since the Second World War. These values were rooted in the French Revolution and European Enlightenment and comprised an alliance of liberty, equality and solidarity, which could accommodate Christian Democrats, liberals, social democrats and orthodox socialists, albeit in different proportions.
The nationalist farright rejects these values. Echoing the rhetorical tropes of antidemocratic forces from the interwar years, populists like Trump promote conspiracy theories in which liberal politicians plot to destroy national sovereignty in the interests of global financial capital. A politics of demonisation, exclusion and “othering” has seeped into mainstream rightwing parties. In the United States, it culminated in Trump’s incitement of his supporters to storm the Capitol on 6th January to overturn the result of the 2020 election.
In a recent essay, Timothy Garton Ash argues that “liberals need to join both conservatives and socialists in fullheartedly embracing the value of solidarity.” But for intellectual conservatives like the late Roger Scruton (whom Garton Ash quotes) as well as chauvinist politicians—like Trump, Le Pen, Viktor Orbán and the Italian League’s Matteo Salvini—solidarity always has to rely on an inherently exclusionary notion of identity: we’re who we are because you’re not. Progressive social solidarity is, by contrast, accepting of difference. However, socialists and liberals have much in common in the battle against the far right: together, they can build on the social gains of the Harold Wilson and Tony Blair governments, allying around social and political liberty as well as the economics of equality.
Which of the following statements can be inferred from the passage?
Option A could be true but cannot be inferred from the passage. The author does not present any detail pertaining to religion's role in shaping the ideologies of social conservatives.
Option B is out of scope as well. Moreover, the economic liberalists do not entirely oppose state intervention in a market economy. They are more concerned about state intervention jeopardising free trade.
{"The British right was not alone in affecting to spurn both liberalisms..."} The author discusses how rightwing politicians in many parts of the world today pretend to reject both types of liberalisms. He then gives several examples of economic interventions supported by these politicians that protect local industries and the workingclass people. Thus, option C can be inferred.
Though the author mentions that since the second world war, there has been a consensus on the core democratic values among the left and the right, the same can't be said about the French Revolution; the author does not present any information in this regard. Hence, Option D can be eliminated.
Read the passage carefully and answer the following questions:
Over the last decade, an increasingly confident right wing has presented disillusioned voters with a simple choice: elitist, neoliberal hyperglobalisation or popular, patriotic nationalism. This new faultline pits economic and social liberalism against social conservatism and the promise of muscular economic intervention. Despite the defeat of Donald Trump in 2020, progressives have yet to find a strategy to combat this potent—if false—divide.
The traditional rightleft dividing line—economic liberalism and social conservatism on the right, economic interventionism and social liberalism on the left—forced workingclass nationalists to choose between their socially conservative instincts (including hostility to immigration) and their support for state intervention in the economy. In essence, they had to decide which liberalism—social or economic—to reject.
The 2016 Brexit referendum freed such voters from this restraint—and it certainly set back the old liberal order. But despite many jumping to the conclusion that fervent nationalism explained the whole Brexit phenomenon, it was not clear which liberalism was being rejected. Many of the towns that repudiated the EU were voting just as much against the deindustrialisation that took place during the years Britain was in the EU as they were voting to restore a supposedly Edenic 1950s. Back in the conventional world of parliamentary elections, in 2017 Labour’s antineoliberal economic programme under Jeremy Corbyn added 3.5m votes to its 2015 general election tally. But by 2019, identity trumped economics—on which the Tories, Labour's opponents, had anyway begun to change their tune under Boris Johnson—and the red wall crumbled.
The British right was not alone in affecting to spurn both liberalisms. From Warsaw via Workington to Wisconsin, workingclass voters received promises from rightwing populists that their economic interests would not be sacrificed on the altar of neoliberalism. Poland’s Law and Justice Party adopted an economic and social programme that would win over “leftbehind” Poles. Marine Le Pen’s National Front professed to abandon its fascist past and moved the spotlight onto protecting French industry. Johnson committed his party to an interventionist “levellingup” agenda. And Trump promised industrial protection against overseas competition, as well as the biggest programme of public works since the New Deal.
This new faultline not only redrew the political map: it fractured the old consensus around core democratic values—stretching from right to left—that had existed since the Second World War. These values were rooted in the French Revolution and European Enlightenment and comprised an alliance of liberty, equality and solidarity, which could accommodate Christian Democrats, liberals, social democrats and orthodox socialists, albeit in different proportions.
The nationalist farright rejects these values. Echoing the rhetorical tropes of antidemocratic forces from the interwar years, populists like Trump promote conspiracy theories in which liberal politicians plot to destroy national sovereignty in the interests of global financial capital. A politics of demonisation, exclusion and “othering” has seeped into mainstream rightwing parties. In the United States, it culminated in Trump’s incitement of his supporters to storm the Capitol on 6th January to overturn the result of the 2020 election.
In a recent essay, Timothy Garton Ash argues that “liberals need to join both conservatives and socialists in fullheartedly embracing the value of solidarity.” But for intellectual conservatives like the late Roger Scruton (whom Garton Ash quotes) as well as chauvinist politicians—like Trump, Le Pen, Viktor Orbán and the Italian League’s Matteo Salvini—solidarity always has to rely on an inherently exclusionary notion of identity: we’re who we are because you’re not. Progressive social solidarity is, by contrast, accepting of difference. However, socialists and liberals have much in common in the battle against the far right: together, they can build on the social gains of the Harold Wilson and Tony Blair governments, allying around social and political liberty as well as the economics of equality.
How is the modernday rightwing(MPRW) ideology different from the traditional rightwing(TRW) ideology?
Options C and D are tangential to the discussion and have not been implied in the passage.
Option A can be eliminated. The former part, which talks about TRW parties acknowledging the role of elite actors in uplifting the economy, cannot be inferred from the passage.
The initial half of Option B can be inferred from the following line: {...The traditional rightleft dividing line—economic liberalism and social conservatism on the right, economic interventionism and social liberalism on the left...}. The latter half can be inferred from the following lines
1. {This new faultline pits economic and social liberalism against social conservatism and the promise of muscular economic intervention.}
2. {The British right was not alone in affecting to spurn both liberalisms. From Warsaw via Workington to Wisconsin, workingclass voters received promises from rightwing populists that their economic interests would not be sacrificed on the altar of neoliberalism.}
Hence, Option B is the correct answer.
Read the passage carefully and answer the following questions:
Over the last decade, an increasingly confident right wing has presented disillusioned voters with a simple choice: elitist, neoliberal hyperglobalisation or popular, patriotic nationalism. This new faultline pits economic and social liberalism against social conservatism and the promise of muscular economic intervention. Despite the defeat of Donald Trump in 2020, progressives have yet to find a strategy to combat this potent—if false—divide.
The traditional rightleft dividing line—economic liberalism and social conservatism on the right, economic interventionism and social liberalism on the left—forced workingclass nationalists to choose between their socially conservative instincts (including hostility to immigration) and their support for state intervention in the economy. In essence, they had to decide which liberalism—social or economic—to reject.
The 2016 Brexit referendum freed such voters from this restraint—and it certainly set back the old liberal order. But despite many jumping to the conclusion that fervent nationalism explained the whole Brexit phenomenon, it was not clear which liberalism was being rejected. Many of the towns that repudiated the EU were voting just as much against the deindustrialisation that took place during the years Britain was in the EU as they were voting to restore a supposedly Edenic 1950s. Back in the conventional world of parliamentary elections, in 2017 Labour’s antineoliberal economic programme under Jeremy Corbyn added 3.5m votes to its 2015 general election tally. But by 2019, identity trumped economics—on which the Tories, Labour's opponents, had anyway begun to change their tune under Boris Johnson—and the red wall crumbled.
The British right was not alone in affecting to spurn both liberalisms. From Warsaw via Workington to Wisconsin, workingclass voters received promises from rightwing populists that their economic interests would not be sacrificed on the altar of neoliberalism. Poland’s Law and Justice Party adopted an economic and social programme that would win over “leftbehind” Poles. Marine Le Pen’s National Front professed to abandon its fascist past and moved the spotlight onto protecting French industry. Johnson committed his party to an interventionist “levellingup” agenda. And Trump promised industrial protection against overseas competition, as well as the biggest programme of public works since the New Deal.
This new faultline not only redrew the political map: it fractured the old consensus around core democratic values—stretching from right to left—that had existed since the Second World War. These values were rooted in the French Revolution and European Enlightenment and comprised an alliance of liberty, equality and solidarity, which could accommodate Christian Democrats, liberals, social democrats and orthodox socialists, albeit in different proportions.
The nationalist farright rejects these values. Echoing the rhetorical tropes of antidemocratic forces from the interwar years, populists like Trump promote conspiracy theories in which liberal politicians plot to destroy national sovereignty in the interests of global financial capital. A politics of demonisation, exclusion and “othering” has seeped into mainstream rightwing parties. In the United States, it culminated in Trump’s incitement of his supporters to storm the Capitol on 6th January to overturn the result of the 2020 election.
In a recent essay, Timothy Garton Ash argues that “liberals need to join both conservatives and socialists in fullheartedly embracing the value of solidarity.” But for intellectual conservatives like the late Roger Scruton (whom Garton Ash quotes) as well as chauvinist politicians—like Trump, Le Pen, Viktor Orbán and the Italian League’s Matteo Salvini—solidarity always has to rely on an inherently exclusionary notion of identity: we’re who we are because you’re not. Progressive social solidarity is, by contrast, accepting of difference. However, socialists and liberals have much in common in the battle against the far right: together, they can build on the social gains of the Harold Wilson and Tony Blair governments, allying around social and political liberty as well as the economics of equality.
Which of the following statements is definitely TRUE according to the passage?
Option A is incorrect. Such an assertion has not been made in the passage.
Option B is a distortion. In the penultimate paragraph, the author posits the following "Echoing the rhetorical tropes of antidemocratic forces from the interwar years, populists like Trump promote conspiracy theories in which liberal politicians plot to destroy national sovereignty in the interests of global financial capital." This is a metaphorical statement and does not necessarily imply the inference stated in option B.
Option C is again a distortion. The farright rejects the values derived from the learnings of the French Revolution and the European Enlightenment, true. But that cannot be equated to a dismissal of the social progress achieved through these events.
The traditional rightleft divide pits economic liberalism (on the right) against social liberalism (on the left). So, both left and right believed in the larger concept but favoured different manifestations. Hence, Option D can be inferred and is the correct answer.
Read the passage carefully and answer the following questions:
Over the last decade, an increasingly confident right wing has presented disillusioned voters with a simple choice: elitist, neoliberal hyperglobalisation or popular, patriotic nationalism. This new faultline pits economic and social liberalism against social conservatism and the promise of muscular economic intervention. Despite the defeat of Donald Trump in 2020, progressives have yet to find a strategy to combat this potent—if false—divide.
The traditional rightleft dividing line—economic liberalism and social conservatism on the right, economic interventionism and social liberalism on the left—forced workingclass nationalists to choose between their socially conservative instincts (including hostility to immigration) and their support for state intervention in the economy. In essence, they had to decide which liberalism—social or economic—to reject.
The 2016 Brexit referendum freed such voters from this restraint—and it certainly set back the old liberal order. But despite many jumping to the conclusion that fervent nationalism explained the whole Brexit phenomenon, it was not clear which liberalism was being rejected. Many of the towns that repudiated the EU were voting just as much against the deindustrialisation that took place during the years Britain was in the EU as they were voting to restore a supposedly Edenic 1950s. Back in the conventional world of parliamentary elections, in 2017 Labour’s antineoliberal economic programme under Jeremy Corbyn added 3.5m votes to its 2015 general election tally. But by 2019, identity trumped economics—on which the Tories, Labour's opponents, had anyway begun to change their tune under Boris Johnson—and the red wall crumbled.
The British right was not alone in affecting to spurn both liberalisms. From Warsaw via Workington to Wisconsin, workingclass voters received promises from rightwing populists that their economic interests would not be sacrificed on the altar of neoliberalism. Poland’s Law and Justice Party adopted an economic and social programme that would win over “leftbehind” Poles. Marine Le Pen’s National Front professed to abandon its fascist past and moved the spotlight onto protecting French industry. Johnson committed his party to an interventionist “levellingup” agenda. And Trump promised industrial protection against overseas competition, as well as the biggest programme of public works since the New Deal.
This new faultline not only redrew the political map: it fractured the old consensus around core democratic values—stretching from right to left—that had existed since the Second World War. These values were rooted in the French Revolution and European Enlightenment and comprised an alliance of liberty, equality and solidarity, which could accommodate Christian Democrats, liberals, social democrats and orthodox socialists, albeit in different proportions.
The nationalist farright rejects these values. Echoing the rhetorical tropes of antidemocratic forces from the interwar years, populists like Trump promote conspiracy theories in which liberal politicians plot to destroy national sovereignty in the interests of global financial capital. A politics of demonisation, exclusion and “othering” has seeped into mainstream rightwing parties. In the United States, it culminated in Trump’s incitement of his supporters to storm the Capitol on 6th January to overturn the result of the 2020 election.
