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Read the passage carefully and answer the following questions:
It is almost universally agreed that the persistence of extreme poverty in many parts of the world is a bad thing. It is less wellagreed, even among philosophers, what should be done about it and by who. An influential movement founded by the philosopher Peter Singer argues that we should each try to do the best we can by donating our surplus income to charities that help those in greatest need. This ‘effective altruism’ movement has two components: i) encouraging individuals in the rich world to donate more; and ii) encouraging us to donate more rationally, to the organisations most efficient at translating those donations into gains in human wellbeing.
The problem with the first component of effective altruism was that it focuses on the internal moral economy of the giver rather than on the realworld problems our giving is supposed to address. The second component of effective altruism might not seem to have that problem because it is explicitly concerned with maximising the amount of good that each unit of resources achieves. However, this concern is better understood as efficiency than as effectiveness. This might seem an innocuous distinction since efficiency is about how we ought to get things done, i.e. a way of being effective. However, there are significant consequences for practical reasoning in the kind of cases effective altruism is concerned with.
If one takes the efficiency view promoted by the effective altruism movement then one assumes a fixed set of resources and the choice of which goal to aim for follows from a calculation of how to maximise the expected value those resources can generate; i.e. the means justifies the end. This should ensure that your donation will achieve the most good, which is to say that you have done the best possible job of giving. However, despite doing so well at the task effective altruism has set you, if you step back you will notice that very little has actually been achieved. The total amount of good we can achieve with our donations is limited to the partial alleviation of some of the symptoms of extreme poverty, symptoms that will recur so long as poverty persists. But effective altruism supplies no plan for the elimination of poverty itself.
The underlying problem is that effective altruism's distinctive combination of political pessimism and consumerhero hubris forecloses the consideration of promising possibilities for achieving far more good. Singer and other effective altruist philosophers believe that their most likely customers find institutional reform too complicated and political action too impersonal and hit and miss to be attractive. So instead they flatter us by promising that we can literally be lifesaving heroes from the comfort of our chairs and using only the superpower of our richworld wallets.
But it just doesn't work. Singer and others have been making this argument for nearly 50 years, yet the level of private donations remain orders of magnitude below what would be required to eliminate global poverty, however efficiently allocated. Also, it needlessly squanders the most obvious and powerful tool we have: the political sphere and institutions of government that we invented to solve complicated and large collective action problems.
Q. The central idea of the passage is that
The author introduces an influential idea that has been suggested (and used) as a potential mechanism to counter global poverty and then highlights its shortcomings in the passage. The author's position is surmised in the last line of the third paragraph "But effective altruism supplies no plan for the elimination of poverty itself." Hence, the author believes that effective altruism cannot end global poverty and lists out reasons to back this argument.
Comparing the options, option A captures this idea precisely.
Option B is not implied in the passage.
Option C talks about an ancillary point. The passage deals with the shortcomings of effective altruism.
The author decries the role of the glorification of individuals and their efforts in solving global poverty only in the penultimate paragraph. This is not the main point of the passage. Hence D is incorrect.
Read the passage carefully and answer the following questions:
It is almost universally agreed that the persistence of extreme poverty in many parts of the world is a bad thing. It is less wellagreed, even among philosophers, what should be done about it and by who. An influential movement founded by the philosopher Peter Singer argues that we should each try to do the best we can by donating our surplus income to charities that help those in greatest need. This ‘effective altruism’ movement has two components: i) encouraging individuals in the rich world to donate more; and ii) encouraging us to donate more rationally, to the organisations most efficient at translating those donations into gains in human wellbeing.
The problem with the first component of effective altruism was that it focuses on the internal moral economy of the giver rather than on the realworld problems our giving is supposed to address. The second component of effective altruism might not seem to have that problem because it is explicitly concerned with maximising the amount of good that each unit of resources achieves. However, this concern is better understood as efficiency than as effectiveness. This might seem an innocuous distinction since efficiency is about how we ought to get things done, i.e. a way of being effective. However, there are significant consequences for practical reasoning in the kind of cases effective altruism is concerned with.
If one takes the efficiency view promoted by the effective altruism movement then one assumes a fixed set of resources and the choice of which goal to aim for follows from a calculation of how to maximise the expected value those resources can generate; i.e. the means justifies the end. This should ensure that your donation will achieve the most good, which is to say that you have done the best possible job of giving. However, despite doing so well at the task effective altruism has set you, if you step back you will notice that very little has actually been achieved. The total amount of good we can achieve with our donations is limited to the partial alleviation of some of the symptoms of extreme poverty, symptoms that will recur so long as poverty persists. But effective altruism supplies no plan for the elimination of poverty itself.
The underlying problem is that effective altruism's distinctive combination of political pessimism and consumerhero hubris forecloses the consideration of promising possibilities for achieving far more good. Singer and other effective altruist philosophers believe that their most likely customers find institutional reform too complicated and political action too impersonal and hit and miss to be attractive. So instead they flatter us by promising that we can literally be lifesaving heroes from the comfort of our chairs and using only the superpower of our richworld wallets.
But it just doesn't work. Singer and others have been making this argument for nearly 50 years, yet the level of private donations remain orders of magnitude below what would be required to eliminate global poverty, however efficiently allocated. Also, it needlessly squanders the most obvious and powerful tool we have: the political sphere and institutions of government that we invented to solve complicated and large collective action problems.
Q. All of the following options represent causes reflective of effective altruism EXCEPT:
An integral component of effective altruism is the presence of "organisations most efficient at translating those donations into gains in human wellbeing." The perceived impact of these institutions is positive and uplifting, especially concerning the poor or needy. Causes that highlight this positive impact on human wellbeing are reflective of effective altruism. Moreover, from the lines
"The underlying problem is that effective altruism's distinctive combination of political pessimism and consumerhero hubris forecloses the consideration of promising possibilities for achieving far more good. Singer and other effective altruist philosophers believe that their most likely customers find institutional reform too complicated and political action too impersonal and hit and miss to be attractive."
We can infer that effective altruism does not typically involve political action and institutional reform.
Option A: The NGO here is utilising the collected funds to build schools in rural regions: a gesture with a positive impact. Hence, this can be eliminated as the potential answer.
Option B: The charity organisation ensures the well being of the povertystricken individuals of the slums through their healthcare drives offered for free; this again indicates positive gains for people. We can, thereby, eliminate Option B as the answer.
Option C: Again, there is some perceptible positive impact that stems from the gesture of offering free legal aid to the poor and marginalised people. Thus, we can discard option C as a possible answer.
Option D: Funding of protest with some political agenda does not reflect any observable impact on human well being (unlike the other cases). Also, this is more in line with what the author wants (political action, changing institutions, holding government accountable) which is in contrast with effective altruism. Hence, Option D is the correct choice.
Read the passage carefully and answer the following questions:
It is almost universally agreed that the persistence of extreme poverty in many parts of the world is a bad thing. It is less wellagreed, even among philosophers, what should be done about it and by who. An influential movement founded by the philosopher Peter Singer argues that we should each try to do the best we can by donating our surplus income to charities that help those in greatest need. This ‘effective altruism’ movement has two components: i) encouraging individuals in the rich world to donate more; and ii) encouraging us to donate more rationally, to the organisations most efficient at translating those donations into gains in human wellbeing.
The problem with the first component of effective altruism was that it focuses on the internal moral economy of the giver rather than on the realworld problems our giving is supposed to address. The second component of effective altruism might not seem to have that problem because it is explicitly concerned with maximising the amount of good that each unit of resources achieves. However, this concern is better understood as efficiency than as effectiveness. This might seem an innocuous distinction since efficiency is about how we ought to get things done, i.e. a way of being effective. However, there are significant consequences for practical reasoning in the kind of cases effective altruism is concerned with.
If one takes the efficiency view promoted by the effective altruism movement then one assumes a fixed set of resources and the choice of which goal to aim for follows from a calculation of how to maximise the expected value those resources can generate; i.e. the means justifies the end. This should ensure that your donation will achieve the most good, which is to say that you have done the best possible job of giving. However, despite doing so well at the task effective altruism has set you, if you step back you will notice that very little has actually been achieved. The total amount of good we can achieve with our donations is limited to the partial alleviation of some of the symptoms of extreme poverty, symptoms that will recur so long as poverty persists. But effective altruism supplies no plan for the elimination of poverty itself.
The underlying problem is that effective altruism's distinctive combination of political pessimism and consumerhero hubris forecloses the consideration of promising possibilities for achieving far more good. Singer and other effective altruist philosophers believe that their most likely customers find institutional reform too complicated and political action too impersonal and hit and miss to be attractive. So instead they flatter us by promising that we can literally be lifesaving heroes from the comfort of our chairs and using only the superpower of our richworld wallets.
But it just doesn't work. Singer and others have been making this argument for nearly 50 years, yet the level of private donations remain orders of magnitude below what would be required to eliminate global poverty, however efficiently allocated. Also, it needlessly squanders the most obvious and powerful tool we have: the political sphere and institutions of government that we invented to solve complicated and large collective action problems.
Q. The passage makes all of the following claims about effective altruism, EXCEPT
{This ‘effective altruism’ movement has two components: i) encouraging individuals in the rich world to donate more; and ii) encouraging us to donate more rationally to the organisations most efficient at translating those donations into gains in human wellbeing.}
From these lines, we can see that 'effective altruism' supports rational donation, which means donating to efficient organisations which will make the best out of it. Hence, Option A can be inferred.
From the same lines, we can infer that affluent people are encouraged to donate more. Hence B can also be inferred.
In the passage, it has been given that an assumption of limited resources is made. Then a goal is decided upon considering the maximisation of these fixed resources. This often results in focus upon superficial problems, which seem to generate more value, instead of the root problem of poverty. Hence C can also be inferred.
Option D is a distortion. In the last paragraph, the author states that "Singer and others have been making this argument for nearly 50 years, yet the level of private donations remain orders of magnitude below what would be required to eliminate global poverty, however efficiently allocated." Here, the author is talking about cumulative donations, not individual donations. And secondly, the author is concerned about private donations' inability to tackle global poverty. Societal problems is a broad term and could involve other extraneous issues as well. Hence, option D cannot be inferred.
Read the passage carefully and answer the following questions:
It is almost universally agreed that the persistence of extreme poverty in many parts of the world is a bad thing. It is less wellagreed, even among philosophers, what should be done about it and by who. An influential movement founded by the philosopher Peter Singer argues that we should each try to do the best we can by donating our surplus income to charities that help those in greatest need. This ‘effective altruism’ movement has two components: i) encouraging individuals in the rich world to donate more; and ii) encouraging us to donate more rationally, to the organisations most efficient at translating those donations into gains in human wellbeing.
The problem with the first component of effective altruism was that it focuses on the internal moral economy of the giver rather than on the realworld problems our giving is supposed to address. The second component of effective altruism might not seem to have that problem because it is explicitly concerned with maximising the amount of good that each unit of resources achieves. However, this concern is better understood as efficiency than as effectiveness. This might seem an innocuous distinction since efficiency is about how we ought to get things done, i.e. a way of being effective. However, there are significant consequences for practical reasoning in the kind of cases effective altruism is concerned with.
If one takes the efficiency view promoted by the effective altruism movement then one assumes a fixed set of resources and the choice of which goal to aim for follows from a calculation of how to maximise the expected value those resources can generate; i.e. the means justifies the end. This should ensure that your donation will achieve the most good, which is to say that you have done the best possible job of giving. However, despite doing so well at the task effective altruism has set you, if you step back you will notice that very little has actually been achieved. The total amount of good we can achieve with our donations is limited to the partial alleviation of some of the symptoms of extreme poverty, symptoms that will recur so long as poverty persists. But effective altruism supplies no plan for the elimination of poverty itself.