In a recent essay, Timothy Garton Ash argues that “liberals need to join both conservatives and socialists in fullheartedly embracing the value of solidarity.” But for intellectual conservatives like the late Roger Scruton (whom Garton Ash quotes) as well as chauvinist politicians—like Trump, Le Pen, Viktor Orbán and the Italian League’s Matteo Salvini—solidarity always has to rely on an inherently exclusionary notion of identity: we’re who we are because you’re not. Progressive social solidarity is, by contrast, accepting of difference. However, socialists and liberals have much in common in the battle against the far right: together, they can build on the social gains of the Harold Wilson and Tony Blair governments, allying around social and political liberty as well as the economics of equality.
According to the passage, which of the following is NOT a strategy adopted by the rightwing populists?
{“ From Warsaw via Workington to Wisconsin, workingclass voters received promises from rightwing populists that their economic interests would not be sacrificed on the altar of neoliberalism.”} Option A can be inferred from this line.{“Echoing the rhetorical tropes of antidemocratic forces from the interwar years, populists like Trump promote conspiracy theories in which liberal politicians plot to destroy national sovereignty in the interests of global financial capital."} Option B can be inferred from this line.
{“A politics of demonisation, exclusion and “othering” has seeped into mainstream rightwing parties.”} Option D can be inferred from this line.
This leaves us with us option C, which is a distortion. According to the passage, {“The nationalist farright rejects these[core democratic] values.”}. Hence, the passage says this about farright nationalists and not rightwing populists. Hence, option C is the answer.
Read the passage carefully and answer the following questions:
Over the last decade, an increasingly confident right wing has presented disillusioned voters with a simple choice: elitist, neoliberal hyperglobalisation or popular, patriotic nationalism. This new faultline pits economic and social liberalism against social conservatism and the promise of muscular economic intervention. Despite the defeat of Donald Trump in 2020, progressives have yet to find a strategy to combat this potent—if false—divide.
The traditional rightleft dividing line—economic liberalism and social conservatism on the right, economic interventionism and social liberalism on the left—forced workingclass nationalists to choose between their socially conservative instincts (including hostility to immigration) and their support for state intervention in the economy. In essence, they had to decide which liberalism—social or economic—to reject.
The 2016 Brexit referendum freed such voters from this restraint—and it certainly set back the old liberal order. But despite many jumping to the conclusion that fervent nationalism explained the whole Brexit phenomenon, it was not clear which liberalism was being rejected. Many of the towns that repudiated the EU were voting just as much against the deindustrialisation that took place during the years Britain was in the EU as they were voting to restore a supposedly Edenic 1950s. Back in the conventional world of parliamentary elections, in 2017 Labour’s antineoliberal economic programme under Jeremy Corbyn added 3.5m votes to its 2015 general election tally. But by 2019, identity trumped economics—on which the Tories, Labour's opponents, had anyway begun to change their tune under Boris Johnson—and the red wall crumbled.
The British right was not alone in affecting to spurn both liberalisms. From Warsaw via Workington to Wisconsin, workingclass voters received promises from rightwing populists that their economic interests would not be sacrificed on the altar of neoliberalism. Poland’s Law and Justice Party adopted an economic and social programme that would win over “leftbehind” Poles. Marine Le Pen’s National Front professed to abandon its fascist past and moved the spotlight onto protecting French industry. Johnson committed his party to an interventionist “levellingup” agenda. And Trump promised industrial protection against overseas competition, as well as the biggest programme of public works since the New Deal.
This new faultline not only redrew the political map: it fractured the old consensus around core democratic values—stretching from right to left—that had existed since the Second World War. These values were rooted in the French Revolution and European Enlightenment and comprised an alliance of liberty, equality and solidarity, which could accommodate Christian Democrats, liberals, social democrats and orthodox socialists, albeit in different proportions.
The nationalist farright rejects these values. Echoing the rhetorical tropes of antidemocratic forces from the interwar years, populists like Trump promote conspiracy theories in which liberal politicians plot to destroy national sovereignty in the interests of global financial capital. A politics of demonisation, exclusion and “othering” has seeped into mainstream rightwing parties. In the United States, it culminated in Trump’s incitement of his supporters to storm the Capitol on 6th January to overturn the result of the 2020 election.
In a recent essay, Timothy Garton Ash argues that “liberals need to join both conservatives and socialists in fullheartedly embracing the value of solidarity.” But for intellectual conservatives like the late Roger Scruton (whom Garton Ash quotes) as well as chauvinist politicians—like Trump, Le Pen, Viktor Orbán and the Italian League’s Matteo Salvini—solidarity always has to rely on an inherently exclusionary notion of identity: we’re who we are because you’re not. Progressive social solidarity is, by contrast, accepting of difference. However, socialists and liberals have much in common in the battle against the far right: together, they can build on the social gains of the Harold Wilson and Tony Blair governments, allying around social and political liberty as well as the economics of equality.
The author cites the example of Brexit referendum to drive home the point that
At the beginning of the second paragraph, the author states the following “The 2016 Brexit referendum freed such voters from this restraint—and it certainly set back the old liberal order. But despite many jumping to the conclusion that fervent nationalism explained the whole Brexit phenomenon, it was not clear which liberalism was being rejected.” The restraint, here, refers to the rejection of either one of social or economic liberalism under the traditional rightleft divide. But through the Brexit example, the author explains that the voters were freed from this restraint and that they might have actually chosen to reject both forms of liberalism.
“Many of the towns that repudiated the EU were voting just as much against the deindustrialisation that took place during the years Britain was in the EU as they were voting to restore a supposedly Edenic 1950s.” This line suggests that the voters may have chosen to reject both forms of liberalism.
Comparing the options, option A conveys this inference. All other options are either tangential to the discussion or distorted.
Option B is a distortion. The referendum actually set back the liberal order that had existed for so long.
Option C, though true, does not capture the larger theme that the author attempts to convey.
Option D is out of scope. The author does not make such an observation.
The passage given below is followed by four summaries. Choose the option that best captures the author’s position.
Language bias in academia is something that researchers have been facing for a long time. Not only are the vast majority of scientific papers published in English, the ‘correctness’ of English used in them is a factor that determines their acceptance into top journals—which, incidentally, also publish exclusively in English. It discourages nonEnglish speaking researchers as it prioritizes the purity of the language over the content of their research. This also puts them at a disadvantage professionally, as they’re robbed of the most common, popular platforms that can further their research and careers. In addition, the overwhelming reliance on, and preference of, English favours only research that looks at the world in specific predisposed ways, brought on by the use of English, such as the tendency to prescribe indigenous knowledge as ‘folklore’ and not something that could have factual validity. It discounts anything that digresses from the norm, even when the information might be highly relevant and important.
In the passage, the author discusses how language bias in academia could deny nonEnglish speaking researchers the opportunity to get published in top journals and subsequently earn recognition and progress in their careers. In addition to this professional disadvantage, established predispositions could also lead to the repudiation of certain research information that is factually correct. Comparing the options, option B comes closest to conveying this inference.
Option A is extreme. The passage talks about professional disadvantage and disillusionment. But, discrimination is too strong a word in this context. Furthermore, it has not been implied that the bias leads to the researchers abandoning their works.
Option C comes close but talks about a drop in research quality, which has not been implied.
Option D, too, is correct for the most part but talks about the publication of substandard articles, which the author does not mention anywhere in the passage.
Hence, option B is the answer .
The four sentences (labelled 1, 2, 3, 4) below, when properly sequenced would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer:
1. This holds troubling implications for freedom of expression and the right to information.
2. However, Electronics and IT Minister Ravi Shankar Prasad, while launching The Information Technology Rules, 2021, presented it as a “softtouch oversight mechanism”, and it also claimed the rules seek to “address people’s varied concerns while removing any misapprehension about curbing creativity and freedom of speech and expression”.
3. The soft tone notwithstanding, these rules force digital news publishers and video streaming services to adhere to a cumbersome threetier structure of regulation, with a government committee at its apex.
4. The new rules introduced by the Centre last week to regulate all types of digital platforms, with the idea of redressing user grievances and ensuring compliance with the law, are deeply unsettling as they will end up giving the government a good deal of leverage over online news publishers and intermediaries.
Statement 4 appears to be the starting sentence since it introduces the topic  regulation of all digital platforms by the government. In sentence 1, 'this' refers to the leverage over digital platforms by the government. Statement 1 gives the impact of the rules mentioned in 4. Hence, 1 will follow 4. In sentence 2, the author cites the comment from the Electronics and IT minister to show the effort by the government to assuage the aforementioned concerns of the public (as stated in 1). Thus, 2 will follow 1. Sentence 3 appears to be the author's concluding remark, which says that regardless of the Minister's attempt to underplay the implications of the decision, digital news publishers and video streaming services will have to adhere to the cumbersome regulations. Hence, the correct sequence is 4123.
The four sentences (labelled 1, 2, 3, 4) below, when properly sequenced would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer:
1. The church prohibited the eating of eggs during Holy Week, but chickens continued to lay eggs during that week, and the notion of especially identifying those as Holy Week eggs brought about their decoration.
2. The tradition of dyeing and decorating Easter eggs is ancient, and its origin is obscure, but it has been practised in both the Eastern Orthodox and the Western churches since the Middle Ages.
3. The egg itself became a symbol of the Resurrection.
4. Just as Jesus rose from the tomb, the egg symbolized new life emerging from the eggshell.
Sentences 2 and 1 will make a pair because 2 introduces the topic, and 1 tells a brief history about why the Easter eggs are decorated. So, 2 will be followed by 1. Similarly, 3 and 4 will make a pair since 3 asserts that the eggs became a symbol of resurrection and 4 explains why this is the case.
Now, we have two pairs, but 2 will be the starting sentence because it is a broader statement and serves as an introduction. Hence, the sequence will be 2134.
Five sentences related to a topic are given below. Four of them can be put together to form a meaningful and coherent short paragraph. Identify the odd one out.
1. Gaura Devi led 27 of the village women to the site and confronted the loggers.
2. On 26 March 2018, a Chipko movement conservation initiative was marked by Google Doodle on its 45th anniversary.
3. On 25 March 1974, the day the lumbermen were to cut the trees, the men of Reni village and DGSS workers were in Chamoli, diverted by the state government and contractors to a fictional compensation payment site, while back home labourers arrived by the truckload to start logging operations.
4. When all talking failed, and the loggers started to shout and abuse the women, threatening them with guns, the women resorted to hugging the trees to stop them from being felled.
5. A local girl, on seeing them, rushed to inform Gaura Devi, the head of the village Mahila Mangal Dal, at Reni village.
Statement 2 is the odd one because the incident narrated by the other sentences need not necessarily refer to the Chipko Movement.
Further, when the other sentences are arranged in sequence 3514, we get a coherent para.
Clearly, 3 will be the starting sentence as it starts by narrating the incident and will be followed by 5 because 'them' in 5 refers to the 'labourers' in 3. Sentence 1 will follow 5 as 5 tells us about a girl informing Gaura Devi, and 1 tells us how she reacted to the information. Finally, 4 follows 1 as it elaborates on the confrontation. Hence, the sequence 3514.
Five sentences related to a topic are given below. Four of them can be put together to form a meaningful and coherent short paragraph. Identify the odd one out.
1. Recently, however, the Chinese room experiment has goaded me into dwelling on the limits of human cognition.
2. John Searle concocted the Chinese room experiment to convince us that computers don’t really “think” as we do; they manipulate symbols mindlessly, without understanding what they are doing.
3. We humans can be pretty mindless too, even when engaged in a pursuit as lofty as quantum physics.
4. Computer pioneer Alan Turing proposed in 1950 that questions be fed to a machine and a human.
5. Searle meant to make a point about the limits of machine cognition.
After reading the given statements, we understand that the author is discussing the Chinese room experiment and tying it to human cognition. Sentence 2 will be the starting sentence as it introduces us to the topic. Sentence 5 will follow 2 because it tells us the motive behind Jean conducting the experiment. Sentence 1 will follow 5 because the author portrays his take on this experiment, and the learning outcome associated with it. Sentence 3 will follow 1 since it continues on the author's perception/take of human cognition and its limitation. We notice that the sequence 2513 forms a coherent paragraph.
Sentence 4 is the odd one as it does not fit anywhere in the sequence. It presents us with a fact which appears irrelevant to the overall discussion.
Directions: Identify the most appropriate summary for the paragraph and write the key for most appropriate option.
Feudalism represents a change from the ancient form of imperialism to the newer forms of European government. It arose out of the ruins of the Roman system as an essential form of social order. It appears to be the only system fitted to bring order out of the chaotic conditions of society, but by the very nature of affairs it could not long continue as an established system. It is rather surprising, indeed, that it became so universal, for every territory in Europe was subjected to its control in a greater or less degree. Frequently those who were forced to adopt its form condemned its principle, and those who sought to maintain the doctrine of Roman imperialism were subjected to its sway. The church itself, seeking to maintain its autocracy, came into direct contact with feudal theory and opposed it bitterly. The people who submitted to the yoke of personal bondage which it entailed hated the system. Yet the whole European world passed under feudalism. But notwithstanding its universality, feudalism could offer nothing permanent, for in the development of social order it was forced to yield to monarchy, although it made a lasting influence on social life and political and economic usage. (key in your answer option)
1. Feudalism, though extensively used in Europe to varying degrees of success, eventually outlives its usefulness and was replaced by monarchy.
2. What feudalism did to the ancient form of imperialism was done to it by monarchy, when it no longer could offer the benefits it once promised.
3. Feudalism, begrudgingly accepted by many parts of the European society, finally outlived its usefulness and found itself replaced by monarchy despite of its positives and near universal application in Europe.
4. Feudalism, accepted by some and resented by some others, took over Europe in a universal way before it found itself replaced by monarchy in a way similar to the one it which it replaced imperialism.
Option 3 is the perfect choice here as it essentially covers all the aspects of paragraph (which is the job of the summary).
Option 4, though partially correct, uses the incorrect logic when it says "itself replaced by monarch in a way similar to the one it which it replaced imperialism." There is no evidence in the passage that the way in which monarchy replaced feudalism was similar to the way in which feudalism replaced imperialism. Option 2 is ruled out on similar grounds.
Option 1 is ruled out as the degrees of success of feudalism find no mention in the passage.
A lock is guarded by a security code that serves as the password. The code is in the following form:
Where a, b, c, d and g are numbers and e, f are alphabets. The following information is also known about the respective characters:
1. 'a' is a prime number from 1 to 10.
2. The 2digit number 'bc' is also a prime number such that b = a + 1.
3. 'd' = 'bc' % 'a', that is, d is the remainder when the 2digit number 'bc' is divided by 'a'.
4. 'e' is the alphabet at the index of n, alphabet[n], where n is the highest number of occurrences of any digit(0 to 9) among a,b,c,d. Here,alphabet[1] = A, alphabet[2] = B,..., alphabet[26] = Z.
5. 'f' is the alphabet either preceding or succeeding the alphabet 'e' when all English alphabets are arranged alphabetically.
6. 'g' is the remainder when the sum of digits a, b, c and d is divided by 10. g = (a+b+c+d)%10.
Based on the information given above, answer the questions that follow.
If we consider all possible codes, which digit(0 to 9) does not occur even once in any of the codes? Enter 1 if all 10 digits appear at least once in any of the codes.
a can be 2, 3, 5, 7.
Hence, when a = 2, b = 3, bc = 31, 37
When a = 3, b = 4, bc = 41, 43, 47
When a = 5, b = 6, bc = 61, 67
When a = 7, b = 8, bc = 83, 89.
Hence, the different possibilities are,
2311 _ _ _
2371 _ _ _
3412 _ _ _
3431 _ _ _
3472 _ _ _
5611 _ _ _
5672 _ _ _
7836 _ _ _
7895 _ _ _
Now, when it is 2311 _ _ _, 1 occurs twice, which is the highest, hence e = alphabet[2] = B.
Similarly, when it is 2371 _ _ _, the highest occurrence of any digit is once, hence e = alphabet[1] = A.
Similarly, we get the remaining as well,
2311B _ _
2371A _ _
3412A _ _
3431B _ _
3472A _ _
5611B _ _
5672A _ _
7836A _ _
7895A _ _
Hence, e is always either B or A. If e is B. f can be either A or C, if e is A, f can only be B. Hence, we get the following codes.
2311BA _
2311BC _
2371AB _
3412AB _
3431BA _
3431BC _
3472AB _
5611BA _
5611BC _
5672AB _
7836AB _
7895AB _
Now, G has to be calculated. For, 2311BA _, g = (2 + 3 + 1 + 1)%10 = 7
Similarly, we calculate for others as well,
2311BA7
2311BC7
2371AB3
3412AB0
3431BA1
3431BC1
3472AB6
5611BA3
5611BC3
5672AB0
7836AB4
7895AB9
As we can see every digit appears at least once if all codes are considered.
Hence, the answer is 1 as asked in the question.
A lock is guarded by a security code that serves as the password. The code is in the following form:
Where a, b, c, d and g are numbers and e, f are alphabets. The following information is also known about the respective characters:
1. 'a' is a prime number from 1 to 10.
2. The 2digit number 'bc' is also a prime number such that b = a + 1.
3. 'd' = 'bc' % 'a', that is, d is the remainder when the 2digit number 'bc' is divided by 'a'.
4. 'e' is the alphabet at the index of n, alphabet[n], where n is the highest number of occurrences of any digit(0 to 9) among a,b,c,d. Here,alphabet[1] = A, alphabet[2] = B,..., alphabet[26] = Z.
5. 'f' is the alphabet either preceding or succeeding the alphabet 'e' when all English alphabets are arranged alphabetically.
6. 'g' is the remainder when the sum of digits a, b, c and d is divided by 10. g = (a+b+c+d)%10.
Based on the information given above, answer the questions that follow.
If we consider all possible codes, how many distinct alphabets appear at least once in any of the codes?
a can be 2, 3, 5, 7.
Hence, when a = 2, b = 3, bc = 31, 37
When a = 3, b = 4, bc = 41, 43, 47
When a = 5, b = 6, bc = 61, 67
When a = 7, b = 8, bc = 83, 89.
Hence, the different possibilities are,
2311 _ _ _
2371 _ _ _
3412 _ _ _
3431 _ _ _
3472 _ _ _
5611 _ _ _
5672 _ _ _
7836 _ _ _
7895 _ _ _
Now, when it is 2311 _ _ _, 1 occurs twice, which is the highest, hence e = alphabet[2] = B.
Similarly, when it is 2371 _ _ _, the highest occurrence of any digit is once, hence e = alphabet[1] = A.
Similarly, we get the remaining as well,
2311B _ _
2371A _ _
3412A _ _
3431B _ _
3472A _ _
5611B _ _
5672A _ _
7836A _ _
7895A _ _
Hence, e is always either B or A. If e is B. f can be either A or C, if e is A, f can only be B. Hence, we get the following codes.
2311BA _
2311BC _
2371AB _
3412AB _
3431BA _
3431BC _
3472AB _
5611BA _
5611BC _
5672AB _
7836AB _
7895AB _
Now, G has to be calculated. For, 2311BA _, g = (2 + 3 + 1 + 1)%10 = 7
Similarly, we calculate for others as well,
2311BA7
2311BC7
2371AB3
3412AB0
3431BA1
3431BC1
3472AB6
5611BA3
5611BC3
5672AB0
7836AB4
7895AB9
As we can see only A, B and C appear. So, there are 3 alphabets.
A lock is guarded by a security code that serves as the password. The code is in the following form:
Where a, b, c, d and g are numbers and e, f are alphabets. The following information is also known about the respective characters:
1. 'a' is a prime number from 1 to 10.
2. The 2digit number 'bc' is also a prime number such that b = a + 1.
3. 'd' = 'bc' % 'a', that is, d is the remainder when the 2digit number 'bc' is divided by 'a'.
4. 'e' is the alphabet at the index of n, alphabet[n], where n is the highest number of occurrences of any digit(0 to 9) among a,b,c,d. Here,alphabet[1] = A, alphabet[2] = B,..., alphabet[26] = Z.
5. 'f' is the alphabet either preceding or succeeding the alphabet 'e' when all English alphabets are arranged alphabetically.
6. 'g' is the remainder when the sum of digits a, b, c and d is divided by 10. g = (a+b+c+d)%10.
Based on the information given above, answer the questions that follow.
How many codes are possible?
a can be 2, 3, 5, 7.
Hence, when a = 2, b = 3, bc = 31, 37
When a = 3, b = 4, bc = 41, 43, 47
When a = 5, b = 6, bc = 61, 67
When a = 7, b = 8, bc = 83, 89.
Hence, the different possibilities are,
2311 _ _ _
2371 _ _ _
3412 _ _ _
3431 _ _ _
3472 _ _ _
5611 _ _ _
5672 _ _ _
7836 _ _ _
7895 _ _ _
Now, when it is 2311 _ _ _, 1 occurs twice, which is the highest, hence e = alphabet[2] = B.
Similarly, when it is 2371 _ _ _, the highest occurrence of any digit is once, hence e = alphabet[1] = A.
Similarly, we get the remaining as well,
2311B _ _
2371A _ _
3412A _ _
3431B _ _
3472A _ _
5611B _ _
5672A _ _
7836A _ _
7895A _ _
Hence, e is always either B or A. If e is B. f can be either A or C, if e is A, f can only be B. Hence, we get the following codes.
2311BA _
2311BC _
2371AB _
3412AB _
3431BA _
3431BC _
3472AB _
5611BA _
5611BC _
5672AB _
7836AB _
7895AB _
Now, G has to be calculated. For, 2311BA _, g = (2 + 3 + 1 + 1)%10 = 7
Similarly, we calculate for others as well,
2311BA7
2311BC7
2371AB3
3412AB0
3431BA1
3431BC1
3472AB6
5611BA3
5611BC3
5672AB0
7836AB4
7895AB9
As we can see there are 12 different valid codes.
A lock is guarded by a security code that serves as the password. The code is in the following form:
Where a, b, c, d and g are numbers and e, f are alphabets. The following information is also known about the respective characters:
1. 'a' is a prime number from 1 to 10.
2. The 2digit number 'bc' is also a prime number such that b = a + 1.
3. 'd' = 'bc' % 'a', that is, d is the remainder when the 2digit number 'bc' is divided by 'a'.
4. 'e' is the alphabet at the index of n, alphabet[n], where n is the highest number of occurrences of any digit(0 to 9) among a,b,c,d. Here,alphabet[1] = A, alphabet[2] = B,..., alphabet[26] = Z.
5. 'f' is the alphabet either preceding or succeeding the alphabet 'e' when all English alphabets are arranged alphabetically.
6. 'g' is the remainder when the sum of digits a, b, c and d is divided by 10. g = (a+b+c+d)%10.
Based on the information given above, answer the questions that follow.
If it is given that no vowel can be used as an alphabet and no digit should be a multiple of 4, how many codes are possible?
a can be 2, 3, 5, 7.
Hence, when a = 2, b = 3, bc = 31, 37
When a = 3, b = 4, bc = 41, 43, 47
When a = 5, b = 6, bc = 61, 67
When a = 7, b = 8, bc = 83, 89.
Hence, the different possibilities are,
2311 _ _ _
2371 _ _ _
3412 _ _ _
3431 _ _ _
3472 _ _ _
5611 _ _ _
5672 _ _ _
7836 _ _ _
7895 _ _ _
Now, when it is 2311 _ _ _, 1 occurs twice, which is the highest, hence e = alphabet[2] = B.
Similarly, when it is 2371 _ _ _, the highest occurrence of any digit is once, hence e = alphabet[1] = A.
Similarly, we get the remaining as well,
2311B _ _
2371A _ _
3412A _ _
3431B _ _
3472A _ _
5611B _ _
5672A _ _
7836A _ _
7895A _ _
Hence, e is always either B or A. If e is B. f can be either A or C, if e is A, f can only be B. Hence, we get the following codes.
2311BA _
2311BC _
2371AB _
3412AB _
3431BA _
3431BC _
3472AB _
5611BA _
5611BC _
5672AB _
7836AB _
7895AB _
Now, G has to be calculated. For, 2311BA _, g = (2 + 3 + 1 + 1)%10 = 7
Similarly, we calculate for others as well,
2311BA7
2311BC7
2371AB3
3412AB0
3431BA1
3431BC1
3472AB6
5611BA3
5611BC3
5672AB0
7836AB4
7895AB9
In the question, we are asked to not include any vowel and any digit that is a multiple of 4. Hence, we are left with 2311BC7 and 5611BC3.
60 students were shortlisted for their Personal Interview by the Indian School of Management. But the interview process was to be conducted online and hence students were sent the KOOM meeting link for the same. All the 60 students were to join the KOOM common room at 9:00 AM sharp and then the admission coordinators would send in a certain number of students to different waiting rooms X, Y and Z prior to their one on one interviews with the panellists. There were 3 panellists A, B and C who were conducting interviews for the candidates waiting in the rooms X, Y and Z respectively. The capacity for the waiting rooms X, Y and Z were 5, 10 and 15 respectively.
The 60 students were given a rank from 1 to 60 based on their composite score and it is known that no two students got the same score. To start off the interviews, the ones with top 5 ranks are sent to panellist A. The 10 below them are sent to B and students ranked 16 to 30 were sent to C. When the last person from the waiting room X, Y and Z gives an interview, the next set of students are immediately sent to the waiting room as soon as the interview gets over and the priority is maintained as students with higher ranks are sent to X, Y and Z respectively if the interviews of the previous batch end simultaneously.
It is known that:
1. Panellist A takes an interview for 15 minutes and takes a break of 5 minutes only after interviewing 3 candidates
2. Panellist B takes an interview for 10 minutes and takes a break of 5 minutes after interviewing 5 students.
3. Panellist C takes an interview of 5 minutes and takes a break of 5 minutes after interviewing 4 students.
4. Lunch break is scheduled between 12:00 noon to 12:30 PM and students are not cut abruptly if their interview began before 12:00 noon, i.e. the interviewers take the break only after finishing the interview if it started before 12:00 noon.