The underlying problem is that effective altruism's distinctive combination of political pessimism and consumerhero hubris forecloses the consideration of promising possibilities for achieving far more good. Singer and other effective altruist philosophers believe that their most likely customers find institutional reform too complicated and political action too impersonal and hit and miss to be attractive. So instead they flatter us by promising that we can literally be lifesaving heroes from the comfort of our chairs and using only the superpower of our richworld wallets.
But it just doesn't work. Singer and others have been making this argument for nearly 50 years, yet the level of private donations remain orders of magnitude below what would be required to eliminate global poverty, however efficiently allocated. Also, it needlessly squanders the most obvious and powerful tool we have: the political sphere and institutions of government that we invented to solve complicated and large collective action problems.
Q. According to the author, the efficiency view promoted by effective altruism
In the third paragraph, the author states that "...If one takes the efficiency view promoted by the effective altruism movement then one assumes a fixed set of resources and the choice of which goal to aim for follows from a calculation of how to maximize the expected value those resources can generate; i.e. the means justifies the end..." So, based on the value maximization of the resources available, the goal is chosen. Option C captures this point correctly and hence, is the correct answer.
In this context, the author does not talk about varying the funding to achieve a goal. Hence option A is irrelevant.
The author does not talk about abandoning difficult goals just because they require prolonged commitment. Thus, B can be eliminated too.
Option D has not been discussed in the passage. It talks about people choosing goals because of personal satisfaction rather than the constraint of resources they have. No such claim has been made.
Hence, Option C is the correct choice.
Read the passage carefully and answer the following questions:
It is almost universally agreed that the persistence of extreme poverty in many parts of the world is a bad thing. It is less wellagreed, even among philosophers, what should be done about it and by who. An influential movement founded by the philosopher Peter Singer argues that we should each try to do the best we can by donating our surplus income to charities that help those in greatest need. This ‘effective altruism’ movement has two components: i) encouraging individuals in the rich world to donate more; and ii) encouraging us to donate more rationally, to the organisations most efficient at translating those donations into gains in human wellbeing.
The problem with the first component of effective altruism was that it focuses on the internal moral economy of the giver rather than on the realworld problems our giving is supposed to address. The second component of effective altruism might not seem to have that problem because it is explicitly concerned with maximising the amount of good that each unit of resources achieves. However, this concern is better understood as efficiency than as effectiveness. This might seem an innocuous distinction since efficiency is about how we ought to get things done, i.e. a way of being effective. However, there are significant consequences for practical reasoning in the kind of cases effective altruism is concerned with.
If one takes the efficiency view promoted by the effective altruism movement then one assumes a fixed set of resources and the choice of which goal to aim for follows from a calculation of how to maximise the expected value those resources can generate; i.e. the means justifies the end. This should ensure that your donation will achieve the most good, which is to say that you have done the best possible job of giving. However, despite doing so well at the task effective altruism has set you, if you step back you will notice that very little has actually been achieved. The total amount of good we can achieve with our donations is limited to the partial alleviation of some of the symptoms of extreme poverty, symptoms that will recur so long as poverty persists. But effective altruism supplies no plan for the elimination of poverty itself.
The underlying problem is that effective altruism's distinctive combination of political pessimism and consumerhero hubris forecloses the consideration of promising possibilities for achieving far more good. Singer and other effective altruist philosophers believe that their most likely customers find institutional reform too complicated and political action too impersonal and hit and miss to be attractive. So instead they flatter us by promising that we can literally be lifesaving heroes from the comfort of our chairs and using only the superpower of our richworld wallets.
But it just doesn't work. Singer and others have been making this argument for nearly 50 years, yet the level of private donations remain orders of magnitude below what would be required to eliminate global poverty, however efficiently allocated. Also, it needlessly squanders the most obvious and powerful tool we have: the political sphere and institutions of government that we invented to solve complicated and large collective action problems.
Q. The author is likely to agree with all of the following statements, EXCEPT:
In the last paragraph, the author highlights the importance of political institutions and collective action in solving largescale problems. The author presents this as an optimal option compared to the effective altruism approach to solving global poverty. Options A and C can be inferred.
{This ‘effective altruism’ movement has two components: i) encouraging individuals in the rich world to donate more; and ii) encouraging us to donate more rationally, to the organisations most efficient at translating those donations into gains in human wellbeing.}
Evidently, the focus is on individual contributions. Hence, option D can be inferred as well.
Option B is wrong. In the third paragraph, the author clearly mentions that the means justify the end'. That is, based on the resources available, the goal is chosen. And this allocation is valuedriven, i.e, resources are allocated so that maximum value is generated. Hence the optimization, rather than minimization of resources is done
Hence, option B is the answer.
Read the passage carefully and answer the following questions:
Once upon a time — just a few years ago, actually — it was not uncommon to see headlines about prominent scientists, tech executives, and engineers warning portentously that the revolt of the robots was nigh. The mechanism varied, but the result was always the same: Uncontrollable machine selfimprovement would one day overcome humanity. A dismal fate awaited us.
Today we fear a different technological threat, one that centers not on machines but other humans. We see ourselves as imperilled by the terrifying social influence unleashed by the Internet in general and social media in particular. We hear warnings that nothing less than our collective ability to perceive reality is at stake, and that if we do not take corrective action we will lose our freedoms and way of life.
Primal terror of mechanical menace has given way to fear of angry primates posting. Ironically, the roles have reversed. The robots are now humanity’s saviors, suppressing bad human mass behavior online with increasingly sophisticated filtering algorithms. We once obsessed about how to restrain machines we could not predict or control — now we worry about how to use machines to restrain humans we cannot predict or control. But the old problem hasn’t gone away: How do we know whether the machines will do as we wish?
The shift away from the fear of unpredictable robots and toward the fear of chaotic human behavior may have been inevitable. For the problem of controlling the machines was always at heart a problem of human desire — the worry that realizing our desires using automated systems might prove catastrophic. The promised solution was to rectify human desire. But once we lost optimism about whether this was possible, the stage was set for the problem to be flipped on its head.
The twentiethcentury cyberneticist Norbert Wiener made what was for his time a rather startling argument: "The machine may be the final instrument of doom, but humanity may be the ultimate cause." In his 1960 essay “Some Moral and Technical Consequences of Automation,” Wiener recounts tales in which a person makes a wish and gets what was requested but not necessarily what he or she really desired. Hence, it's imperative that we be absolutely sure of what desire we put into the machine. Wiener was of course not talking about social media, but we can easily see the analogy: It too achieves purposes, like mob frenzy or erroneous post deletions, that its human designers did not actually desire, even though they built the machines in a way that achieves those purposes. Nor does he envision, as in Terminator, a general intelligence that becomes selfaware and nukes everyone. Rather, he imagined a system that humans cannot easily stop and that acts on a misleading substitute for the military objectives humans actually value.
However, there is a risk in Wiener’s distinction between what we desire and what actually happens in the end. It may create a false image of ourselves — an image in which our desires and our behaviors are wholly separable from each other. Instead of examining carefully whether our desires are in fact good, we may simply assume they are, and so blame bad behavior on the messy cooperation between ourselves and the “system.”
Q. In the third paragraph, why does the author remark that "ironically, the roles have reversed?"?
The author makes the following observation in the third paragraph {The robots are now humanity’s saviors, suppressing bad human mass behaviour online with increasingly sophisticated filtering algorithms. We once obsessed about how to restrain machines we could not predict or control — now we worry about how to use machines to restrain humans we cannot predict or control.}
So, humans feared that selfimproving machines would go out of control and that it would be difficult for humans to restrain them. However, in a role reversal, the machines today help curb bad human behaviour online. Hence, ironically, the roles have reversed.
Only option B conveys this inference and hence is the right answer.
Option A is outside the scope of discussion. Machines evolving to differentiate between good and bad has not been mentioned anywhere. Hence they can be eliminated.
Though an irony, Option C has not been mentioned in the passage as such. Hence can be eliminated.
Option D is close but contains the distortion that we cannot do without machines. The passage does not say that machines are indispensable. Hence, D can be eliminated.
Read the passage carefully and answer the following questions:
Once upon a time — just a few years ago, actually — it was not uncommon to see headlines about prominent scientists, tech executives, and engineers warning portentously that the revolt of the robots was nigh. The mechanism varied, but the result was always the same: Uncontrollable machine selfimprovement would one day overcome humanity. A dismal fate awaited us.
Today we fear a different technological threat, one that centers not on machines but other humans. We see ourselves as imperilled by the terrifying social influence unleashed by the Internet in general and social media in particular. We hear warnings that nothing less than our collective ability to perceive reality is at stake, and that if we do not take corrective action we will lose our freedoms and way of life.
Primal terror of mechanical menace has given way to fear of angry primates posting. Ironically, the roles have reversed. The robots are now humanity’s saviors, suppressing bad human mass behavior online with increasingly sophisticated filtering algorithms. We once obsessed about how to restrain machines we could not predict or control — now we worry about how to use machines to restrain humans we cannot predict or control. But the old problem hasn’t gone away: How do we know whether the machines will do as we wish?
The shift away from the fear of unpredictable robots and toward the fear of chaotic human behavior may have been inevitable. For the problem of controlling the machines was always at heart a problem of human desire — the worry that realizing our desires using automated systems might prove catastrophic. The promised solution was to rectify human desire. But once we lost optimism about whether this was possible, the stage was set for the problem to be flipped on its head.
The twentiethcentury cyberneticist Norbert Wiener made what was for his time a rather startling argument: "The machine may be the final instrument of doom, but humanity may be the ultimate cause." In his 1960 essay “Some Moral and Technical Consequences of Automation,” Wiener recounts tales in which a person makes a wish and gets what was requested but not necessarily what he or she really desired. Hence, it's imperative that we be absolutely sure of what desire we put into the machine. Wiener was of course not talking about social media, but we can easily see the analogy: It too achieves purposes, like mob frenzy or erroneous post deletions, that its human designers did not actually desire, even though they built the machines in a way that achieves those purposes. Nor does he envision, as in Terminator, a general intelligence that becomes selfaware and nukes everyone. Rather, he imagined a system that humans cannot easily stop and that acts on a misleading substitute for the military objectives humans actually value.
However, there is a risk in Wiener’s distinction between what we desire and what actually happens in the end. It may create a false image of ourselves — an image in which our desires and our behaviors are wholly separable from each other. Instead of examining carefully whether our desires are in fact good, we may simply assume they are, and so blame bad behavior on the messy cooperation between ourselves and the “system.”
Q. According to the author, what was the reason for the shift toward the fear of chaotic human behavior?
In the fourth paragraph, the author mentions that humans feared the consequences of attaining their desires through complicated machines. And hence, they attempted to rectify their desires. However, when they lost hope in this endeavour, they shifted away from the fear of unpredictable robots and toward the fear of chaotic human behaviour, flipping the problem on its head.
Option A conveys the idea elucidated above. Option A is the answer.
Option B is partially correct but misses out on the remedying theme.
Options C and D have not been implied in the passage.
Read the passage carefully and answer the following questions:
Once upon a time — just a few years ago, actually — it was not uncommon to see headlines about prominent scientists, tech executives, and engineers warning portentously that the revolt of the robots was nigh. The mechanism varied, but the result was always the same: Uncontrollable machine selfimprovement would one day overcome humanity. A dismal fate awaited us.
Today we fear a different technological threat, one that centers not on machines but other humans. We see ourselves as imperilled by the terrifying social influence unleashed by the Internet in general and social media in particular. We hear warnings that nothing less than our collective ability to perceive reality is at stake, and that if we do not take corrective action we will lose our freedoms and way of life.
Primal terror of mechanical menace has given way to fear of angry primates posting. Ironically, the roles have reversed. The robots are now humanity’s saviors, suppressing bad human mass behavior online with increasingly sophisticated filtering algorithms. We once obsessed about how to restrain machines we could not predict or control — now we worry about how to use machines to restrain humans we cannot predict or control. But the old problem hasn’t gone away: How do we know whether the machines will do as we wish?