5. Batches of 5, 10 and 15 students enter the waiting room together such that students who enter the waiting room at a time have continuous ranks. For example, if the interviewer X is ending up the interview of the last student from the previous batch, 5 students with continuous ranks (say 2125) enter the waiting room X together.
6. Students allotted to a particular waiting room is only interviewed by the designated interviewer and is not interviewed by anyone else even if the other interviewer is free.
7. If panellist A goes into the lunch break after having interviewed 1 student, he will again take his 5 minute break after interviewing 2 students post the lunch break so as to satisfy the condition 1 always. The same applies for panellist B and C who follow conditions 2 and 3 respectively.
When does interviewer B finish his last interview?
Students ranked from 1 to 5 will be interviewed by A and thus are moved to the waiting room X.
Similarly, students ranked 6 to 15 (10 students) will be interviewed by B and are moved to waiting room Y.
And students ranked 16 to 30 (15 students) will be interviewed by C and are moved to waiting room Z.
A takes a break after every 3 interviews. B and C take breaks after every 5 and 4 interviews respectively.
So, a map of the first few students will look like:
Here, M, N, X and Y are the ranks of the students. M to M+4 are the set of 5 students who will be interviewed once the interview of the student ranked 5th gets over and similarly for others.
We see that interviewer A finishes his first batch of interviews first (at 10:20) and hence M must be 31. Students ranked 31 to 35 move to waiting room X.
Next to finish interviewing his/her first batch of interviewees is B (at 10:30) and hence Y=36. Students ranked from 36 to 50 will move into waiting room Z.
Finally, interviewer Y will get the next 10 students ranked from 51 to 60 and hence X=51.
We do not require N.
Interviewer A interviews students ranked from 1 to 5, 31 to 35.
Interviewer B interviews students ranked from 6 to 15 and 51 to 60.
Interviewer C interviews students ranked from 16 to 30 and 36 to 50.
An updated table will look like:
We can break down the interviews of students ranked 41 to 50 for interviewer C as:
Each set of 4 consecutively ranked students will be interviewed in 20 minutes. The fifth student will be interviewed after 20+5(break) minutes= 25 minutes.
So, the interview of student ranked 41 starts at 11:05 am and that of student ranked 45 starts at 11:05+25= 11:30 am. Similarly the interview of student ranked 49 starts at 11:55 am and so on.
We can see from the table that interviewer B ends his interviews at 1:00 pm.
60 students were shortlisted for their Personal Interview by the Indian School of Management. But the interview process was to be conducted online and hence students were sent the KOOM meeting link for the same. All the 60 students were to join the KOOM common room at 9:00 AM sharp and then the admission coordinators would send in a certain number of students to different waiting rooms X, Y and Z prior to their one on one interviews with the panellists. There were 3 panellists A, B and C who were conducting interviews for the candidates waiting in the rooms X, Y and Z respectively. The capacity for the waiting rooms X, Y and Z were 5, 10 and 15 respectively.
The 60 students were given a rank from 1 to 60 based on their composite score and it is known that no two students got the same score. To start off the interviews, the ones with top 5 ranks are sent to panellist A. The 10 below them are sent to B and students ranked 16 to 30 were sent to C. When the last person from the waiting room X, Y and Z gives an interview, the next set of students are immediately sent to the waiting room as soon as the interview gets over and the priority is maintained as students with higher ranks are sent to X, Y and Z respectively if the interviews of the previous batch end simultaneously.
It is known that:
1. Panellist A takes an interview for 15 minutes and takes a break of 5 minutes only after interviewing 3 candidates
2. Panellist B takes an interview for 10 minutes and takes a break of 5 minutes after interviewing 5 students.
3. Panellist C takes an interview of 5 minutes and takes a break of 5 minutes after interviewing 4 students.
4. Lunch break is scheduled between 12:00 noon to 12:30 PM and students are not cut abruptly if their interview began before 12:00 noon, i.e. the interviewers take the break only after finishing the interview if it started before 12:00 noon.
5. Batches of 5, 10 and 15 students enter the waiting room together such that students who enter the waiting room at a time have continuous ranks. For example, if the interviewer X is ending up the interview of the last student from the previous batch, 5 students with continuous ranks (say 2125) enter the waiting room X together.
6. Students allotted to a particular waiting room is only interviewed by the designated interviewer and is not interviewed by anyone else even if the other interviewer is free.
7. If panellist A goes into the lunch break after having interviewed 1 student, he will again take his 5 minute break after interviewing 2 students post the lunch break so as to satisfy the condition 1 always. The same applies for panellist B and C who follow conditions 2 and 3 respectively.
Which of the following ranked students was interviewed by panellist C?
Students ranked from 1 to 5 will be interviewed by A and thus are moved to the waiting room X.
Similarly, students ranked 6 to 15 (10 students) will be interviewed by B and are moved to waiting room Y.
And students ranked 16 to 30 (15 students) will be interviewed by C and are moved to waiting room Z.
A takes a break after every 3 interviews. B and C take breaks after every 5 and 4 interviews respectively.
So, a map of the first few students will look like:
Here, M, N, X and Y are the ranks of the students. M to M+4 are the set of 5 students who will be interviewed once the interview of the student ranked 5th gets over and similarly for others.
We see that interviewer A finishes his first batch of interviews first (at 10:20) and hence M must be 31. Students ranked 31 to 35 move to waiting room X.
Next to finish interviewing his/her first batch of interviewees is B (at 10:30) and hence Y=36. Students ranked from 36 to 50 will move into waiting room Z.
Finally, interviewer Y will get the next 10 students ranked from 51 to 60 and hence X=51.
We do not require N.
Interviewer A interviews students ranked from 1 to 5, 31 to 35.
Interviewer B interviews students ranked from 6 to 15 and 51 to 60.
Interviewer C interviews students ranked from 16 to 30 and 36 to 50.
An updated table will look like:
We can break down the interviews of students ranked 41 to 50 for interviewer C as:
Each set of 4 consecutively ranked students will be interviewed in 20 minutes. The fifth student will be interviewed after 20+5(break) minutes= 25 minutes.
So, the interview of student ranked 41 starts at 11:05 am and that of student ranked 45 starts at 11:05+25= 11:30 am. Similarly the interview of student ranked 49 starts at 11:55 am and so on.
60 students were shortlisted for their Personal Interview by the Indian School of Management. But the interview process was to be conducted online and hence students were sent the KOOM meeting link for the same. All the 60 students were to join the KOOM common room at 9:00 AM sharp and then the admission coordinators would send in a certain number of students to different waiting rooms X, Y and Z prior to their one on one interviews with the panellists. There were 3 panellists A, B and C who were conducting interviews for the candidates waiting in the rooms X, Y and Z respectively. The capacity for the waiting rooms X, Y and Z were 5, 10 and 15 respectively.
The 60 students were given a rank from 1 to 60 based on their composite score and it is known that no two students got the same score. To start off the interviews, the ones with top 5 ranks are sent to panellist A. The 10 below them are sent to B and students ranked 16 to 30 were sent to C. When the last person from the waiting room X, Y and Z gives an interview, the next set of students are immediately sent to the waiting room as soon as the interview gets over and the priority is maintained as students with higher ranks are sent to X, Y and Z respectively if the interviews of the previous batch end simultaneously.
It is known that:
1. Panellist A takes an interview for 15 minutes and takes a break of 5 minutes only after interviewing 3 candidates
2. Panellist B takes an interview for 10 minutes and takes a break of 5 minutes after interviewing 5 students.
3. Panellist C takes an interview of 5 minutes and takes a break of 5 minutes after interviewing 4 students.
4. Lunch break is scheduled between 12:00 noon to 12:30 PM and students are not cut abruptly if their interview began before 12:00 noon, i.e. the interviewers take the break only after finishing the interview if it started before 12:00 noon.
5. Batches of 5, 10 and 15 students enter the waiting room together such that students who enter the waiting room at a time have continuous ranks. For example, if the interviewer X is ending up the interview of the last student from the previous batch, 5 students with continuous ranks (say 2125) enter the waiting room X together.
6. Students allotted to a particular waiting room is only interviewed by the designated interviewer and is not interviewed by anyone else even if the other interviewer is free.
7. If panellist A goes into the lunch break after having interviewed 1 student, he will again take his 5 minute break after interviewing 2 students post the lunch break so as to satisfy the condition 1 always. The same applies for panellist B and C who follow conditions 2 and 3 respectively.
When was the interview of the student ranked 53 finished?
Students ranked from 1 to 5 will be interviewed by A and thus are moved to the waiting room X.
Similarly, students ranked 6 to 15 (10 students) will be interviewed by B and are moved to waiting room Y.
And students ranked 16 to 30 (15 students) will be interviewed by C and are moved to waiting room Z.
A takes a break after every 3 interviews. B and C take breaks after every 5 and 4 interviews respectively.
So, a map of the first few students will look like:
Here, M, N, X and Y are the ranks of the students. M to M+4 are the set of 5 students who will be interviewed once the interview of the student ranked 5th gets over and similarly for others.
We see that interviewer A finishes his first batch of interviews first (at 10:20) and hence M must be 31. Students ranked 31 to 35 move to waiting room X.
Next to finish interviewing his/her first batch of interviewees is B (at 10:30) and hence Y=36. Students ranked from 36 to 50 will move into waiting room Z.
Finally, interviewer Y will get the next 10 students ranked from 51 to 60 and hence X=51.
We do not require N.
Interviewer A interviews students ranked from 1 to 5, 31 to 35.
Interviewer B interviews students ranked from 6 to 15 and 51 to 60.
Interviewer C interviews students ranked from 16 to 30 and 36 to 50.
An updated table will look like:
We can break down the interviews of students ranked 41 to 50 for interviewer C as:
Each set of 4 consecutively ranked students will be interviewed in 20 minutes. The fifth student will be interviewed after 20+5(break) minutes= 25 minutes.
So, the interview of student ranked 41 starts at 11:05 am and that of student ranked 45 starts at 11:05+25= 11:30 am. Similarly the interview of student ranked 49 starts at 11:55 am and so on.
Student ranked 53 was interviewed by B. We can see from the table that a set of 5 interviews get their interviews done in 50 minutes (including the 5 min break).
Students with rank 51 finish his interview at 11:00 AM.
Student with rank 52 finish at 11:10 AM and the one ranked 53 finish at 11:20 AM
60 students were shortlisted for their Personal Interview by the Indian School of Management. But the interview process was to be conducted online and hence students were sent the KOOM meeting link for the same. All the 60 students were to join the KOOM common room at 9:00 AM sharp and then the admission coordinators would send in a certain number of students to different waiting rooms X, Y and Z prior to their one on one interviews with the panellists. There were 3 panellists A, B and C who were conducting interviews for the candidates waiting in the rooms X, Y and Z respectively. The capacity for the waiting rooms X, Y and Z were 5, 10 and 15 respectively.
The 60 students were given a rank from 1 to 60 based on their composite score and it is known that no two students got the same score. To start off the interviews, the ones with top 5 ranks are sent to panellist A. The 10 below them are sent to B and students ranked 16 to 30 were sent to C. When the last person from the waiting room X, Y and Z gives an interview, the next set of students are immediately sent to the waiting room as soon as the interview gets over and the priority is maintained as students with higher ranks are sent to X, Y and Z respectively if the interviews of the previous batch end simultaneously.
It is known that:
1. Panellist A takes an interview for 15 minutes and takes a break of 5 minutes only after interviewing 3 candidates
2. Panellist B takes an interview for 10 minutes and takes a break of 5 minutes after interviewing 5 students.
3. Panellist C takes an interview of 5 minutes and takes a break of 5 minutes after interviewing 4 students.
4. Lunch break is scheduled between 12:00 noon to 12:30 PM and students are not cut abruptly if their interview began before 12:00 noon, i.e. the interviewers take the break only after finishing the interview if it started before 12:00 noon.
5. Batches of 5, 10 and 15 students enter the waiting room together such that students who enter the waiting room at a time have continuous ranks. For example, if the interviewer X is ending up the interview of the last student from the previous batch, 5 students with continuous ranks (say 2125) enter the waiting room X together.
6. Students allotted to a particular waiting room is only interviewed by the designated interviewer and is not interviewed by anyone else even if the other interviewer is free.
7. If panellist A goes into the lunch break after having interviewed 1 student, he will again take his 5 minute break after interviewing 2 students post the lunch break so as to satisfy the condition 1 always. The same applies for panellist B and C who follow conditions 2 and 3 respectively.
When did the 50th ranked student finish his/her interview?
Students ranked from 1 to 5 will be interviewed by A and thus are moved to the waiting room X.
Similarly, students ranked 6 to 15 (10 students) will be interviewed by B and are moved to waiting room Y.
And students ranked 16 to 30 (15 students) will be interviewed by C and are moved to waiting room Z.
A takes a break after every 3 interviews. B and C take breaks after every 5 and 4 interviews respectively.
So, a map of the first few students will look like:
Here, M, N, X and Y are the ranks of the students. M to M+4 are the set of 5 students who will be interviewed once the interview of the student ranked 5th gets over and similarly for others.
We see that interviewer A finishes his first batch of interviews first (at 10:20) and hence M must be 31. Students ranked 31 to 35 move to waiting room X.