The shift away from the fear of unpredictable robots and toward the fear of chaotic human behavior may have been inevitable. For the problem of controlling the machines was always at heart a problem of human desire — the worry that realizing our desires using automated systems might prove catastrophic. The promised solution was to rectify human desire. But once we lost optimism about whether this was possible, the stage was set for the problem to be flipped on its head.
The twentiethcentury cyberneticist Norbert Wiener made what was for his time a rather startling argument: "The machine may be the final instrument of doom, but humanity may be the ultimate cause." In his 1960 essay “Some Moral and Technical Consequences of Automation,” Wiener recounts tales in which a person makes a wish and gets what was requested but not necessarily what he or she really desired. Hence, it's imperative that we be absolutely sure of what desire we put into the machine. Wiener was of course not talking about social media, but we can easily see the analogy: It too achieves purposes, like mob frenzy or erroneous post deletions, that its human designers did not actually desire, even though they built the machines in a way that achieves those purposes. Nor does he envision, as in Terminator, a general intelligence that becomes selfaware and nukes everyone. Rather, he imagined a system that humans cannot easily stop and that acts on a misleading substitute for the military objectives humans actually value.
However, there is a risk in Wiener’s distinction between what we desire and what actually happens in the end. It may create a false image of ourselves — an image in which our desires and our behaviors are wholly separable from each other. Instead of examining carefully whether our desires are in fact good, we may simply assume they are, and so blame bad behavior on the messy cooperation between ourselves and the “system.”
Q. The risk in Wiener's distinction between what we desire and what actually happens, in the end, is that:
In the last paragraph, the author posits the following in regard to Wiener's distinction "Instead of examining carefully whether our desires are in fact good, we may simply assume they are, and so blame bad behavior on the messy cooperation between ourselves and the “system.” That is, we assume, without proper examination, that our desires are good, and instead choose to blame the system and other factors for the bad consequences. Option C conveys this idea and is the answer.
Options B and D have not been implied in the passage.
Option A is close, but the latter part is extraneous to the discussion.
Read the passage carefully and answer the following questions:
Once upon a time — just a few years ago, actually — it was not uncommon to see headlines about prominent scientists, tech executives, and engineers warning portentously that the revolt of the robots was nigh. The mechanism varied, but the result was always the same: Uncontrollable machine selfimprovement would one day overcome humanity. A dismal fate awaited us.
Today we fear a different technological threat, one that centers not on machines but other humans. We see ourselves as imperilled by the terrifying social influence unleashed by the Internet in general and social media in particular. We hear warnings that nothing less than our collective ability to perceive reality is at stake, and that if we do not take corrective action we will lose our freedoms and way of life.
Primal terror of mechanical menace has given way to fear of angry primates posting. Ironically, the roles have reversed. The robots are now humanity’s saviors, suppressing bad human mass behavior online with increasingly sophisticated filtering algorithms. We once obsessed about how to restrain machines we could not predict or control — now we worry about how to use machines to restrain humans we cannot predict or control. But the old problem hasn’t gone away: How do we know whether the machines will do as we wish?
The shift away from the fear of unpredictable robots and toward the fear of chaotic human behavior may have been inevitable. For the problem of controlling the machines was always at heart a problem of human desire — the worry that realizing our desires using automated systems might prove catastrophic. The promised solution was to rectify human desire. But once we lost optimism about whether this was possible, the stage was set for the problem to be flipped on its head.
The twentiethcentury cyberneticist Norbert Wiener made what was for his time a rather startling argument: "The machine may be the final instrument of doom, but humanity may be the ultimate cause." In his 1960 essay “Some Moral and Technical Consequences of Automation,” Wiener recounts tales in which a person makes a wish and gets what was requested but not necessarily what he or she really desired. Hence, it's imperative that we be absolutely sure of what desire we put into the machine. Wiener was of course not talking about social media, but we can easily see the analogy: It too achieves purposes, like mob frenzy or erroneous post deletions, that its human designers did not actually desire, even though they built the machines in a way that achieves those purposes. Nor does he envision, as in Terminator, a general intelligence that becomes selfaware and nukes everyone. Rather, he imagined a system that humans cannot easily stop and that acts on a misleading substitute for the military objectives humans actually value.
However, there is a risk in Wiener’s distinction between what we desire and what actually happens in the end. It may create a false image of ourselves — an image in which our desires and our behaviors are wholly separable from each other. Instead of examining carefully whether our desires are in fact good, we may simply assume they are, and so blame bad behavior on the messy cooperation between ourselves and the “system.”
Q. Why does the author term Norbert Weiner's argument as 'startling'?
"The twentiethcentury cyberneticist Norbert Wiener made what was for his time a rather startling argument"
From the above line, we can infer that the author considers Wiener's argument to be unsettling because it was contentious for his time. Hence it was both anachronous and unsettling, considering the established norms of that time. Only Option C captures this point completely.
It has not been mentioned that his argument was responsible for turning the problem on its head. Option A is incorrect.
Though a part of the argument, it does not capture the points mentioned above completely. Hence Option B is also incorrect.
Option D is a distortion. The argument was unsettling for Wiener's time and not contemporary times. Hence, Option D is also incorrect.
Read the passage carefully and answer the following questions:
Once upon a time — just a few years ago, actually — it was not uncommon to see headlines about prominent scientists, tech executives, and engineers warning portentously that the revolt of the robots was nigh. The mechanism varied, but the result was always the same: Uncontrollable machine selfimprovement would one day overcome humanity. A dismal fate awaited us.
Today we fear a different technological threat, one that centers not on machines but other humans. We see ourselves as imperilled by the terrifying social influence unleashed by the Internet in general and social media in particular. We hear warnings that nothing less than our collective ability to perceive reality is at stake, and that if we do not take corrective action we will lose our freedoms and way of life.
Primal terror of mechanical menace has given way to fear of angry primates posting. Ironically, the roles have reversed. The robots are now humanity’s saviors, suppressing bad human mass behavior online with increasingly sophisticated filtering algorithms. We once obsessed about how to restrain machines we could not predict or control — now we worry about how to use machines to restrain humans we cannot predict or control. But the old problem hasn’t gone away: How do we know whether the machines will do as we wish?
The shift away from the fear of unpredictable robots and toward the fear of chaotic human behavior may have been inevitable. For the problem of controlling the machines was always at heart a problem of human desire — the worry that realizing our desires using automated systems might prove catastrophic. The promised solution was to rectify human desire. But once we lost optimism about whether this was possible, the stage was set for the problem to be flipped on its head.
The twentiethcentury cyberneticist Norbert Wiener made what was for his time a rather startling argument: "The machine may be the final instrument of doom, but humanity may be the ultimate cause." In his 1960 essay “Some Moral and Technical Consequences of Automation,” Wiener recounts tales in which a person makes a wish and gets what was requested but not necessarily what he or she really desired. Hence, it's imperative that we be absolutely sure of what desire we put into the machine. Wiener was of course not talking about social media, but we can easily see the analogy: It too achieves purposes, like mob frenzy or erroneous post deletions, that its human designers did not actually desire, even though they built the machines in a way that achieves those purposes. Nor does he envision, as in Terminator, a general intelligence that becomes selfaware and nukes everyone. Rather, he imagined a system that humans cannot easily stop and that acts on a misleading substitute for the military objectives humans actually value.
However, there is a risk in Wiener’s distinction between what we desire and what actually happens in the end. It may create a false image of ourselves — an image in which our desires and our behaviors are wholly separable from each other. Instead of examining carefully whether our desires are in fact good, we may simply assume they are, and so blame bad behavior on the messy cooperation between ourselves and the “system.”
Q. Which of the following could be an example of Weiner's desireoutcome disparity argument?
I. A weapons system, which cannot be stopped easily, starts bombing after receiving an erroneous command.
II. An AI program developed to mitigate global warming starts eliminating a fraction of the human population to complete its objective.
III. A Social media platform allows groups of militants to communicate their plans and coordinate their attacks.
Weiner's desireoutcome disparity is about advanced systems which achieve undesired outcomes because of their inherent nature and them acting on misleading substitutes of the objectives fed.
Since the command itself was erroneous, hence the system acted on incorrect information instead of acting on a misleading substitute of the objective. Hence I does not fit the argument.
The AI program was designed to mitigate global warming. But eliminating humans to achieve the same is an undesired outcome, which arises due to the program acting on the misleading substitute of the objective assigned. The substitute being 'achieving the goal without a care for the humans', which the scientists would not have desired. Hence II fits the argument.
Though the author mentions that Weiner did not talk about social media, he also mentions that an analogy can be drawn between the two, hence the argument can be extended to include the misuse of social media, as mentioned in Statement III.
Hence Statements II and III fit Weiner's argument.
Read the passage carefully and answer the following questions:
Iceland, Norway, Finland and Sweden are, according to the World Economic Forum, the most genderequal countries in the world, while Denmark is in 14th place. Iceland has been named the most genderequal in the world for 11 years running. Strong economic and work participation, together with political empowerment, has led many to see the Nordic countries as a “gender equality utopia”. However, behind women participation statistics and progressive policies, gender stereotypes prevail, particularly in the workplace, and women in the region say that there is still a lot of work to be done.
A recent report by intergovernmental forum the Nordic Council of Ministers found that, whereas Nordic governments’ policies have contributed to reducing the income disparities between men and women, financial gender equality is far from a reality yet. Occupational segregation still exists across the region’s industries and sectors and “social norms continue to restrict occupational choices”, the study points out. This gender segregation is more pronounced in Stem industries, which in turn is linked to a segregation in education on these subjects
Gabriele Griffin, professor of gender research at the University of Uppsala, says that closer examination of the statistics about gender equality in Nordic countries shows that most of the people who believe it has already been achieved are men, whereas women are more sceptical. Griffin says that there is still a rooted stereotype of technology being a male field and humanities and medicine being female. Progressive legislation and policy have not prevented the continuation of gender stereotypes.
The modern concept of gender equality has its foundations in the postwar welfare state. In Sweden, it was motivated by the need for more women in the workforce after the Second World War, explains Jenny Björklund, associate professor of gender studies at the University of Uppsala. During the 1960s and 1970s, the feminist movement demanded that the social democratic government introduce childcare to allow women to have fulltime jobs. Men were also encouraged to take care of the family. “There’s this dualearner/dualcarer ideal that Swedish gender equality is based on,” says Björklund.
Policies in Sweden have since then focused on facilitating that workfamily balance. However, the expectations on women to be fulltime workers, selfsacrificing mothers and still have leisure time have put unrealistic pressure on this ideal. Expectations on men are not as high, and Björklund says that fathers can get away with being less caring than mothers  an idea underpinned by traditional stereotypes and middleclass values.
Furthermore, the ideal of gender equality has been made a key element of a white and middleclass “Swedishness”  a national trait hijacked by farright political parties promoting antiimmigration policies, says Björklund. These parties stereotype the immigrant woman as “less genderequal” and repressed, and present immigrant men as patriarchal and aggressive, diverting attention away from the issues still at stake. Professor Griffin adds that this rising conservatism in Sweden has led to a liberalisation of discourses that are in many ways discriminatory, where it becomes acceptable to say that gender equality has gone too far.
Q. Which of the following statements CANNOT be inferred from the passage concerning the Nordic regions?
I. Progressive policies have not addressed the presence of gender stereotypes in the workplace.
II. Competition among women has exacerbated the income gap between men and women.
III. Occupational gender segregation has led to segregation in education on major subjects.
IV. Social norms discourage women from taking up certain occupations.
In the last line of the third paragraph, the author notes that " Progressive legislation and policy have not prevented the continuation of gender stereotypes." Hence, though they have failed in arresting the continuation of gender stereotypes, they have tried to address them. Statement I is wrong.