Next to finish interviewing his/her first batch of interviewees is B (at 10:30) and hence Y=36. Students ranked from 36 to 50 will move into waiting room Z.
Finally, interviewer Y will get the next 10 students ranked from 51 to 60 and hence X=51.
We do not require N.
Interviewer A interviews students ranked from 1 to 5, 31 to 35.
Interviewer B interviews students ranked from 6 to 15 and 51 to 60.
Interviewer C interviews students ranked from 16 to 30 and 36 to 50.
An updated table will look like:
We can break down the interviews of students ranked 41 to 50 for interviewer C as:
Each set of 4 consecutively ranked students will be interviewed in 20 minutes. The fifth student will be interviewed after 20+5(break) minutes= 25 minutes.
So, the interview of student ranked 41 starts at 11:05 am and that of student ranked 45 starts at 11:05+25= 11:30 am. Similarly the interview of student ranked 49 starts at 11:55 am and so on.
Student ranked 46 was interviewed by C. We can see from the table that a set of 4 interviews get their interviews done in 25 minutes (including the 5 min break).
Students with rank 41 to 44 get their interviews done between 11:05 and 11:25.
Students with rank 45 to 48 get their interviews done between 11:30 and 11:50.
The student ranked 49 is the last one to finish his interview before lunch at exactly 12:00 noon.
So, the student with a rank of 50 starts his interview at 12:30, finishes at 12:35.
60 students were shortlisted for their Personal Interview by the Indian School of Management. But the interview process was to be conducted online and hence students were sent the KOOM meeting link for the same. All the 60 students were to join the KOOM common room at 9:00 AM sharp and then the admission coordinators would send in a certain number of students to different waiting rooms X, Y and Z prior to their one on one interviews with the panellists. There were 3 panellists A, B and C who were conducting interviews for the candidates waiting in the rooms X, Y and Z respectively. The capacity for the waiting rooms X, Y and Z were 5, 10 and 15 respectively.
The 60 students were given a rank from 1 to 60 based on their composite score and it is known that no two students got the same score. To start off the interviews, the ones with top 5 ranks are sent to panellist A. The 10 below them are sent to B and students ranked 16 to 30 were sent to C. When the last person from the waiting room X, Y and Z gives an interview, the next set of students are immediately sent to the waiting room as soon as the interview gets over and the priority is maintained as students with higher ranks are sent to X, Y and Z respectively if the interviews of the previous batch end simultaneously.
It is known that:
1. Panellist A takes an interview for 15 minutes and takes a break of 5 minutes only after interviewing 3 candidates
2. Panellist B takes an interview for 10 minutes and takes a break of 5 minutes after interviewing 5 students.
3. Panellist C takes an interview of 5 minutes and takes a break of 5 minutes after interviewing 4 students.
4. Lunch break is scheduled between 12:00 noon to 12:30 PM and students are not cut abruptly if their interview began before 12:00 noon, i.e. the interviewers take the break only after finishing the interview if it started before 12:00 noon.
5. Batches of 5, 10 and 15 students enter the waiting room together such that students who enter the waiting room at a time have continuous ranks. For example, if the interviewer X is ending up the interview of the last student from the previous batch, 5 students with continuous ranks (say 2125) enter the waiting room X together.
6. Students allotted to a particular waiting room is only interviewed by the designated interviewer and is not interviewed by anyone else even if the other interviewer is free.
7. If panellist A goes into the lunch break after having interviewed 1 student, he will again take his 5 minute break after interviewing 2 students post the lunch break so as to satisfy the condition 1 always. The same applies for panellist B and C who follow conditions 2 and 3 respectively.
At what time does Interviewer A finish all his interviews?
Students ranked from 1 to 5 will be interviewed by A and thus are moved to the waiting room X.
Similarly, students ranked 6 to 15 (10 students) will be interviewed by B and are moved to waiting room Y.
And students ranked 16 to 30 (15 students) will be interviewed by C and are moved to waiting room Z.
A takes a break after every 3 interviews. B and C take breaks after every 5 and 4 interviews respectively.
So, a map of the first few students will look like:
Here, M, N, X and Y are the ranks of the students. M to M+4 are the set of 5 students who will be interviewed once the interview of the student ranked 5th gets over and similarly for others.
We see that interviewer A finishes his first batch of interviews first (at 10:20) and hence M must be 31. Students ranked 31 to 35 move to waiting room X.
Next to finish interviewing his/her first batch of interviewees is B (at 10:30) and hence Y=36. Students ranked from 36 to 50 will move into waiting room Z.
Finally, interviewer Y will get the next 10 students ranked from 51 to 60 and hence X=51.
We do not require N.
Interviewer A interviews students ranked from 1 to 5, 31 to 35.
Interviewer B interviews students ranked from 6 to 15 and 51 to 60.
Interviewer C interviews students ranked from 16 to 30 and 36 to 50.
An updated table will look like:
We can break down the interviews of students ranked 41 to 50 for interviewer C as:
Each set of 4 consecutively ranked students will be interviewed in 20 minutes. The fifth student will be interviewed after 20+5(break) minutes= 25 minutes.
So, the interview of student ranked 41 starts at 11:05 am and that of student ranked 45 starts at 11:05+25= 11:30 am. Similarly the interview of student ranked 49 starts at 11:55 am and so on.
Interviewer A finished his interviews at 11:45 AM
60 students were shortlisted for their Personal Interview by the Indian School of Management. But the interview process was to be conducted online and hence students were sent the KOOM meeting link for the same. All the 60 students were to join the KOOM common room at 9:00 AM sharp and then the admission coordinators would send in a certain number of students to different waiting rooms X, Y and Z prior to their one on one interviews with the panellists. There were 3 panellists A, B and C who were conducting interviews for the candidates waiting in the rooms X, Y and Z respectively. The capacity for the waiting rooms X, Y and Z were 5, 10 and 15 respectively.
The 60 students were given a rank from 1 to 60 based on their composite score and it is known that no two students got the same score. To start off the interviews, the ones with top 5 ranks are sent to panellist A. The 10 below them are sent to B and students ranked 16 to 30 were sent to C. When the last person from the waiting room X, Y and Z gives an interview, the next set of students are immediately sent to the waiting room as soon as the interview gets over and the priority is maintained as students with higher ranks are sent to X, Y and Z respectively if the interviews of the previous batch end simultaneously.
It is known that:
1. Panellist A takes an interview for 15 minutes and takes a break of 5 minutes only after interviewing 3 candidates
2. Panellist B takes an interview for 10 minutes and takes a break of 5 minutes after interviewing 5 students.
3. Panellist C takes an interview of 5 minutes and takes a break of 5 minutes after interviewing 4 students.
4. Lunch break is scheduled between 12:00 noon to 12:30 PM and students are not cut abruptly if their interview began before 12:00 noon, i.e. the interviewers take the break only after finishing the interview if it started before 12:00 noon.
5. Batches of 5, 10 and 15 students enter the waiting room together such that students who enter the waiting room at a time have continuous ranks. For example, if the interviewer X is ending up the interview of the last student from the previous batch, 5 students with continuous ranks (say 2125) enter the waiting room X together.
6. Students allotted to a particular waiting room is only interviewed by the designated interviewer and is not interviewed by anyone else even if the other interviewer is free.
7. If panellist A goes into the lunch break after having interviewed 1 student, he will again take his 5 minute break after interviewing 2 students post the lunch break so as to satisfy the condition 1 always. The same applies for panellist B and C who follow conditions 2 and 3 respectively.
When did the student ranked 57th finish his/her interview?
Students ranked from 1 to 5 will be interviewed by A and thus are moved to the waiting room X.
Similarly, students ranked 6 to 15 (10 students) will be interviewed by B and are moved to waiting room Y.
And students ranked 16 to 30 (15 students) will be interviewed by C and are moved to waiting room Z.
A takes a break after every 3 interviews. B and C take breaks after every 5 and 4 interviews respectively.
So, a map of the first few students will look like:
Here, M, N, X and Y are the ranks of the students. M to M+4 are the set of 5 students who will be interviewed once the interview of the student ranked 5th gets over and similarly for others.
We see that interviewer A finishes his first batch of interviews first (at 10:20) and hence M must be 31. Students ranked 31 to 35 move to waiting room X.
Next to finish interviewing his/her first batch of interviewees is B (at 10:30) and hence Y=36. Students ranked from 36 to 50 will move into waiting room Z.
Finally, interviewer Y will get the next 10 students ranked from 51 to 60 and hence X=51.
We do not require N.
Interviewer A interviews students ranked from 1 to 5, 31 to 35.
Interviewer B interviews students ranked from 6 to 15 and 51 to 60.
Interviewer C interviews students ranked from 16 to 30 and 36 to 50.
An updated table will look like:
We can break down the interviews of students ranked 41 to 50 for interviewer C as:
Each set of 4 consecutively ranked students will be interviewed in 20 minutes. The fifth student will be interviewed after 20+5(break) minutes= 25 minutes.
So, the interview of student ranked 41 starts at 11:05 am and that of student ranked 45 starts at 11:05+25= 11:30 am. Similarly the interview of student ranked 49 starts at 11:55 am and so on.
Student ranked 57 finished his interview at 12:05 PM.
5 persons P1, P2, P3, P4 and P5 took part in a unique high jump competition where each one was given 10 chances to maximise their points. Each one of them started with a height of 150 cm to clear. If a particular participant cleared the height, in the next jump he was to clear a height of 5 cm more than the previous one. For eg. if a participant cleared 150 cm in his first jump, he will need to clear the height of 155 cm in his next jump. A foul is said to be committed if the participant fails to clear the barrier height. 3 continuous fouls would lead to straight elimination. 10 points are given to a participant who clears the given height and 2 points are deducted for every foul. Also, a participant is said to face an elimination jump if he had committed fouls on both of his two previous attempts. The following additional information is known about the jumps made by the 5 participants
1. P5 was eliminated in his 5th jump and managed to score a total of points in single digit.
2. P1 and P2 faced elimination jumps thrice but managed to escape elimination. P1 never cleared two jumps continuously without a foul but P2 did this exactly once. Both of them scored 28 points each and cleared the 10th jump.
3. P4 was the only participant who made a maximum of 3 jumps continuously twice and he faced elimination jump once and escaped elimination.
4. P3 was eliminated in his 8th jump and he never faced the elimination jump before his 8th jump. Also, he cleared two different heights in two jumps continuously exactly once.
5. P2 failed in his 4th and 7th jumps.
6. P4 made a foul in his second jump.
In how many possible ways can the jumps be made by all the 5 participants to satisfy all the given points in the question?
We will start off by using the information given in point 1.
It says that P5 was eliminated in his 5th jump. We will try to represent the jump in which he cleared the height successfully with 'Y' and the jumps in which he fouled using 'N'. Since he was eliminated in his fifth jump, he must have made fouls in his 3rd, 4th and 5th jumps and cleared the 2nd jump successfully. Had this not been the case, he would have been eliminated in his 4th jump with fouls in 2nd, 3rd and 4th jumps.
So,
In his first jump, he cannot have made the jump successful, else his points would then become 206=14 which is a doubledigit.
.'. P5 must have had the following set of jumps:
Moving on to point 3 and 6 for P4.
It is said that he made a maximum of 3 continuous correct attempts twice and failed in his second jump.
We can have the following possibilities:
Next, we will look into point 4. P3 was eliminated in his 8th jump. So, we can have:
We know the logic behind putting YNNN in the last 4 jumps as he was eliminated in his 8th jump. Also, he never faced elimination before his 8th jump. So, 2 Ns cannot be together. A N has to be preceded and followed by a Y. If J4 is an N, J2 and J3 must be the continuous jumps. Similarly for the other case, if J4 is a Y, we have the continuous jumps and all the previous jumps will alternate between Y and N.
Now, for P1 using the second point, we can see that he scored 28 points with facing the elimination jump thrice. He must have cleared the heights successfully 4 times (40 points) and committed a foul 6 times (12 points) to have scored 28 points. Also, all his 6 fouls are part of 2 continuous fouls because of which he faced the elimination jump thrice. The only possible way to do this without any two successful jumps is:
For P2, he also has 4 successful jumps and 6 fouls. Also, using point 5, we can infer that:
Now, jumps 3 and 4 cannot be the first set of fouls, because in that case, we will have only two elimination jumps for P2 5th jump after 3rd and 4th fouls and 8th jump after 6th and 7th foul. Jump 10 is already successful. Therefore, jump 4 must be part of the second continuous fouls. Hence, we have:
.'. For P1, P2 and P5, there is just one case.
For P3, there are 2 cases and for P4, we have 3 cases.
So, the possible ways in which the jumps may have been made= 1\times1\times1\times2\times31×1×1×2×3= 6 ways.