Statement II has not been implied anywhere in the passage.
Statement III is a vague statement and attempts to generalise a singular observation. In the second paragraph, the author links occupation segregation in STEM industries with segregation in education on these subjects. This cannot be generalised. Furthermore, we cannot say if occupational segregation causes educational segregation or the other way around. Hence, II is not inferrable.
According to the intergovernmental study, “social norms continue to restrict occupational choices”. Statement IV can be inferred.
Statements I, II and III cannot be inferred. Option B is the answer.
Read the passage carefully and answer the following questions:
Iceland, Norway, Finland and Sweden are, according to the World Economic Forum, the most genderequal countries in the world, while Denmark is in 14th place. Iceland has been named the most genderequal in the world for 11 years running. Strong economic and work participation, together with political empowerment, has led many to see the Nordic countries as a “gender equality utopia”. However, behind women participation statistics and progressive policies, gender stereotypes prevail, particularly in the workplace, and women in the region say that there is still a lot of work to be done.
A recent report by intergovernmental forum the Nordic Council of Ministers found that, whereas Nordic governments’ policies have contributed to reducing the income disparities between men and women, financial gender equality is far from a reality yet. Occupational segregation still exists across the region’s industries and sectors and “social norms continue to restrict occupational choices”, the study points out. This gender segregation is more pronounced in Stem industries, which in turn is linked to a segregation in education on these subjects
Gabriele Griffin, professor of gender research at the University of Uppsala, says that closer examination of the statistics about gender equality in Nordic countries shows that most of the people who believe it has already been achieved are men, whereas women are more sceptical. Griffin says that there is still a rooted stereotype of technology being a male field and humanities and medicine being female. Progressive legislation and policy have not prevented the continuation of gender stereotypes.
The modern concept of gender equality has its foundations in the postwar welfare state. In Sweden, it was motivated by the need for more women in the workforce after the Second World War, explains Jenny Björklund, associate professor of gender studies at the University of Uppsala. During the 1960s and 1970s, the feminist movement demanded that the social democratic government introduce childcare to allow women to have fulltime jobs. Men were also encouraged to take care of the family. “There’s this dualearner/dualcarer ideal that Swedish gender equality is based on,” says Björklund.
Policies in Sweden have since then focused on facilitating that workfamily balance. However, the expectations on women to be fulltime workers, selfsacrificing mothers and still have leisure time have put unrealistic pressure on this ideal. Expectations on men are not as high, and Björklund says that fathers can get away with being less caring than mothers  an idea underpinned by traditional stereotypes and middleclass values.
Furthermore, the ideal of gender equality has been made a key element of a white and middleclass “Swedishness”  a national trait hijacked by farright political parties promoting antiimmigration policies, says Björklund. These parties stereotype the immigrant woman as “less genderequal” and repressed, and present immigrant men as patriarchal and aggressive, diverting attention away from the issues still at stake. Professor Griffin adds that this rising conservatism in Sweden has led to a liberalisation of discourses that are in many ways discriminatory, where it becomes acceptable to say that gender equality has gone too far.
Q. All of the following have been discussed about gender equality in Sweden, EXCEPT:
"However, behind women participation statistics and progressive policies, gender stereotypes prevail, particularly in the workplace, and women in the region say that there is still a lot of work to be done."
Though referred to as one of the most genderequal countries, the above lines show that Sweden is still far from being genderequal. Hence Option A can be inferred.
In the fourth and fifth paragraphs, the author states the following regarding the gender equality situation in Sweden "Men were also encouraged to take care of the family. “There’s this dualearner/dualcarer ideal that Swedish gender equality is based on,” says Björklund. Policies in Sweden have since then focused on facilitating that workfamily balance."
Option B can be clearly inferred from these lines.
"The modern concept of gender equality has its foundations in the postwar welfare state. In Sweden, it was motivated by the need for more women in the workforce after the Second World War". Option C has been discussed as well.
Option D is a distortion. In the last paragraph, the author says that the national trait of "Swedishness" has been hijacked by farright parties. However, we cannot say if Swedishness was introduced by them or that it was introduced to push antiimmigrant policies. As this has not been discussed, we can say that it is the right answer.
Read the passage carefully and answer the following questions:
Iceland, Norway, Finland and Sweden are, according to the World Economic Forum, the most genderequal countries in the world, while Denmark is in 14th place. Iceland has been named the most genderequal in the world for 11 years running. Strong economic and work participation, together with political empowerment, has led many to see the Nordic countries as a “gender equality utopia”. However, behind women participation statistics and progressive policies, gender stereotypes prevail, particularly in the workplace, and women in the region say that there is still a lot of work to be done.
A recent report by intergovernmental forum the Nordic Council of Ministers found that, whereas Nordic governments’ policies have contributed to reducing the income disparities between men and women, financial gender equality is far from a reality yet. Occupational segregation still exists across the region’s industries and sectors and “social norms continue to restrict occupational choices”, the study points out. This gender segregation is more pronounced in Stem industries, which in turn is linked to a segregation in education on these subjects
Gabriele Griffin, professor of gender research at the University of Uppsala, says that closer examination of the statistics about gender equality in Nordic countries shows that most of the people who believe it has already been achieved are men, whereas women are more sceptical. Griffin says that there is still a rooted stereotype of technology being a male field and humanities and medicine being female. Progressive legislation and policy have not prevented the continuation of gender stereotypes.
The modern concept of gender equality has its foundations in the postwar welfare state. In Sweden, it was motivated by the need for more women in the workforce after the Second World War, explains Jenny Björklund, associate professor of gender studies at the University of Uppsala. During the 1960s and 1970s, the feminist movement demanded that the social democratic government introduce childcare to allow women to have fulltime jobs. Men were also encouraged to take care of the family. “There’s this dualearner/dualcarer ideal that Swedish gender equality is based on,” says Björklund.
Policies in Sweden have since then focused on facilitating that workfamily balance. However, the expectations on women to be fulltime workers, selfsacrificing mothers and still have leisure time have put unrealistic pressure on this ideal. Expectations on men are not as high, and Björklund says that fathers can get away with being less caring than mothers  an idea underpinned by traditional stereotypes and middleclass values.
Furthermore, the ideal of gender equality has been made a key element of a white and middleclass “Swedishness”  a national trait hijacked by farright political parties promoting antiimmigration policies, says Björklund. These parties stereotype the immigrant woman as “less genderequal” and repressed, and present immigrant men as patriarchal and aggressive, diverting attention away from the issues still at stake. Professor Griffin adds that this rising conservatism in Sweden has led to a liberalisation of discourses that are in many ways discriminatory, where it becomes acceptable to say that gender equality has gone too far.
Q. The central idea in the fifth paragraph is that
{"...However, the expectations on women to be fulltime workers, selfsacrificing mothers and still have leisure time have put unrealistic pressure on this ideal. Expectations on men are not as high, and Björklund says that fathers can get away with being less caring than mothers  an idea underpinned by traditional stereotypes and middleclass values..."} In the fifth paragraph, the author talks about how the existing stereotypes lead to a disparity in the expectations from men and women to maintain a worklife balance. The difference in expectation is then highlighted. The author mentions how, in reality, gender stereotypes lead people to expect a lot more from women regarding caregiving responsibilities. Option C conveys the idea correctly.
Option A asserts that men are expected to fare better in the earner role, which has not been implied in the passage.
Option B states that traditional stereotypes allow men to ignore their caregiving duties. The passage states that men can get away with doing much lesser than women  and not completely ignoring their responsibilities. Moreover, the impact on women due to the imbalanced expectations is missed out in this option. Hence, we can eliminate Option B.
Option D can be safely eliminated. The author does not discuss the need for a new Swedish dualearner/dualgiver ideal but talks about the threat to the same.
Hence, Option C is the correct answer.
Read the passage carefully and answer the following questions:
Iceland, Norway, Finland and Sweden are, according to the World Economic Forum, the most genderequal countries in the world, while Denmark is in 14th place. Iceland has been named the most genderequal in the world for 11 years running. Strong economic and work participation, together with political empowerment, has led many to see the Nordic countries as a “gender equality utopia”. However, behind women participation statistics and progressive policies, gender stereotypes prevail, particularly in the workplace, and women in the region say that there is still a lot of work to be done.
A recent report by intergovernmental forum the Nordic Council of Ministers found that, whereas Nordic governments’ policies have contributed to reducing the income disparities between men and women, financial gender equality is far from a reality yet. Occupational segregation still exists across the region’s industries and sectors and “social norms continue to restrict occupational choices”, the study points out. This gender segregation is more pronounced in Stem industries, which in turn is linked to a segregation in education on these subjects
Gabriele Griffin, professor of gender research at the University of Uppsala, says that closer examination of the statistics about gender equality in Nordic countries shows that most of the people who believe it has already been achieved are men, whereas women are more sceptical. Griffin says that there is still a rooted stereotype of technology being a male field and humanities and medicine being female. Progressive legislation and policy have not prevented the continuation of gender stereotypes.
The modern concept of gender equality has its foundations in the postwar welfare state. In Sweden, it was motivated by the need for more women in the workforce after the Second World War, explains Jenny Björklund, associate professor of gender studies at the University of Uppsala. During the 1960s and 1970s, the feminist movement demanded that the social democratic government introduce childcare to allow women to have fulltime jobs. Men were also encouraged to take care of the family. “There’s this dualearner/dualcarer ideal that Swedish gender equality is based on,” says Björklund.
Policies in Sweden have since then focused on facilitating that workfamily balance. However, the expectations on women to be fulltime workers, selfsacrificing mothers and still have leisure time have put unrealistic pressure on this ideal. Expectations on men are not as high, and Björklund says that fathers can get away with being less caring than mothers  an idea underpinned by traditional stereotypes and middleclass values.
Furthermore, the ideal of gender equality has been made a key element of a white and middleclass “Swedishness”  a national trait hijacked by farright political parties promoting antiimmigration policies, says Björklund. These parties stereotype the immigrant woman as “less genderequal” and repressed, and present immigrant men as patriarchal and aggressive, diverting attention away from the issues still at stake. Professor Griffin adds that this rising conservatism in Sweden has led to a liberalisation of discourses that are in many ways discriminatory, where it becomes acceptable to say that gender equality has gone too far.
Q. Which of the following is likely to be the next course of discussion?
The author concludes the passage on a foreboding note, highlighting how certain discussions now assume gender equality has gone too far. In the same paragraph, the author discusses how the disparity among different women groups, especially white, middleclass and immigrant women has been used as a tool against immigration. Hence, any discussion about how gender equality has not gone too far and how it is needed for all women would be the right way to continue the line of thought. Option C gives a rebuttal of sorts to the xenophobic idea presented in the last paragraph. Hence, C is the aptest answer.
The author does not explicitly discuss diversity in workplaces. It does not connect with any previous discussion. Hence, option A can be eliminated.
Option B is narrow. The author does not discuss anything related to intersectional groups in the passage and is focused on the larger group of women.
Option D is extreme and has not been implied in the passage. Moreover, the focus would shift from gender equality to minorities which is inconsistent with the passage.
Read the passage carefully and answer the following questions:
Five years ago we launched the Simons Foundation Powering Autism Research for Knowledge (SPARK) to harness the power of big data by engaging hundreds of thousands of individuals with autism and their family members to participate in research. The more people who participate, the deeper and richer these data sets become, catalyzing research that is expanding our knowledge of both biology and behavior to develop more precise approaches to medical and behavioural issues.
Genetic research has taught us that what we commonly call autism is actually a spectrum of hundreds of conditions that vary widely among adults and children. Across this spectrum, individuals share core symptoms and challenges with social interaction, restricted interests and/or repetitive behaviours.
We now know that genes play a central role in the causes of these “autisms,” which are the result of genetic changes in combination with other causes including prenatal factors. Essentially, we will take a page from the playbook that oncologists use to treat certain types of cancerbased upon their genetic signatures and apply targeted therapeutic strategies to help people with autism.
But in order to get answers faster and be certain of these results, SPARK and our research partners need a huge sample size: “bigger data.” To ensure an accurate inventory of all the major genetic contributors, and learn if and how different genetic variants contribute to autistic behaviours, we need not only the largest but also the most diverse group of participants.
The genetic, medical and behavioural data SPARK collects from people with autism and their families is rich in detail and can be leveraged by many different investigators. Access to rich data sets draws talented scientists to the field of autism science to develop new methods of finding patterns in the data, better predicting associated behavioural and medical issues, and, perhaps, identifying more effective supports and treatments.
Genetic research is already providing answers and insights about prognosis. For example, one SPARK family’s genetic result is strongly associated with a lack of spoken language but an ability to understand language. Armed with this information, the medical team provided the child with an assistive communication device that decreased tantrums that arose from the child’s frustration at being unable to express himself.
SPARK has identified genetic causes of autism that can be treated. Through whole exome sequencing, SPARK identified a case of phenylketonuria (PKU) that was missed during newborn screening. This inherited disorder causes a buildup of amino acid in the blood, which can cause behaviour and movement problems, seizures and developmental disabilities. With this knowledge, the family started their child on treatment with a specialized diet including low levels of phenylalanine.
We know that big data, with each person representing their unique profile of someone impacted by autism, will lead to many of the answers we seek. Better genetic insights, gleaned through a complex analysis of rich data, will help provide the means to support individuals—children and adults across the spectrum—through early intervention, assistive communication, tailored education and, someday, geneticallybased treatments. We strive to enable every person with autism to be the best possible version of themselves.
Q. The purpose of the last three paragraphs is to:
The last three paragraphs talk about how genetic research aided by SPARK has helped in the treatment and mitigation of various kinds of autism. The author further says that the addition of rich data to this will help provide better analysis and support. So the author tries to show the benefits of SPARK and how the addition of rich data will help provide better support. Option C captures the points correctly.
Option A contains a distortion in the second half. The passage does not imply that Spark can reach its true potential only through greater participation. Hence, A can be eliminated.
The author does not talk about various developments but the achievements due to a particular method. Additionally, the need for more academic participation has not been emphasised. Hence Option B is a distortion.
The author does not focus on the plight of children suffering from autism. Instead, he highlights how SPARK helps these children and how promoting participation in genetic research could render valuable data. Hence Option D is incorrect.
Read the passage carefully and answer the following questions:
Five years ago we launched the Simons Foundation Powering Autism Research for Knowledge (SPARK) to harness the power of big data by engaging hundreds of thousands of individuals with autism and their family members to participate in research. The more people who participate, the deeper and richer these data sets become, catalyzing research that is expanding our knowledge of both biology and behavior to develop more precise approaches to medical and behavioural issues.
Genetic research has taught us that what we commonly call autism is actually a spectrum of hundreds of conditions that vary widely among adults and children. Across this spectrum, individuals share core symptoms and challenges with social interaction, restricted interests and/or repetitive behaviours.
We now know that genes play a central role in the causes of these “autisms,” which are the result of genetic changes in combination with other causes including prenatal factors. Essentially, we will take a page from the playbook that oncologists use to treat certain types of cancerbased upon their genetic signatures and apply targeted therapeutic strategies to help people with autism.
But in order to get answers faster and be certain of these results, SPARK and our research partners need a huge sample size: “bigger data.” To ensure an accurate inventory of all the major genetic contributors, and learn if and how different genetic variants contribute to autistic behaviours, we need not only the largest but also the most diverse group of participants.
The genetic, medical and behavioural data SPARK collects from people with autism and their families is rich in detail and can be leveraged by many different investigators. Access to rich data sets draws talented scientists to the field of autism science to develop new methods of finding patterns in the data, better predicting associated behavioural and medical issues, and, perhaps, identifying more effective supports and treatments.
Genetic research is already providing answers and insights about prognosis. For example, one SPARK family’s genetic result is strongly associated with a lack of spoken language but an ability to understand language. Armed with this information, the medical team provided the child with an assistive communication device that decreased tantrums that arose from the child’s frustration at being unable to express himself.
SPARK has identified genetic causes of autism that can be treated. Through whole exome sequencing, SPARK identified a case of phenylketonuria (PKU) that was missed during newborn screening. This inherited disorder causes a buildup of amino acid in the blood, which can cause behaviour and movement problems, seizures and developmental disabilities. With this knowledge, the family started their child on treatment with a specialized diet including low levels of phenylalanine.
We know that big data, with each person representing their unique profile of someone impacted by autism, will lead to many of the answers we seek. Better genetic insights, gleaned through a complex analysis of rich data, will help provide the means to support individuals—children and adults across the spectrum—through early intervention, assistive communication, tailored education and, someday, geneticallybased treatments. We strive to enable every person with autism to be the best possible version of themselves.
Q. Which of the following is the author most likely to agree with?
{"Essentially, we will take a page from the playbook that oncologists use to treat certain types of cancerbased upon their genetic signatures and apply targeted therapeutic strategies to help people with autism."} The above line means that just like oncologists treat different types of cancers based on their genetic signatures differently, we need to use targeted treatment strategies to treat people with autism. But option A says that we need oncologists to treat autism, which distorts the author's message. Hence A is incorrect.
{"... learn if and how different genetic variants contribute to autistic behaviours, we need not only the largest but also the most diverse group of participants." }The author says that to learn about the contribution of genetic variants to autistic behaviours, we would need a large and diverse data set. Hence, we can clearly infer option B.
It is not mentioned in the passage that the treatment strategies used to treat cancer can be extended to autism. Option C is incorrect.
{"We now know that genes play a central role in the causes of these “autisms,” which are the result ..." } Option D is incorrect because it is quite the opposite of what has been mentioned in the line above. Moreover, the author says 'missed' during newborn screening, means something that was there but was not detected because of an error.
Hence, the author would most likely agree with option B.
Read the passage carefully and answer the following questions:
Five years ago we launched the Simons Foundation Powering Autism Research for Knowledge (SPARK) to harness the power of big data by engaging hundreds of thousands of individuals with autism and their family members to participate in research. The more people who participate, the deeper and richer these data sets become, catalyzing research that is expanding our knowledge of both biology and behavior to develop more precise approaches to medical and behavioural issues.
Genetic research has taught us that what we commonly call autism is actually a spectrum of hundreds of conditions that vary widely among adults and children. Across this spectrum, individuals share core symptoms and challenges with social interaction, restricted interests and/or repetitive behaviours.
We now know that genes play a central role in the causes of these “autisms,” which are the result of genetic changes in combination with other causes including prenatal factors. Essentially, we will take a page from the playbook that oncologists use to treat certain types of cancerbased upon their genetic signatures and apply targeted therapeutic strategies to help people with autism.
But in order to get answers faster and be certain of these results, SPARK and our research partners need a huge sample size: “bigger data.” To ensure an accurate inventory of all the major genetic contributors, and learn if and how different genetic variants contribute to autistic behaviours, we need not only the largest but also the most diverse group of participants.
The genetic, medical and behavioural data SPARK collects from people with autism and their families is rich in detail and can be leveraged by many different investigators. Access to rich data sets draws talented scientists to the field of autism science to develop new methods of finding patterns in the data, better predicting associated behavioural and medical issues, and, perhaps, identifying more effective supports and treatments.
Genetic research is already providing answers and insights about prognosis. For example, one SPARK family’s genetic result is strongly associated with a lack of spoken language but an ability to understand language. Armed with this information, the medical team provided the child with an assistive communication device that decreased tantrums that arose from the child’s frustration at being unable to express himself.
SPARK has identified genetic causes of autism that can be treated. Through whole exome sequencing, SPARK identified a case of phenylketonuria (PKU) that was missed during newborn screening. This inherited disorder causes a buildup of amino acid in the blood, which can cause behaviour and movement problems, seizures and developmental disabilities. With this knowledge, the family started their child on treatment with a specialized diet including low levels of phenylalanine.
We know that big data, with each person representing their unique profile of someone impacted by autism, will lead to many of the answers we seek. Better genetic insights, gleaned through a complex analysis of rich data, will help provide the means to support individuals—children and adults across the spectrum—through early intervention, assistive communication, tailored education and, someday, geneticallybased treatments. We strive to enable every person with autism to be the best possible version of themselves.
Q. Which of the following cannot be inferred?
I. The effectiveness of 'big data' is determined not by its size but by its diversity.
II. Genes are a major factor influencing autism.
III. Consumption of a diet containing low levels of phenylalanine helps decrease the level of amino acid in the blood.
"..we need not only the largest but also the most diverse group of participants."
From this line, we can infer that along with a large dataset, we also need diversity to make big data effective. But is has not been mentioned that the size of the data is not important. Hence Statement I is a distortion and cannot be inferred.
"We now know that genes play a central role in the causes of these autisms,...”
From this line, we can infer that the role of genes in causing autism is prominent. Hence Statement II can be inferred.
In paragraph 7, it is implied that a diet containing low levels of phenylalanine was given to stabilize the level of amino acid in the blood. It has not been implied that the level of amino acid is decreased because of it. Hence Statement III cannot be inferred.
Read the passage carefully and answer the following questions:
Five years ago we launched the Simons Foundation Powering Autism Research for Knowledge (SPARK) to harness the power of big data by engaging hundreds of thousands of individuals with autism and their family members to participate in research. The more people who participate, the deeper and richer these data sets become, catalyzing research that is expanding our knowledge of both biology and behavior to develop more precise approaches to medical and behavioural issues.
Genetic research has taught us that what we commonly call autism is actually a spectrum of hundreds of conditions that vary widely among adults and children. Across this spectrum, individuals share core symptoms and challenges with social interaction, restricted interests and/or repetitive behaviours.
We now know that genes play a central role in the causes of these “autisms,” which are the result of genetic changes in combination with other causes including prenatal factors. Essentially, we will take a page from the playbook that oncologists use to treat certain types of cancerbased upon their genetic signatures and apply targeted therapeutic strategies to help people with autism.
But in order to get answers faster and be certain of these results, SPARK and our research partners need a huge sample size: “bigger data.” To ensure an accurate inventory of all the major genetic contributors, and learn if and how different genetic variants contribute to autistic behaviours, we need not only the largest but also the most diverse group of participants.
The genetic, medical and behavioural data SPARK collects from people with autism and their families is rich in detail and can be leveraged by many different investigators. Access to rich data sets draws talented scientists to the field of autism science to develop new methods of finding patterns in the data, better predicting associated behavioural and medical issues, and, perhaps, identifying more effective supports and treatments.
Genetic research is already providing answers and insights about prognosis. For example, one SPARK family’s genetic result is strongly associated with a lack of spoken language but an ability to understand language. Armed with this information, the medical team provided the child with an assistive communication device that decreased tantrums that arose from the child’s frustration at being unable to express himself.
SPARK has identified genetic causes of autism that can be treated. Through whole exome sequencing, SPARK identified a case of phenylketonuria (PKU) that was missed during newborn screening. This inherited disorder causes a buildup of amino acid in the blood, which can cause behaviour and movement problems, seizures and developmental disabilities. With this knowledge, the family started their child on treatment with a specialized diet including low levels of phenylalanine.
We know that big data, with each person representing their unique profile of someone impacted by autism, will lead to many of the answers we seek. Better genetic insights, gleaned through a complex analysis of rich data, will help provide the means to support individuals—children and adults across the spectrum—through early intervention, assistive communication, tailored education and, someday, geneticallybased treatments. We strive to enable every person with autism to be the best possible version of themselves.
Q. All of the following have been discussed in the passage as benefits of having richer and bigger datasets EXCEPT:
Option A: While the first half of A's statement is true, the latter half appears distorted. There is no mention of "untreatable diseases", and 'phenylketonuria' has been presented in a different context. Hence, Option A is the correct choice.