5 persons P1, P2, P3, P4 and P5 took part in a unique high jump competition where each one was given 10 chances to maximise their points. Each one of them started with a height of 150 cm to clear. If a particular participant cleared the height, in the next jump he was to clear a height of 5 cm more than the previous one. For eg. if a participant cleared 150 cm in his first jump, he will need to clear the height of 155 cm in his next jump. A foul is said to be committed if the participant fails to clear the barrier height. 3 continuous fouls would lead to straight elimination. 10 points are given to a participant who clears the given height and 2 points are deducted for every foul. Also, a participant is said to face an elimination jump if he had committed fouls on both of his two previous attempts. The following additional information is known about the jumps made by the 5 participants
1. P5 was eliminated in his 5th jump and managed to score a total of points in single digit.
2. P1 and P2 faced elimination jumps thrice but managed to escape elimination. P1 never cleared two jumps continuously without a foul but P2 did this exactly once. Both of them scored 28 points each and cleared the 10th jump.
3. P4 was the only participant who made a maximum of 3 jumps continuously twice and he faced elimination jump once and escaped elimination.
4. P3 was eliminated in his 8th jump and he never faced the elimination jump before his 8th jump. Also, he cleared two different heights in two jumps continuously exactly once.
5. P2 failed in his 4th and 7th jumps.
6. P4 made a foul in his second jump.
How many points did P4 score?
We will start off by using the information given in point 1.
It says that P5 was eliminated in his 5th jump. We will try to represent the jump in which he cleared the height successfully with 'Y' and the jumps in which he fouled using 'N'. Since he was eliminated in his fifth jump, he must have made fouls in his 3rd, 4th and 5th jumps and cleared the 2nd jump successfully. Had this not been the case, he would have been eliminated in his 4th jump with fouls in 2nd, 3rd and 4th jumps.
So,
In his first jump, he cannot have made the jump successful, else his points would then become 206=14 which is a doubledigit.
.'. P5 must have had the following set of jumps:
Moving on to point 3 and 6 for P4.
It is said that he made a maximum of 3 continuous correct attempts twice and failed in his second jump.
We can have the following possibilities:
Next, we will look into point 4. P3 was eliminated in his 8th jump. So, we can have:
We know the logic behind putting YNNN in the last 4 jumps as he was eliminated in his 8th jump. Also, he never faced elimination before his 8th jump. So, 2 Ns cannot be together. A N has to be preceded and followed by a Y. If J4 is an N, J2 and J3 must be the continuous jumps. Similarly for the other case, if J4 is a Y, we have the continuous jumps and all the previous jumps will alternate between Y and N.
Now, for P1 using the second point, we can see that he scored 28 points with facing the elimination jump thrice. He must have cleared the heights successfully 4 times (40 points) and committed a foul 6 times (12 points) to have scored 28 points. Also, all his 6 fouls are part of 2 continuous fouls because of which he faced the elimination jump thrice. The only possible way to do this without any two successful jumps is:
For P2, he also has 4 successful jumps and 6 fouls. Also, using point 5, we can infer that:
Now, jumps 3 and 4 cannot be the first set of fouls, because in that case, we will have only two elimination jumps for P2 5th jump after 3rd and 4th fouls and 8th jump after 6th and 7th foul. Jump 10 is already successful. Therefore, jump 4 must be part of the second continuous fouls. Hence, we have:
We can see that P4 can either make 6 correct jumps or 7 correct jumps.
So, his score can either be 52 or 64.
5 persons P1, P2, P3, P4 and P5 took part in a unique high jump competition where each one was given 10 chances to maximise their points. Each one of them started with a height of 150 cm to clear. If a particular participant cleared the height, in the next jump he was to clear a height of 5 cm more than the previous one. For eg. if a participant cleared 150 cm in his first jump, he will need to clear the height of 155 cm in his next jump. A foul is said to be committed if the participant fails to clear the barrier height. 3 continuous fouls would lead to straight elimination. 10 points are given to a participant who clears the given height and 2 points are deducted for every foul. Also, a participant is said to face an elimination jump if he had committed fouls on both of his two previous attempts. The following additional information is known about the jumps made by the 5 participants
1. P5 was eliminated in his 5th jump and managed to score a total of points in single digit.
2. P1 and P2 faced elimination jumps thrice but managed to escape elimination. P1 never cleared two jumps continuously without a foul but P2 did this exactly once. Both of them scored 28 points each and cleared the 10th jump.
3. P4 was the only participant who made a maximum of 3 jumps continuously twice and he faced elimination jump once and escaped elimination.
4. P3 was eliminated in his 8th jump and he never faced the elimination jump before his 8th jump. Also, he cleared two different heights in two jumps continuously exactly once.
5. P2 failed in his 4th and 7th jumps.
6. P4 made a foul in his second jump.
How many participants did not commit a foul in their 5th attempt?
We will start off by using the information given in point 1.
It says that P5 was eliminated in his 5th jump. We will try to represent the jump in which he cleared the height successfully with 'Y' and the jumps in which he fouled using 'N'. Since he was eliminated in his fifth jump, he must have made fouls in his 3rd, 4th and 5th jumps and cleared the 2nd jump successfully. Had this not been the case, he would have been eliminated in his 4th jump with fouls in 2nd, 3rd and 4th jumps.
So,
In his first jump, he cannot have made the jump successful, else his points would then become 206=14 which is a doubledigit.
.'. P5 must have had the following set of jumps:
Moving on to point 3 and 6 for P4.
It is said that he made a maximum of 3 continuous correct attempts twice and failed in his second jump.
We can have the following possibilities:
Next, we will look into point 4. P3 was eliminated in his 8th jump. So, we can have:
We know the logic behind putting YNNN in the last 4 jumps as he was eliminated in his 8th jump. Also, he never faced elimination before his 8th jump. So, 2 Ns cannot be together. A N has to be preceded and followed by a Y. If J4 is an N, J2 and J3 must be the continuous jumps. Similarly for the other case, if J4 is a Y, we have the continuous jumps and all the previous jumps will alternate between Y and N.
Now, for P1 using the second point, we can see that he scored 28 points with facing the elimination jump thrice. He must have cleared the heights successfully 4 times (40 points) and committed a foul 6 times (12 points) to have scored 28 points. Also, all his 6 fouls are part of 2 continuous fouls because of which he faced the elimination jump thrice. The only possible way to do this without any two successful jumps is:
For P2, he also has 4 successful jumps and 6 fouls. Also, using point 5, we can infer that:
Now, jumps 3 and 4 cannot be the first set of fouls, because in that case, we will have only two elimination jumps for P2 5th jump after 3rd and 4th fouls and 8th jump after 6th and 7th foul. Jump 10 is already successful. Therefore, jump 4 must be part of the second continuous fouls. Hence, we have:
P3 and P4 did not commit any foul in every case in the 5th jump. The rest of the participants did commit the foul.
5 persons P1, P2, P3, P4 and P5 took part in a unique high jump competition where each one was given 10 chances to maximise their points. Each one of them started with a height of 150 cm to clear. If a particular participant cleared the height, in the next jump he was to clear a height of 5 cm more than the previous one. For eg. if a participant cleared 150 cm in his first jump, he will need to clear the height of 155 cm in his next jump. A foul is said to be committed if the participant fails to clear the barrier height. 3 continuous fouls would lead to straight elimination. 10 points are given to a participant who clears the given height and 2 points are deducted for every foul. Also, a participant is said to face an elimination jump if he had committed fouls on both of his two previous attempts. The following additional information is known about the jumps made by the 5 participants
1. P5 was eliminated in his 5th jump and managed to score a total of points in single digit.
2. P1 and P2 faced elimination jumps thrice but managed to escape elimination. P1 never cleared two jumps continuously without a foul but P2 did this exactly once. Both of them scored 28 points each and cleared the 10th jump.
3. P4 was the only participant who made a maximum of 3 jumps continuously twice and he faced elimination jump once and escaped elimination.
4. P3 was eliminated in his 8th jump and he never faced the elimination jump before his 8th jump. Also, he cleared two different heights in two jumps continuously exactly once.
5. P2 failed in his 4th and 7th jumps.
6. P4 made a foul in his second jump.
What is the maximum height (in cm) that P4 could have cleared?
We will start off by using the information given in point 1.
It says that P5 was eliminated in his 5th jump. We will try to represent the jump in which he cleared the height successfully with 'Y' and the jumps in which he fouled using 'N'. Since he was eliminated in his fifth jump, he must have made fouls in his 3rd, 4th and 5th jumps and cleared the 2nd jump successfully. Had this not been the case, he would have been eliminated in his 4th jump with fouls in 2nd, 3rd and 4th jumps.
So,
In his first jump, he cannot have made the jump successful, else his points would then become 206=14 which is a doubledigit.
.'. P5 must have had the following set of jumps:
Moving on to point 3 and 6 for P4.
It is said that he made a maximum of 3 continuous correct attempts twice and failed in his second jump.
We can have the following possibilities:
Next, we will look into point 4. P3 was eliminated in his 8th jump. So, we can have:
We know the logic behind putting YNNN in the last 4 jumps as he was eliminated in his 8th jump. Also, he never faced elimination before his 8th jump. So, 2 Ns cannot be together. A N has to be preceded and followed by a Y. If J4 is an N, J2 and J3 must be the continuous jumps. Similarly for the other case, if J4 is a Y, we have the continuous jumps and all the previous jumps will alternate between Y and N.
Now, for P1 using the second point, we can see that he scored 28 points with facing the elimination jump thrice. He must have cleared the heights successfully 4 times (40 points) and committed a foul 6 times (12 points) to have scored 28 points. Also, all his 6 fouls are part of 2 continuous fouls because of which he faced the elimination jump thrice. The only possible way to do this without any two successful jumps is:
For P2, he also has 4 successful jumps and 6 fouls. Also, using point 5, we can infer that:
Now, jumps 3 and 4 cannot be the first set of fouls, because in that case, we will have only two elimination jumps for P2 5th jump after 3rd and 4th fouls and 8th jump after 6th and 7th foul. Jump 10 is already successful. Therefore, jump 4 must be part of the second continuous fouls. Hence, we have:
For P4 to have cleared the maximum height, we will consider the case where he made the minimum fouls. He jumped 7 times without any foul. So, the maximum height he could have cleared is 150 (in his first attempt) + 6(5) cm = (150+30) cm = 180 cm.
A survey was conducted among the people of a colony as to which news channel(s) they watch. The results of the survey displayed that 271 people watched Channel A, 361 people watched Channel B, 492 people watched Channel C and 295 people watched Channel D. It was also observed that a single person can watch more than one channel. Based on the information given, answer the questions that follow.
People who watched A also watched B. People who watched C or D or both did not watch A. What can be the minimum number of people surveyed?
People who followed A also followed B. So we get a Venn Diagram as the following.
Any person following C or D won't overlap with A, but might overlap with B. SInce 492 people watch C(which is the highest), we need to include the people who watched B but not A in this number to minimise the number of people. Also, people who watch D (295) should definitely be a subset of D. Hence, we get the following:
People who watch D can either come in the only C region(since 295<402), or they might be distributed between only C and B and C region. In both cases, it won't add any additional count to the total number of people.
Hence, the total number of people surveyed = 271 + 90 + 402 = 763.
Management School of India had an intake of 478 students this year. The admitted students have to select at least one specialisation as soon as they join the Bschool. The five available choices are Finance, Marketing, HRM, Operations and Consulting. The students can opt for as many specialisations as they can as it is up to the dean who will separate out the specialisations later for each one based on the choices made by the students. The following is known about the choices made by the students
1. The number of students who choose Operations is 200% of the students who choose HRM.
2. No student who chooses Consulting chooses Operations.
3. The students who choose Finance and Marketing is 40% more than the ones who choose Finance without Marketing.
4. 26 students choose Consulting alone and no other specialisation.
5. The students who choose Finance also choose Consulting. Similarly, the students who choose HRM also select Operations.
6. The students who choose only marketing is 10 more than the students who choose Operations.
7. The students who choose Consulting and Marketing is 6 more than twice the students who choose Finance and Marketing.
8. The students who select Operations also select Marketing.
9. A total of 432 students choose Marketing.
How many students chose Consulting in total?
We will use the information given in points 2, 5 and 8 to form the Venn diagram as follows:
It is given that 26 students choose Consulting alone. Also, if we take the students who choose HRM to be x, the number of students who choose Operations will be 2x. Also, the number of students who choose only Marketing is 10 more than the number of students who choose Operations.
So, we will try and enter the partial information inferred so far in the Venn diagram.
Using the information given in point number 3, we can let that the number of students who choose Finance without Marketing as y. So, students who choose Finance and Marketing thus becomes 1.4y
In point 7, we see that the students who choose Consulting and Marketing are 6 more than twice the number of students who choose Finance and Marketing. But since students who choose Finance is also chooses Consulting, we can add the following information to the Venn diagram:
It is given that 424 students choose Marketing (point 9).
So, 2x+10+x+x+1.4y+1.4y+6= 432 ......(1)
Also, total students= 478.
.'. y+26= 478432= 46
⇒ y= 20.
Putting y=20 in equation (1), we get
4x+2.8y+16= 432
⇒ 4x+56= 416
⇒ 4x=360
.'. x= 90.