Option B: {The more people who participate, the deeper and richer these data sets become, catalyzing research that is expanding our knowledge of both biology and behaviour to develop more precise approaches to medical and behavioural issues.} Option B has been presented as an advantage of having larger and richer datasets. Hence, we can eliminate Option B.
Option C: {Access to rich data sets draws talented scientists to the field of autism science to develop new methods of finding patterns in the data, better predicting associated behavioural and medical issues, and, perhaps, identifying more effective supports and treatments.} The author highlights the utility of richer datasets in drawing more talent to the field of autism science. Thus, Option C can be eliminated.
Option D: {To ensure an accurate inventory of all the major genetic contributors, and learn if and how different genetic variants contribute to autistic behaviours, we need not only the largest but also the most diverse group of participants.}. The use of larger datasets in developing an accurate repository has been presented above. Therefore, Option D can be rejected as the potential answer.
Hence, Option A is the correct choice.
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. On the contrary, the industry is happy reducing the wage bills, doing mechanisation and raising its profits.
2. During the pandemic, nearly 31 million families have moved down from the middle class and nearly 100 million people have lost jobs.
3. The industries that are most likely to create employment, i.e. the medium and small industries, are going down under and the large ones which do not create employment are the poster boys.
4. They are the ones that will get the 6 per cent productivitylinked incentive from the tax paid by the average taxpayers, with unknown consequences.
Sentence 2 is the opening sentence since it highlights the damaging effect of the pandemic, especially with regard to the loss of jobs. The author draws a parallel between this group and the industries in general by continuing the idea in 1, which mentions the measures taken by certain industries.
34 is a bloc. 3 describes the industrial scenario at large  how largescale industries are doing well, despite laying off employees and not doing enough to arrest the pandemic's effects. Sentence 4 talks about the tax incentives these largescale industries get, further critiquing the current situation. Hence, 2134 form a coherent paragraph.
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. For others, Trump’s loss makes him into a loser—especially damaging given how much Trump hates losers.
2. In the more immediate future, however, no one will remain as personally angry about it as Trump.
3. Polls show that many Republicans believe the 2020 election was tainted, and the damage that will do to faith in democracy in the long term is dangerous.
4. Some followers who saw him as a man who could challenge the establishment will view his defeat as proof that politics is irredeemable, and will slide into apathy and disengagement.
Statement 3 is independent and has to be the opening sentence; it highlights the damage to the faith in democracy and the deleterious effect this could have. 41 is a bloc, describing why the republican loss in the elections could be damaging in the long term. The author covers how one faction of followers might become apathetic or disengaged from politics. The perception with regard to Trump is further elaborated in 1. Hence, 4 and 1 together extend on the damage that is mentioned in 3. On the other hand, 2 talks about ramifications in the immediate future. Sentence 2 has to precede 4 because 4 has the pronoun 'him'. Hence, the reference to Trump must have been made before sentence 4. Therefore, 3241 is the correct answer.
The passage given below is followed by four summaries. Choose the option that best captures the author’s position.
Taken from Darwin’s theory of evolution, survival of the fittest is often conceptualized as the advantage that accrues with certain traits, allowing an individual to both thrive and survive in their environment by outcompeting for limited resources. Qualities such as strength and speed were beneficial to our ancestors, allowing them to survive in demanding environments, and thus our general admiration for these qualities is now understood through this evolutionary lens. Humans, however, also display a wide range of behavior that seems counterintuitive to the survival of the fittest mentality until you consider that we are an inherently social species, and that keeping our group fit is a wise investment of our time and energy. One of the behaviors that humans display a lot of is “indirect reciprocity”. Distinguished from “direct reciprocity”, in which I help you and you help me, indirect reciprocity confers no immediate benefit to the one doing the helping.
In the passage, the author touches upon the survival of the fittest mentality and certain traits associated with it. But humans, being social species, behave in a way that defies the survival of the fittest mentality at times, as they are also concerned about the survival of their group. The main point of the author here is that humans consider the survival of their group important too, which results in behaviour that seems counterintuitive.
Option A can be eliminated. The passage does not talk about improving individual survival.
The author does not assert that humans prioritize group survival over individual survival. The comparison between the importance of the two has not been done. Hence, option C is wrong.
Option D is out of scope. The comparative performance of groups has not been discussed in the passage.
Option B captures the idea elucidated above. Option B is the answer.
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. Without robust national privacy safeguards, entire databases of citizen information are ready for purchase, whether to predatory loan companies, law enforcement agencies, or even malicious foreign actors.
2. Federal privacy bills that don’t give sufficient attention to data brokerage will therefore fail to tackle an enormous portion of the data surveillance economy.
3. Data brokerage is a threat to democracy.
4. This is why the largest data brokers are lobbying more aggressively in Washington.
5. This will leave civil rights, national security, and publicprivate boundaries vulnerable in the process.
After reading all the sentences, it can be inferred that the passage discusses data brokerage and the threats it poses to the proper functioning of a democracy.
Sentence 3 is independent and is the opening sentence. 12 is a bloc as it discusses the situation in the absence of strong data safeguards. 5 has to follow 2 as it describes the larger consequences the word 'this' is the link. Hence, 3125 form a coherent paragraph.
Sentence 4 does not fit the context as it talks about data brokers lobbying more aggressively. Though it is not an independent sentence, none of the other sentences logically lead to the idea discussed in sentence 4. Hence 4 is the odd one out here.
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. Researchers see signs of this in sperm whales in the Galápagos and the Caribbean, in humpbacks across the South Pacific, in Arctic belugas, and in the Pacific Northwest’s killer whales.
2. Today many scientists believe some whales and dolphins, like humans, have distinct cultures.
3. Whale culture, it seems, is rattling timeworn conceptions of ourselves.
4. The possibility is prompting new thinking about how some marine species evolve.
5. Cultural traditions may help drive genetic shifts, altering what it means to be a whale.
After reading all the sentences, it can be inferred that the passage talks about the existence of distinct cultures among whales and dolphins and how this may have shaped their evolutionary paths.
Sentence 2 introduces the topic and is the opening sentence. 1 follows 2 as it provides further evidence to the scientists' claim. 45 is a bloc. 4 talks about the new findings changing our understanding of how marine species evolve. 5 builds on that thought, highlighting how cultural shifts may have caused genetic shifts.
Sentence 3, on the other hand, asserts that the new findings could alter the way we understand ourselves. None of the other sentences alludes to this line of thought. Hence, 3 is out of context.
Identify the odd word from Cease, Launch, Initiate, Commence
Launch, initiate ad commence all mean to begin or start something while cease means to bring to halt. Hence, it is the odd one out
Given below is a chart showing the average of a batsman, which gets updated after every match that he plays in a tournament. Before the start of the tournament, wherein he played 10 matches, he averaged 58 in 20 innings. He got out in each one of them. The batsman played the tournament with an intent to remain not out in as many innings he can. In this tournament, the highest he could score was 115.
Consider, average of a batsman= Total runs scored in his career/Total time he was out
NOTE: Averages shown in the graph above are in multiples of 0.5
Q. What was the total career runs for the batsman just after the finish of the tournament?
It is clear that a batsman can score a minimum of 0 runs in an innings. When he remains not out, his average remains the same (with 0 runs) and does not decrease. Therefore, if a batsman is not out in an innings, his average after the innings will not drop in any case.
Using this, we can infer that the batsman must have been out in 2nd, 5th and 8th match. In the rest of the matches, he can either be out or not out, both.
It is given that before the start of the tournament, the batsman averaged 58 in 20 innings. So, his total runs= 58 x 20 = 1160
After match 1
CASE 1 He is out. Total times, batsman was out = 20+1= 21.
Total runs after this match= Average after this match x Total number of times he was out= 61.5 × 21= 1291.5, which is not possible (He cannot score runs in decimal).
CASE 2 He was not out in that innings. Total times, the batsman was out = 20
Total runs after this match= Average after this match ×Total number of times he was out=61.5 x 20 = 1230, which is possible. Therefore, Case 2 is true and he scored (12301160)= 70 not out in the first match.
Match 2 As discussed earlier, the batsman cannot remain not out when the average drops. He must have been out in this match.
Total times, the batsman was out = 20+1= 21.
Total runs after this match= Average after this match ×Total number of times he was out= 59×21= 1239.
So, he scored a total of 1239 1230= 9 runs in this match.
Match 3
CASE 1 The batsman was out. Total number of times he was out= 21+1= 22.
Total runs after this match= Average after this match ×Total number of times he was out= 62 x 22 = 1364.
Runs scored if he was out= 1364 1239= 125, which is not possible because his highest score in the tournament was that of 115.
CASE 2 The batsman remained not out. Total number of times he was out= 21.
Total runs after this match= Average after this match ×Total number of times he was out=62 x 21 = 1302.
Runs scored in this match= 1302 1239= 63 not out.
Match 4
CASE 1 The batsman was out. Total number of times he was out= 21+1= 22.
Total runs after this match= Average after this match ×Total number of times he was out= 63.5 ×22= 1397.
Runs scored in this match= 13971302=95.
CASE 2 The batsman remained not out. Total number of times he was out= 21.
Total runs after this match= Average after this match ×Total number of times he was out= 63.5 ×21= 1333.5, which is not possible.
Hence, case 1 is true and he scored 95 in this match before getting out.
Match 5 It is clear that the batsman was out in this match as there is a drop of average after this match. So, total number of times the batsman was out after this match= 22+1= 23.
Total runs after this match= Average after this match ×Total number of times he was out= 62 ×23= 1426.
Runs scored in this match= 14261397=29.
Match 6
CASE 1 The batsman was out. Total number of times he was out= 23+1= 24.
Total runs after this match= Average after this match ×Total number of times he was out= 67 ×24= 1608.
Runs scored in this match= 16081426= 182, which is not possible because his highest score was 115.
CASE 2 The batsman was not out. Total number of times he was out= 23
Total runs after this match= Average after this match ×Total number of times he was out= 67 ×23= 1541.
Runs scored in this match= 15411426= 115, which is possible. So, case 2 is true and he scored 115 not out in this match.
Match 7
CASE 1 The batsman was out. Total number of times he was out= 23+1= 24.
Total runs after this match= Average after this match ×Total number of times he was out= 67.5 ×24= 1620.
Runs scored in this match= 16201541= 79, which is possible.
CASE 2 The batsman was not out. Total number of times he was out= 23
Total runs after this match= Average after this match ×Total number of times he was out= 67.5 ×23= 1552.5, which is not possible as runs cannot be in decimals.
So, in match 7, the batsman scored 79 before getting out.
Match 8 As discussed earlier, he was out in this match as there is a drop in average. Total number of times he was out= 24+1= 25.
Total runs after this match= Average after this match ×Total number of times he was out= 65 ×25= 1625.
Runs scored in this match= 16251620= 5.
Match 9
CASE 1 The batsman was out. Total number of times he was out= 25+1= 26.
Total runs after this match= Average after this match ×Total number of times he was out= 67 ×26= 1742.
Runs scored in this match= 17421625= 117, which is not possible as his highest score is of 115.
CASE 2 The batsman was not out. Total number of times he was out= 25
Total runs after this match= Average after this match ×Total number of times he was out= 67 ×25= 1675.
Runs scored in this match= 16751625= 50.
So, he scored 50 not out in the 9th match of the tournament.
Match 10
CASE 1 The batsman was out. Total number of times he was out= 25+1= 26.
Total runs after this match= Average after this match ×Total number of times he was out= 68.5 ×26= 1781.
Runs scored in this match= 17811675= 106, which is possible as his highest score is 115.
CASE 2 The batsman was not out. Total number of times he was out= 25
Total runs after this match= Average after this match ×Total number of times he was out= 68.5 ×25= 1712.5, which is not possible as the runs cannot be in decimal.
.'. In the last match, the batsman scored a total of 106 runs before getting out.
The final scorecard of the batsman in the tournament will look like:
* Shows that the batsman was not out.
Given below is a chart showing the average of a batsman, which gets updated after every match that he plays in a tournament. Before the start of the tournament, wherein he played 10 matches, he averaged 58 in 20 innings. He got out in each one of them. The batsman played the tournament with an intent to remain not out in as many innings he can. In this tournament, the highest he could score was 115.
Consider, average of a batsman= Total runs scored in his career/Total time he was out
NOTE: Averages shown in the graph above are in multiples of 0.5
Q. How many times was the batsman out in this tournament?
It is clear that a batsman can score a minimum of 0 runs in an innings. When he remains not out, his average remains the same (with 0 runs) and does not decrease. Therefore, if a batsman is not out in an innings, his average after the innings will not drop in any case.
Using this, we can infer that the batsman must have been out in 2nd, 5th and 8th match. In the rest of the matches, he can either be out or not out, both.
It is given that before the start of the tournament, the batsman averaged 58 in 20 innings. So, his total runs= 58 x 20 = 1160
After match 1
CASE 1 He is out. Total times, batsman was out = 20+1= 21.
Total runs after this match= Average after this match x Total number of times he was out= 61.5 × 21= 1291.5, which is not possible (He cannot score runs in decimal).
CASE 2 He was not out in that innings. Total times, the batsman was out = 20
Total runs after this match= Average after this match ×Total number of times he was out=61.5 x 20 = 1230, which is possible. Therefore, Case 2 is true and he scored (12301160)= 70 not out in the first match.
Match 2 As discussed earlier, the batsman cannot remain not out when the average drops. He must have been out in this match.
Total times, the batsman was out = 20+1= 21.
Total runs after this match= Average after this match ×Total number of times he was out= 59×21= 1239.
So, he scored a total of 1239 1230= 9 runs in this match.
Match 3
CASE 1 The batsman was out. Total number of times he was out= 21+1= 22.
Total runs after this match= Average after this match ×Total number of times he was out= 62 x 22 = 1364.
Runs scored if he was out= 1364 1239= 125, which is not possible because his highest score in the tournament was that of 115.
CASE 2 The batsman remained not out. Total number of times he was out= 21.
Total runs after this match= Average after this match ×Total number of times he was out=62 x 21 = 1302.
Runs scored in this match= 1302 1239= 63 not out.
Match 4
CASE 1 The batsman was out. Total number of times he was out= 21+1= 22.
Total runs after this match= Average after this match ×Total number of times he was out= 63.5 ×22= 1397.
Runs scored in this match= 13971302=95.
CASE 2 The batsman remained not out. Total number of times he was out= 21.
Total runs after this match= Average after this match ×Total number of times he was out= 63.5 ×21= 1333.5, which is not possible.
Hence, case 1 is true and he scored 95 in this match before getting out.
Match 5 It is clear that the batsman was out in this match as there is a drop of average after this match. So, total number of times the batsman was out after this match= 22+1= 23.
Total runs after this match= Average after this match ×Total number of times he was out= 62 ×23= 1426.
Runs scored in this match= 14261397=29.
Match 6
CASE 1 The batsman was out. Total number of times he was out= 23+1= 24.
Total runs after this match= Average after this match ×Total number of times he was out= 67 ×24= 1608.
Runs scored in this match= 16081426= 182, which is not possible because his highest score was 115.
CASE 2 The batsman was not out. Total number of times he was out= 23
Total runs after this match= Average after this match ×Total number of times he was out= 67 ×23= 1541.
Runs scored in this match= 15411426= 115, which is possible. So, case 2 is true and he scored 115 not out in this match.
Match 7
CASE 1 The batsman was out. Total number of times he was out= 23+1= 24.
Total runs after this match= Average after this match ×Total number of times he was out= 67.5 ×24= 1620.
Runs scored in this match= 16201541= 79, which is possible.
CASE 2 The batsman was not out. Total number of times he was out= 23
Total runs after this match= Average after this match ×Total number of times he was out= 67.5 ×23= 1552.5, which is not possible as runs cannot be in decimals.
So, in match 7, the batsman scored 79 before getting out.
Match 8 As discussed earlier, he was out in this match as there is a drop in average. Total number of times he was out= 24+1= 25.
Total runs after this match= Average after this match ×Total number of times he was out= 65 ×25= 1625.
Runs scored in this match= 16251620= 5.
Match 9
CASE 1 The batsman was out. Total number of times he was out= 25+1= 26.
Total runs after this match= Average after this match ×Total number of times he was out= 67 ×26= 1742.
Runs scored in this match= 17421625= 117, which is not possible as his highest score is of 115.
CASE 2 The batsman was not out. Total number of times he was out= 25
Total runs after this match= Average after this match ×Total number of times he was out= 67 ×25= 1675.
Runs scored in this match= 16751625= 50.
So, he scored 50 not out in the 9th match of the tournament.
Match 10
CASE 1 The batsman was out. Total number of times he was out= 25+1= 26.
Total runs after this match= Average after this match ×Total number of times he was out= 68.5 ×26= 1781.
Runs scored in this match= 17811675= 106, which is possible as his highest score is 115.
CASE 2 The batsman was not out. Total number of times he was out= 25
Total runs after this match= Average after this match ×Total number of times he was out= 68.5 ×25= 1712.5, which is not possible as the runs cannot be in decimal.
.'. In the last match, the batsman scored a total of 106 runs before getting out.
The final scorecard of the batsman in the tournament will look like:
* Shows that the batsman was not out.
Given below is a chart showing the average of a batsman, which gets updated after every match that he plays in a tournament. Before the start of the tournament, wherein he played 10 matches, he averaged 58 in 20 innings. He got out in each one of them. The batsman played the tournament with an intent to remain not out in as many innings he can. In this tournament, the highest he could score was 115.
Consider, average of a batsman= Total runs scored in his career/Total time he was out
NOTE: Averages shown in the graph above are in multiples of 0.5
Q. What was the highest score of the batsman in the innings where he got out?
It is clear that a batsman can score a minimum of 0 runs in an innings. When he remains not out, his average remains the same (with 0 runs) and does not decrease. Therefore, if a batsman is not out in an innings, his average after the innings will not drop in any case.
Using this, we can infer that the batsman must have been out in 2nd, 5th and 8th match. In the rest of the matches, he can either be out or not out, both.
It is given that before the start of the tournament, the batsman averaged 58 in 20 innings. So, his total runs= 58 x 20 = 1160
After match 1
CASE 1 He is out. Total times, batsman was out = 20+1= 21.
Total runs after this match= Average after this match x Total number of times he was out= 61.5 × 21= 1291.5, which is not possible (He cannot score runs in decimal).
CASE 2 He was not out in that innings. Total times, the batsman was out = 20
Total runs after this match= Average after this match ×Total number of times he was out=61.5 x 20 = 1230, which is possible. Therefore, Case 2 is true and he scored (12301160)= 70 not out in the first match.
Match 2 As discussed earlier, the batsman cannot remain not out when the average drops. He must have been out in this match.
Total times, the batsman was out = 20+1= 21.
Total runs after this match= Average after this match ×Total number of times he was out= 59×21= 1239.
So, he scored a total of 1239 1230= 9 runs in this match.
Match 3
CASE 1 The batsman was out. Total number of times he was out= 21+1= 22.
Total runs after this match= Average after this match ×Total number of times he was out= 62 x 22 = 1364.
Runs scored if he was out= 1364 1239= 125, which is not possible because his highest score in the tournament was that of 115.
CASE 2 The batsman remained not out. Total number of times he was out= 21.
Total runs after this match= Average after this match ×Total number of times he was out=62 x 21 = 1302.
Runs scored in this match= 1302 1239= 63 not out.
Match 4
CASE 1 The batsman was out. Total number of times he was out= 21+1= 22.
Total runs after this match= Average after this match ×Total number of times he was out= 63.5 ×22= 1397.
Runs scored in this match= 13971302=95.
CASE 2 The batsman remained not out. Total number of times he was out= 21.
Total runs after this match= Average after this match ×Total number of times he was out= 63.5 ×21= 1333.5, which is not possible.
Hence, case 1 is true and he scored 95 in this match before getting out.
Match 5 It is clear that the batsman was out in this match as there is a drop of average after this match. So, total number of times the batsman was out after this match= 22+1= 23.
Total runs after this match= Average after this match ×Total number of times he was out= 62 ×23= 1426.
Runs scored in this match= 14261397=29.
Match 6
CASE 1 The batsman was out. Total number of times he was out= 23+1= 24.
Total runs after this match= Average after this match ×Total number of times he was out= 67 ×24= 1608.
Runs scored in this match= 16081426= 182, which is not possible because his highest score was 115.
CASE 2 The batsman was not out. Total number of times he was out= 23
Total runs after this match= Average after this match ×Total number of times he was out= 67 ×23= 1541.
Runs scored in this match= 15411426= 115, which is possible. So, case 2 is true and he scored 115 not out in this match.
Match 7
CASE 1 The batsman was out. Total number of times he was out= 23+1= 24.
Total runs after this match= Average after this match ×Total number of times he was out= 67.5 ×24= 1620.
Runs scored in this match= 16201541= 79, which is possible.
CASE 2 The batsman was not out. Total number of times he was out= 23
Total runs after this match= Average after this match ×Total number of times he was out= 67.5 ×23= 1552.5, which is not possible as runs cannot be in decimals.
So, in match 7, the batsman scored 79 before getting out.
Match 8 As discussed earlier, he was out in this match as there is a drop in average. Total number of times he was out= 24+1= 25.
Total runs after this match= Average after this match ×Total number of times he was out= 65 ×25= 1625.
Runs scored in this match= 16251620= 5.
Match 9
CASE 1 The batsman was out. Total number of times he was out= 25+1= 26.
Total runs after this match= Average after this match ×Total number of times he was out= 67 ×26= 1742.
Runs scored in this match= 17421625= 117, which is not possible as his highest score is of 115.
CASE 2 The batsman was not out. Total number of times he was out= 25
Total runs after this match= Average after this match ×Total number of times he was out= 67 ×25= 1675.
Runs scored in this match= 16751625= 50.
So, he scored 50 not out in the 9th match of the tournament.
Match 10
CASE 1 The batsman was out. Total number of times he was out= 25+1= 26.
Total runs after this match= Average after this match ×Total number of times he was out= 68.5 ×26= 1781.
Runs scored in this match= 17811675= 106, which is possible as his highest score is 115.
CASE 2 The batsman was not out. Total number of times he was out= 25
Total runs after this match= Average after this match ×Total number of times he was out= 68.5 ×25= 1712.5, which is not possible as the runs cannot be in decimal.
.'. In the last match, the batsman scored a total of 106 runs before getting out.
The final scorecard of the batsman in the tournament will look like:
* Shows that the batsman was not out.
Given below is a chart showing the average of a batsman, which gets updated after every match that he plays in a tournament. Before the start of the tournament, wherein he played 10 matches, he averaged 58 in 20 innings. He got out in each one of them. The batsman played the tournament with an intent to remain not out in as many innings he can. In this tournament, the highest he could score was 115.
Consider, average of a batsman= Total runs scored in his career/Total time he was out
NOTE: Averages shown in the graph above are in multiples of 0.5
Q. What was the batsman's total career runs after the finish of the 6th match in the tournament?
It is clear that a batsman can score a minimum of 0 runs in an innings. When he remains not out, his average remains the same (with 0 runs) and does not decrease. Therefore, if a batsman is not out in an innings, his average after the innings will not drop in any case.
Using this, we can infer that the batsman must have been out in 2nd, 5th and 8th match. In the rest of the matches, he can either be out or not out, both.