Students who chose Consulting= 2.8y+y+26+6= 3.8y+32= 76+32=108
Management School of India had an intake of 478 students this year. The admitted students have to select at least one specialisation as soon as they join the Bschool. The five available choices are Finance, Marketing, HRM, Operations and Consulting. The students can opt for as many specialisations as they can as it is up to the dean who will separate out the specialisations later for each one based on the choices made by the students. The following is known about the choices made by the students
1. The number of students who choose Operations is 200% of the students who choose HRM.
2. No student who chooses Consulting chooses Operations.
3. The students who choose Finance and Marketing is 40% more than the ones who choose Finance without Marketing.
4. 26 students choose Consulting alone and no other specialisation.
5. The students who choose Finance also choose Consulting. Similarly, the students who choose HRM also select Operations.
6. The students who choose only marketing is 10 more than the students who choose Operations.
7. The students who choose Consulting and Marketing is 6 more than twice the students who choose Finance and Marketing.
8. The students who select Operations also select Marketing.
9. A total of 432 students choose Marketing.
What is the total number of students who chose Consulting and Marketing?
We will use the information given in points 2, 5 and 8 to form the Venn diagram as follows:
It is given that 26 students choose Consulting alone. Also, if we take the students who choose HRM to be x, the number of students who choose Operations will be 2x. Also, the number of students who choose only Marketing is 10 more than the number of students who choose Operations.
So, we will try and enter the partial information inferred so far in the Venn diagram.
Using the information given in point number 3, we can let that the number of students who choose Finance without Marketing as y. So, students who choose Finance and Marketing thus becomes 1.4y
In point 7, we see that the students who choose Consulting and Marketing are 6 more than twice the number of students who choose Finance and Marketing. But since students who choose Finance is also chooses Consulting, we can add the following information to the Venn diagram:
It is given that 424 students choose Marketing (point 9).
So, 2x+10+x+x+1.4y+1.4y+6= 432 ......(1)
Also, total students= 478.
.'. y+26= 478432= 46
⇒ y= 20.
Putting y=20 in equation (1), we get
4x+2.8y+16= 432
⇒ 4x+56= 416
⇒ 4x=360
.'. x= 90.
Students who chose Consulting and Marketing = 2.8y+6= 56+6= 62
Management School of India had an intake of 478 students this year. The admitted students have to select at least one specialisation as soon as they join the Bschool. The five available choices are Finance, Marketing, HRM, Operations and Consulting. The students can opt for as many specialisations as they can as it is up to the dean who will separate out the specialisations later for each one based on the choices made by the students. The following is known about the choices made by the students
1. The number of students who choose Operations is 200% of the students who choose HRM.
2. No student who chooses Consulting chooses Operations.
3. The students who choose Finance and Marketing is 40% more than the ones who choose Finance without Marketing.
4. 26 students choose Consulting alone and no other specialisation.
5. The students who choose Finance also choose Consulting. Similarly, the students who choose HRM also select Operations.
6. The students who choose only marketing is 10 more than the students who choose Operations.
7. The students who choose Consulting and Marketing is 6 more than twice the students who choose Finance and Marketing.
8. The students who select Operations also select Marketing.
9. A total of 432 students choose Marketing.
How many students chose Operations?
We will use the information given in points 2, 5 and 8 to form the Venn diagram as follows:
It is given that 26 students choose Consulting alone. Also, if we take the students who choose HRM to be x, the number of students who choose Operations will be 2x. Also, the number of students who choose only Marketing is 10 more than the number of students who choose Operations.
So, we will try and enter the partial information inferred so far in the Venn diagram.
Using the information given in point number 3, we can let that the number of students who choose Finance without Marketing as y. So, students who choose Finance and Marketing thus becomes 1.4y
In point 7, we see that the students who choose Consulting and Marketing are 6 more than twice the number of students who choose Finance and Marketing. But since students who choose Finance is also chooses Consulting, we can add the following information to the Venn diagram:
It is given that 424 students choose Marketing (point 9).
So, 2x+10+x+x+1.4y+1.4y+6= 432 ......(1)
Also, total students= 478.
.'. y+26= 478432= 46
⇒ y= 20.
Putting y=20 in equation (1), we get
4x+2.8y+16= 432
⇒ 4x+56= 416
⇒ 4x=360
.'. x= 90.
Students who chose Operations= 2x= 180.
Management School of India had an intake of 478 students this year. The admitted students have to select at least one specialisation as soon as they join the Bschool. The five available choices are Finance, Marketing, HRM, Operations and Consulting. The students can opt for as many specialisations as they can as it is up to the dean who will separate out the specialisations later for each one based on the choices made by the students. The following is known about the choices made by the students
1. The number of students who choose Operations is 200% of the students who choose HRM.
2. No student who chooses Consulting chooses Operations.
3. The students who choose Finance and Marketing is 40% more than the ones who choose Finance without Marketing.
4. 26 students choose Consulting alone and no other specialisation.
5. The students who choose Finance also choose Consulting. Similarly, the students who choose HRM also select Operations.
6. The students who choose only marketing is 10 more than the students who choose Operations.
7. The students who choose Consulting and Marketing is 6 more than twice the students who choose Finance and Marketing.
8. The students who select Operations also select Marketing.
9. A total of 432 students choose Marketing.
How many students chose Finance?
We will use the information given in points 2, 5 and 8 to form the Venn diagram as follows:
It is given that 26 students choose Consulting alone. Also, if we take the students who choose HRM to be x, the number of students who choose Operations will be 2x. Also, the number of students who choose only Marketing is 10 more than the number of students who choose Operations.
So, we will try and enter the partial information inferred so far in the Venn diagram.
Using the information given in point number 3, we can let that the number of students who choose Finance without Marketing as y. So, students who choose Finance and Marketing thus becomes 1.4y
In point 7, we see that the students who choose Consulting and Marketing are 6 more than twice the number of students who choose Finance and Marketing. But since students who choose Finance is also chooses Consulting, we can add the following information to the Venn diagram:
It is given that 424 students choose Marketing (point 9).
So, 2x+10+x+x+1.4y+1.4y+6= 432 ......(1)
Also, total students= 478.
.'. y+26= 478432= 46
⇒ y= 20.
Putting y=20 in equation (1), we get
4x+2.8y+16= 432
⇒ 4x+56= 416
⇒ 4x=360
.'. x= 90.
Students who chose Finance= 1.4y+y = 2.4y = 48
Directions : In the 1st Semester at NIM, students have five papers, each of which is graded on a 9 point grading scale. The marks to grade conversion is as follows:
The below table depicts the marks scored by each students in the 5 papers they had to appear for in Semester  1. The values of X, Y and Z have been intentionally removed from the Table.
The following additional information is also known:
(i) Only 2 of the six students have the same CQPI, and they are Shujoy and Pooja
(ii) The average of the CQPI obtained by Abhishek and Namrata is equal to that of Shujoy and Sanjay
(iii) Though Namrata's total marks obtained is not the lowest, she has the lowest CQPI of the six students
(iv) The total marks obtained by the six students in Marketing  I is more than what was obtained by them in exactly 2 of the remaining 4 papers
(v) The CQPI for the students are computed by dividing the total Grade Points obtained by the number of papers they appeared for in each semester
What is the sum of the marks obtained by Shujoy in his five papers in Semester  1?
The Grades obtained by the students in the courses are as follows:
The total marks obtained by the 6 students are as follows:
Manish = 351
Shujoy = 276 + X
Pooja = 357
Abhishek = 301 + Y
Namrata = 321 + Z
Sanjay = 360
Now let us try to combine and compare the above results, based on the additional information provided.
From (i), we get that Pooja and Shujoy have the same CQPI(same Grade Point sum). Thus Shujoy's total Grade points must be 28, which means he must have got 6 Grade Points (B + grade) in Operations  I. Thus his marks will be in the range of X = 70  79 and x = 6. Thus Shujoy's total marks will be in the range of 346  355
From (iii), we get that Namrata has the lowest CQPI. Thus she must have got either 0 or 1 Grade Point in Accounting  1. But since she did not get the lowest total marks, she must have got more than Shujoy's total (346  355). Thus Namrata must have scored at least 26 marks. Combining we get that Namrata got Grade  D (Grade Point  1) in Accounting  I, with a score(Z) in the range of 26  29, and z = 1. Thus Shujoy's total must be less than 350, which means he must have obtained a score in the range of 70  73 in Operations  I.
The expression linking X and Z can be stated as follows,
276 + X < 321 + Z
or X < 45 + Z
Now from Point (ii), we get that (24 + y)/5 + (26 + z)/5 = (22 + x)/5 + 30/5
Multiplying throughout by 5, and replacing x = 6 & z = 1.
Thus we get y = 7, which translates to a score of 8089 in HR  I.
The total mark obtained by all six students in each paper is as follows:
Quants  I = 467
Operations  I = 421  424
Marketing  I = 422
HR  I = 455  464
Accounting  I = 377  380
Now from Point (iv), we get that the total marks obtained by the six students in Marketing  I is more than what was obtained by them in exactly 2 of the remaining 4 papers
Thus Operations  I total must be less than that of Marketing  I, and hence must be equal to 421. This also implies that X = 70. Thus Shujoy's total score = 346.
Shujoy's total score is 346.
CBiz is a network marketing platform wherein a pyramid scheme is followed. The member who joins initially gets 25% of the revenue generated as commission. He is also liable to get an additional 25% of the commissions generated by a member who was referred by him. And this scheme goes on till infinity. If the revenue generated by each of the members of CBiz is Rs. 20,000; then what amount is earned by the first member who referred another member only once, who in turn referred another only once and so on?
The person, say A, gets 25% of revenue as a commission directly, which is
Let B be the person referred by him. A gets 25% of B's commision as well, which is equal to
Let C be the person referred by B. C's commision=
B's commission because of C =
And A's commission because of C=
Therefore, A is seen to earn in the following pattern
Total earnings for A= Sum to infinite G.P. with a= 5000 and
Total earnings =
Grapes when dried up turn into raisins. A raisin has only 5% of water and grapes have 80% of water. 2 faulty weighing machines A and B are used to measure grapes and raisins respectively. Faulty weighing machine A shows 10% less weight than the correct weight and faulty weighing machine B shows 10% more weight than the correct weight. A certain amount of grapes and raisins was measured, and according to the readings displayed by the balances, the mixture had 20% water content. What approximately was the true water content of the mixture of raisins and grapes that were measured?
Let the amount of grapes be x kg and the amount of raisins be y kg.
Weight displayed by A = 0.9x
Weight displayed by B = 1.1y
Now,
% of water in the mixture = 20%
72x+5.5y=18x+22y
54x=16.5y54x=16.5y
To find out the original water content,
Replacing x with 11/36 y, we get the following
A city is classified as a green city when its forest cover is greater than or equal to 20%. The mayor of Hyderabad wanted the city to fall under this category. When calculated, it was seen that the forest area cannot increase by more than 4% annually. If the current forest area of Hyderabad is 17%, then after 'x' years, Hyderabad falls under the category of Green city, where x is the smallest possible integer. Then x=?
Let the area of Hyderabad be x sq. Kms
Current forest area= 0.17x
Every year the forest area can increase by 4% max.
So, we will compound 4% on 0.17x to check the value of 'n', the number of years after which the forest area increases to 20%.
0.17x(1.04)^{ n} =0.2x
By checking the value of n=2, we get L.H.S.= 1.0816 <1.1765
When n=4, we get L.H.S.= 1.1698< 1.1765
When n=5, we get L.H.S.= 1.2167>1.1765
Therefore min. value of n has to be 5.
Nimbooz, a beverage manufacturing company made a 500 ml of packaged drink that had 80% water, 15% sugar and 5% lemon juice in it. To target special consumers, it also began manufacturing Lemonkiss, a 200 ml packaged drink that had 70% water, 15% sugar, 5% salt and 10% lemon juice in it. Raghu observed that when he mixed one bottle of Nimbooz and Lemonkiss each, the drink was extremely delicious. Raghu was now considering packaging this hybrid drink to sell in the market. If 15 ml lemon juice can be extracted from a lemon, what is the minimum number of lemons needed to make 10 litres of this hybrid drink?
For Nimbooz, containing 500 ml drink, amount of lemon juice= 5% of 500 ml= 25 ml.
For Lemonkiss a 200 ml drink, amount of lemon juice= 10%of 200= 20 ml.
So, total lemon juice= 45 ml in 500+200 ml of the drink= 45 ml in 700 ml of the drink.
Raghu wants to produce 10L of this drink, which will have ml of lemon juice.
'.' 1 lemon is used to extract 15 ml of lemon juice.
.'. Lemons required for ml of lemon juice=
Lemons to be used= 42.85 or 43 lemons.
A polynomial of four degree, f(x) exists such that the coefficient of x^{4} is 1. It is given that f(2)= 6, f(2)= 6, f(3)= 9 and f(4)= 12.
What is the value of f(5)?
We see that the value of f(x) increases linearly w.r.t. the change in the value of x.
f(x) feels like 3x for values 2, 2, 3 and 4. But f(x) is actually a 4 degree polynomial.
So, f(x)= (xa)(xb)(xc)(xd) + g(x) can be the 4th degree polynomial. And for f(x) to be linear at given points, we see that 2, 2, 3 and 4 has to be the values of a,b,c and d such that the first term becomes 0 and g(x) drives the value of f(x).
g(x) has to be 3x as discussed before and hence f(x) is nothing but (x+2)(x2)(x3)(x4)+ 3x.
f(x)=(x+2)(x2)(x3)(x4)+ 3x satisfies all the given values of x and so we will find f(5) using this.
f(5)= (5+2)(52)(53)(54)+ 15= (7)(3)(2)(1)+15= 57.
What is the number of integers in the domain of ^{(15−2x) C} (x+3) ?
The domain of ^{n}C_{r} is such that r > 0 and n > r.
So, x+3 ≥ 0 and 152x≥x+3 are the only two conditions which needs to be satisfied.
x > 3 and 12> 3x x > 3 x < 4 are the two conditions.
.'. The possible integer values of x are 3, 2, 1, 0, 1, 2, 3 and 4.
A rightangled triangle ABC has an inradius and circumradius of 4 cm and 10 cm respectively. What is the area of triangle ABC in sq. cm?
For any rightangled triangle with hypotenuse=h and the other two sides= 'a' and 'b', we know that:
Circumradius= h/2 and inradius=
So, h= 2(10) cm= 20 cm.
Also, (a+b20)=2(4)
⇒ a+b20=8
.'. a+b= 28 ....(1)
Also, we have: a^{2 }+b^{2 }= h^{2}
From equation (1),we have a^{2}+ (28a)^{2}=20^{2}
⇒ a^{2} + 784 + a^{2}  56a = 400
⇒ 2a^{2 + }384  56a = 0
⇒ a^{2 }_{ }28a + 192 = 0.
The two roots of this equation will be a and (28a) which is nothing but a and b. Also, the product of the roots then become 192.
Area of a right angled triangle with nonhypotenuse sides 'a' and 'b'=
What is the area of the unshaded region in the diagram shown below if the length of the shortest diagonal of the regular hexagon is 2√3 cms?
AE is the shortest diagonal of the hexagon and AO= √3.
.'. AF= 2 cm. We know that the longest diagonal of the hexagon = diameter of the circle= 2(Side of the regular hexagon)
So, diameter of the circle= 4 cm. Area of the circle= π (2^{2}) = 4π sq. cm.
Also, the area of the hexagon= 6( area of an equilateral triangle with side length= side length of the hexagon).
.'. Area of the hexagon=
So, area of unshaded region= (4π  6√3) sq.cm
If the area of the equilateral triangle drawn below is 49√3 sq. units and NC= 6 units, what is the area of the circle if AB and AC are its tangents?
Let us assume that AN= x units. Then, AC= AN+NC= (x+6) units.
Area of the equilateral triangle=
⇒ x+6= 14 and x= 8 units.
ON is the radius of the circle with the centre at O. The tangent forms 90^{∘}
with the centre,
So, triangle AON is a rightangled triangle with AN=x= 8 units.
The exact time after 12:00 noon :after which the minute hand and the hour hand are exactly opposite to each other for the second time is?
When the hour hand and the minute hands are opposite to each other for the first time, relative angle covered = 180^{∘}
But when the two hands are opposite to each other for the second time, the relative angle covered = 180^{∘ +} 360^{∘} = 540^{∘}.
The hour hand covers 360^{∘} in 12 hours and 30^{∘} in 1 hour.
So, it covers 0.5^{∘} in 1 minute.
The minute hand on the other hand covers 360^{∘ }in 60 minutes or 6^{∘} in 1 minute.
Therefore the relative speed = (6  0.5)^{∘} = 5.5^{∘ }per minute.
To cover 540^{∘}, it will take minutes after 12 i.e
If A, B, C and D are distinct natural numbers, the sum of which adds up to 50. Then, the maximum value of their product is __?
Given, A, B, C and D are 4 distinct integers and A+B+C+D= 50.
The products of four numbers will be maximum if the numbers are as close to each other as possible.
The A.M. of the four numbers=
.'. The four numbers are around 12 and continuous. A, B, C and D are 11, 12, 13 and 14.
And hence, the maximum value of the products of the four number=11×12×13×14=24024.
If A, B, C and D are distinct natural numbers, the sum of which adds up to 50. Then, the maximum value of their product is __?
Given, A, B, C and D are 4 distinct integers and A+B+C+D= 50.
The products of four numbers will be maximum if the numbers are as close to each other as possible.
The A.M. of the four numbers= 50/4 = 12.5
.'. The four numbers are around 12 and continuous. A, B, C and D are 11, 12, 13 and 14.
And hence, the maximum value of the products of the four number= 11 x 12 x 13 x 14 = 24024.
Consider an A.P. such that the product of its first term and the fourth term is 32 less than the product of the second and third term. If the sum of the first 4 terms of the same A.P. is equal to 12, then the sum of all the possible third terms of the A.P. is?
Let the first 4 terms of the A.P. be (a3d), (ad), (a+d) and (a+3d).
Sum of the 4 terms of the A.P.= 4a= 12
.'. a= 3.
It is given that (a3d)(a+3d)=(ad)(a+d)32
⇒ a^{2}  9d^{2 }= a^{2}  d^{2}  32
⇒ 8d^{2} = 32
⇒ d^{2} = 4
⇒ d = d = + 2.
When d=2, the first 4 terms are (36), (32), (3+2) and (3+6) which is 3,1,5 and 9.
.'. n=8
And log_{2}n= log_{2}8 = 3
For how many integer values of x is the inequality given by log_{(x +1)} (x  4) (x  3) < 1 defined?
For a logarithm function to be defined, we need the base to be greater than 0. So x+1 > 0 or x > 1.
As the base can't equal 1, x+1 has to be greater than 1 or x>0.
x can be 1,2,3,4.... (natural numbers)
Also, as the argument of a logarithm can't be equal to 0, x can't equal 3 or 4.
So x belongs to {1,2,5,6,7,8,9,...}
log_{(x+1)}(x−4)(x−3) <1,
(x4)(x3)<(x+1)
⇒ x^{2}−7x + 12 < x + 1
⇒ x^{2 }− 8x + 11< 0
⇒ x^{2 }− 8x + 16 < 5
⇒ (x − 4)^{2 }< 5
For the above inequality to satisfy, we can only have 3 natural number values in the form of x= 2, 5 or 6.
Alternate Solution:
We have the given inequality: log_{(x+1)}(x−4)(x−3) < 0,
For this to be defined, we need to satisfy the basic conditions For any log function log_{a}b,
(i) a>0 (ii) a ≠ 1 and (iii) b>0
So, in log_{(x+1)} {x  4) (x  3) < 1,
(i) x+1 >0
=>x > 1.
(ii) x+1 ≠ 1
=>x ≠ 0.
(iii) (x3)(x4)>0
x ∈ {∞,3) U(4,∞).
Combining all three, we have the domain as: x ∈ (1,0) U {0, 3)U{4, ∞).
Now,for log_{(x+1)} {x  4) {x  3) < 1 to be satisfied, we need to have:
and 0<(x4)(x3) ....(2)
Solving (1), we get:
For the numerator, we will use x= to rewrite the expression.
So, x^{2}8x+11 has its roots=
Now,
Critical points of this inequality are: 1,4  y√5 , 4 + √5 .
Using the wavy curve method, the values of x which satisfy this are (∞,1) U(4  √5, 4 + √5).
But we already have the domain of the function as: x∈ (1,0) U (0,3) U (4, ∞)..
Using these two, the possible values of x becomes: x∈ (4  √5, 3) U(4, 4 + √5).
Solving the inequality (2), we get:
(x4)(x3)>0
=> x∈ (∞,3) U (4,∞)
Combining (1) and (2), we get x∈ (4  √5,3)U (4, 4 + √5)
.'. The possible integers in this range are 2, 5 and 6 only.
if (256)_{7}+(X)_{7}=(434)_{7}, where (N)_{7 }means a number N written in base 7, then X=?
So, we need to find the value of X which is (434)_{7}−(256)_{7}
The easiest way (but a little longer way to do this is by converting the bases to base 7 followed by subtraction and then converting to base 7 again. This will help to reduce the confusion.
X= 4+21+196=2214+3×7+4× 7^{2}= 4+21+196=221) 6+35+98=1396+5×7+2× 7^{2}= 6+35+98=139= 82.
Using the remainder method, we can find 82 in base 7 as 145.
Raja had an unbiased die with him and he challenged Radha, who had two unbiased dice with her. He said that he could produce a number on his die after rolling such that the number is greater than the sum of the numbers that Radha's dice produced. What is the probability that Raja's number is actually greater than the sum of the numbers of Radha's dice?
The minimum number that Radha's die can show is 1 and 1, which sums up to 2.
So. Raja must have his dice show numbers from 3 to 6 including both,
When Raja's dice shows 3, Radha's die can show only (1,1). Probability of this happening=
When Raja's dice shows 4, Radha's die can show (1,1), (1,2) or (2,1). Probability of this happening=
When Raja's dice shows 5, Radha's die can show (1,1), (1,2), (2,1), (2,2), (1,3), (3,1). Probability of this happening=
When Raja's dice shows 6, Radha's die can show (1,1), (1,2), (2,1), (2,2), (1,3), (3,1), (3,2), (2,3), (4,1), (1,4). Probability of this happening=
.'. Required probability=
A sponsor for the Indian Premier League generated a revenue of 3.1 million in INR and had a profit of 21% for the year 2020 before sponsoring the league. If the board calculates that the cost will rise this year by 10% by sponsoring a team and that the expected revenue will go up by 20%, what is the new profit percentage for the company?
Let the cost of the company before sponsoring the league be Rs. x
It made a profit of 21% and generated a revenue of 3.1 million Ruppes.
So, 1.21x= 3100000
If the costs go up by 10% this year, new cost=
New revenue= .21x 3100000
So, new revenue is times the new cost.
Or, new revenue is 1.32 times the new cost.
.'. New profit= 32%.
Alok took a loan of Rs. 24000 at 5% simple interest per annum from Bhanu. He immediately lent out onethird of the money to Clara at 4% compound interest for two years and the rest to Dhruv at 8% simple interest. How much did Alok earn (in rupees) from the entire transactions if the money was returned back by Clara and Dhruv at the end of the second year? Consider Alok paying back the loan to Bhanu as soon as he got the money back from the other two.
Initially, Alok lent out all the money he borrowed from Bhanu. Alok will earn only when the amount received by him by lending out to Clara and Dhruv is greater than the amount payable to Bhanu at the end of 2 years.
Amount payable to Bhanu at the end of two years= Principal+ S.I.= 24000+ = 24000+2400= Rs. 26,400.
Amount receivable from Clara=
Principal amount for Dhruv= Rs. 24000 Rs. 8000= Rs. 16000.
Amount receivable from Dhruv= 16000+ = 16000+2560= Rs. 18560.
Total amount receivable by Alok= Rs. (8652.8+ 18,560)= Rs. 27212.8
Profit for Alok= Rs. (27212.8 26400)= Rs. 812.8
An A.P. with n terms, where n is an odd number is given to us. What is the ratio of the sum of odd terms to the sum of even terms?
It is given that the A.P. has n terms, where n is an odd number.
So, the number of odd terms in the A.P. is one more than the number of even terms in the same A.P.
Total odd terms= and total even terms=
If we have the A.P. with terms t1, t2, t3, t4, t5.... We can make two A.Ps out of it such that t1, t3, t5... forms one with first term 'a' and common difference '2d'. The second A.P. will similarly have 'a+d' as its first terms and '2d' as its common difference.
Sum of odd terms=
Sum of even terms=
.'. The required ratio=
If Sn=2n^{3}+n^{2}+3n+1, where S_nS n denotes sum to first n terms of a series. It is given that t_{x} , which is the xth term of the series is equal to 84, then x=?
We are given with S_{n}=2n^{3}+n^{2}+3n+1.
We know that any term t_{n} can be found using t_{n}=S_{n}−S_{n}−1.
Here, t_{x}=S_{x}−S_{x}−1
So, 2x^{3}+x^{2}+3x+1−[2(x−1)^{3}(x−1)^{2}+3(x−1)+1]=84
⇒ 2x^{3} + x^{2} + 3x + 1  [2 (x^{3}  1  3x^{2} + 3x) + x^{2} + 1  2x + 3x — 3 + 1] =84
⇒ 2x^{3} + x^{2} + 3x + 1  2x^{3} + 2 + 6x^{2}  6x  x^{2}  1 + 2x  3x + 3  1 = 84
⇒ 4 + 6x^{2}  6x + 2x = 84
⇒ 6x^{2}  4x = 80
⇒ 3x^{2}  2x  40 = 0
∴ x cannot be negative.
∴ x=4.
The two roots of the quadratic equation ax2 + bx + c are reciprocal to one another. One of the roots of this equation is common with that of 3x^{2} + 17x + 10. What is the sum of all the possible values of ?
3x^{2}+17x+10 can be rewritten as 3x^{2}
+15x+2x+10= 3x(x+5)+2(x+5)= (3x+2)(x+5). So, the roots of this quadratic equation are 5 and
So, the possible roots for ax^{2}
+bx+c are
is the sum of roots of the quadratic equation.
The possible values of are and
Possible values of sums of roots =
.'. The sums of the possible sum of roots of the quadratic equation=
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