It is given that before the start of the tournament, the batsman averaged 58 in 20 innings. So, his total runs= 58 x 20 = 1160
After match 1
CASE 1 He is out. Total times, batsman was out = 20+1= 21.
Total runs after this match= Average after this match x Total number of times he was out= 61.5 × 21= 1291.5, which is not possible (He cannot score runs in decimal).
CASE 2 He was not out in that innings. Total times, the batsman was out = 20
Total runs after this match= Average after this match ×Total number of times he was out=61.5 x 20 = 1230, which is possible. Therefore, Case 2 is true and he scored (12301160)= 70 not out in the first match.
Match 2 As discussed earlier, the batsman cannot remain not out when the average drops. He must have been out in this match.
Total times, the batsman was out = 20+1= 21.
Total runs after this match= Average after this match ×Total number of times he was out= 59×21= 1239.
So, he scored a total of 1239 1230= 9 runs in this match.
Match 3
CASE 1 The batsman was out. Total number of times he was out= 21+1= 22.
Total runs after this match= Average after this match ×Total number of times he was out= 62 x 22 = 1364.
Runs scored if he was out= 1364 1239= 125, which is not possible because his highest score in the tournament was that of 115.
CASE 2 The batsman remained not out. Total number of times he was out= 21.
Total runs after this match= Average after this match ×Total number of times he was out=62 x 21 = 1302.
Runs scored in this match= 1302 1239= 63 not out.
Match 4
CASE 1 The batsman was out. Total number of times he was out= 21+1= 22.
Total runs after this match= Average after this match ×Total number of times he was out= 63.5 ×22= 1397.
Runs scored in this match= 13971302=95.
CASE 2 The batsman remained not out. Total number of times he was out= 21.
Total runs after this match= Average after this match ×Total number of times he was out= 63.5 ×21= 1333.5, which is not possible.
Hence, case 1 is true and he scored 95 in this match before getting out.
Match 5 It is clear that the batsman was out in this match as there is a drop of average after this match. So, total number of times the batsman was out after this match= 22+1= 23.
Total runs after this match= Average after this match ×Total number of times he was out= 62 ×23= 1426.
Runs scored in this match= 14261397=29.
Match 6
CASE 1 The batsman was out. Total number of times he was out= 23+1= 24.
Total runs after this match= Average after this match ×Total number of times he was out= 67 ×24= 1608.
Runs scored in this match= 16081426= 182, which is not possible because his highest score was 115.
CASE 2 The batsman was not out. Total number of times he was out= 23
Total runs after this match= Average after this match ×Total number of times he was out= 67 ×23= 1541.
Runs scored in this match= 15411426= 115, which is possible. So, case 2 is true and he scored 115 not out in this match.
Match 7
CASE 1 The batsman was out. Total number of times he was out= 23+1= 24.
Total runs after this match= Average after this match ×Total number of times he was out= 67.5 ×24= 1620.
Runs scored in this match= 16201541= 79, which is possible.
CASE 2 The batsman was not out. Total number of times he was out= 23
Total runs after this match= Average after this match ×Total number of times he was out= 67.5 ×23= 1552.5, which is not possible as runs cannot be in decimals.
So, in match 7, the batsman scored 79 before getting out.
Match 8 As discussed earlier, he was out in this match as there is a drop in average. Total number of times he was out= 24+1= 25.
Total runs after this match= Average after this match ×Total number of times he was out= 65 ×25= 1625.
Runs scored in this match= 16251620= 5.
Match 9
CASE 1 The batsman was out. Total number of times he was out= 25+1= 26.
Total runs after this match= Average after this match ×Total number of times he was out= 67 ×26= 1742.
Runs scored in this match= 17421625= 117, which is not possible as his highest score is of 115.
CASE 2 The batsman was not out. Total number of times he was out= 25
Total runs after this match= Average after this match ×Total number of times he was out= 67 ×25= 1675.
Runs scored in this match= 16751625= 50.
So, he scored 50 not out in the 9th match of the tournament.
Match 10
CASE 1 The batsman was out. Total number of times he was out= 25+1= 26.
Total runs after this match= Average after this match ×Total number of times he was out= 68.5 ×26= 1781.
Runs scored in this match= 17811675= 106, which is possible as his highest score is 115.
CASE 2 The batsman was not out. Total number of times he was out= 25
Total runs after this match= Average after this match ×Total number of times he was out= 68.5 ×25= 1712.5, which is not possible as the runs cannot be in decimal.
.'. In the last match, the batsman scored a total of 106 runs before getting out.
The final scorecard of the batsman in the tournament will look like:
* Shows that the batsman was not out.
Bhalla was a landlord who paid his servants using golden rings in a gold chain. To make a certain payment, he needs to cut the rings such that he can pay his servants any amount they ask. He hires Kattapa to cut the chain intelligently. Bhalla has to pay Kattapa Rs.10 for every cut up to a maximum of 5 cuts, post which he is charged Rs.15 for every additional cut after 5. Note: When chain of length 'n' (n>2) is cut once, you will get 3 pieces of length 1, k, nk1
Q. If the number of rings in a gold chain is 1024, what is the minimum amount in Rs. that Bhalla has to pay to Katappa to ensure that he can pay in any denomination up to 1024?
For a chain based puzzles, we need to understand two things to solve any question.
1. Number of cuts Vs. Number of pieces:
When we cut a ring once, we will have 3 pieces formed The ring where the cut is made, opens up and the group of rings to the left and right of the ring where cut is made detaches itself.
Similarly, when 2 cuts are made on 2 different rings, we will have 5 groups of rings:
The two rings where cuts are not a part of any group, but rest 3 forms a group by detaching itself in the following way:
Therefore, we can say that in general, when 'n' cuts are made, n rings of 1 piece each are formed exactly where the cuts are made. The regions between the cuts (n1) groups of ring detach itself from the chain and finally 2 pieces from each of the two ends form two separate groups. In total, for 'n' cuts, we have a maximum of (n)+(n1)+(2)= 2n+1 groups of chain with n chains of unit rings.
2. Maximum payment of each denomination from a given number of cuts:
When we cut the ring, we must ensure that the rings or group of rings can add up to any natural number. So, when we have 1 cut, which gives us three pieces, we already have a chain with 1 ring. To count 2 rings, we will cut the chain such that one of the part have a group of 2 rings. Doing this will ensure that we have 1, 2 and 3( Adding groups with 1 and 2 rings together) separate rings.
For eg. if we have to make 2 cuts, we will have 5 groups of chain A, B, C, D and E. Since we made two cuts, we will have exactly 2 single rings. So, A=1 and B=1. We can pay up to 2 rings using them both. Therefore, C must be 3. With A, B and C, we can make payments up to (1+1+3) units= 5 units. So, D should be 6 and using A, B, C and D together will ensure payment of up to 11 units. And hence, the last part E should be of 12 rings so as to make every payment from 1 ring to 23 rings. We notice that the number of rings get doubled for every subsequent group when cut intelligently.
Using the above two concepts, we will make n cuts so as to divide 1024 rings efficiently.
Let us assume that we make 7 cuts. We will thus have 2n+1= 15 groups of chains. Here 7 pieces are each of unit ring, which can make payments up to 7 rings together. So, the next group (8th) has to be of length 8 rings. The 9th group will have 16 rings because all the first 8 groups can make payments up to 7+8= 15 rings. The number of rings gets doubled for every subsequent group.
10th group= 32 rings. (Can pay any amount up to 63)
11th group= 64 rings. (Can pay any amount up to 127)
12th group= 128 rings (Can pay any amount up to 255)
13th group= 256 rings (Can pay any amount up to 511)
14th group= 512 rings (Can pay any amount up to 1023)
15th group= 1024 rings. (Can pay any amount up to 2047)
In total, we can pay up to 7+8+16+32+64+128+256+512+1024= 2047 rings, which is more than what we need.
When we make 6 cuts, we will have 2n+1= 13 groups of rings, where 6 groups will have 1 ring each which can pay any amount up to 6 rings.
7th group= 7 rings. (Can pay any amount up to 13)
8th group= 14 rings. (Can pay any amount up to 63)
9th group= 28 rings. (Can pay any amount up to 55)
10th group= 56 rings (Can pay any amount up to 111)
11th group= 112 rings. (Can pay any amount up to 223)
12th group= 224 rings. (Can pay any amount up to 447)
13th group= 448 rings. (Can pay any amount up to 895).
'.' We cannot pay any amount from 896 to 1024, we will have to make more cuts.
.'. 7 cuts is the least possible amount of cuts required to pay any amount from 1 to 1024.
Money needed for 7 cuts= Rs.(10 x 5) + (15 x 2) = Rs. 80
ALTERNATE SOLUTION:
For n cuts, we have a general formula of forming 2^{(n+1)} x (n + 1)  1 rings.
To pay 1024 rings,
We will approximate 1025 to be equal to 2^{10}
When n=6, LHS= 7 and RHS= 8.
When n=7, LHS= 8 and RHS= 4.
.'. 7 cuts are required.
Money needed for 7 cuts= Rs. (10 x 5) + (15 x 2) = Rs. 80
Bhalla was a landlord who paid his servants using golden rings in a gold chain. To make a certain payment, he needs to cut the rings such that he can pay his servants any amount they ask. He hires Kattapa to cut the chain intelligently. Bhalla has to pay Kattapa Rs.10 for every cut up to a maximum of 5 cuts, post which he is charged Rs.15 for every additional cut after 5. Note: When chain of length 'n' (n>2) is cut once, you will get 3 pieces of length 1, k, nk1
Q. If Bhalla made a payment of Rs. 95 towards cutting the chain, at most how many rings can he pay to his servants?
For a chain based puzzles, we need to understand two things to solve any question.
1. Number of cuts Vs. Number of pieces:
When we cut a ring once, we will have 3 pieces formed The ring where the cut is made, opens up and the group of rings to the left and right of the ring where cut is made detaches itself.
Similarly, when 2 cuts are made on 2 different rings, we will have 5 groups of rings:
The two rings where cuts are not a part of any group, but rest 3 forms a group by detaching itself in the following way:
Therefore, we can say that in general, when 'n' cuts are made, n rings of 1 piece each are formed exactly where the cuts are made. The regions between the cuts (n1) groups of ring detach itself from the chain and finally 2 pieces from each of the two ends form two separate groups. In total, for 'n' cuts, we have a maximum of (n)+(n1)+(2)= 2n+1 groups of chain with n chains of unit rings.
2. Maximum payment of each denomination from a given number of cuts:
When we cut the ring, we must ensure that the rings or group of rings can add up to any natural number. So, when we have 1 cut, which gives us three pieces, we already have a chain with 1 ring. To count 2 rings, we will cut the chain such that one of the part have a group of 2 rings. Doing this will ensure that we have 1, 2 and 3( Adding groups with 1 and 2 rings together) separate rings.
For eg. if we have to make 2 cuts, we will have 5 groups of chain A, B, C, D and E. Since we made two cuts, we will have exactly 2 single rings. So, A=1 and B=1. We can pay up to 2 rings using them both. Therefore, C must be 3. With A, B and C, we can make payments up to (1+1+3) units= 5 units. So, D should be 6 and using A, B, C and D together will ensure payment of up to 11 units. And hence, the last part E should be of 12 rings so as to make every payment from 1 ring to 23 rings. We notice that the number of rings get doubled for every subsequent group when cut intelligently.
Let the number of cuts made be x.
Excess cuts= x5.
Total amount paid for cutting= 10(5)+ 15(x5)= 50+15x75= 15x25
Given, 15x25= 95
=> 15x= 120. .'. x= 8.
So, for 8 cuts, we will have 2x+1= 17 groups of rings. The First 8 groups will have groups with 1 ring each, which can help pay a maximum of 8 rings.
9th group 9 rings. (Can pay up to 17 rings)
10th group 18 rings. (Can pay up to 35 rings)
11th group 36 rings. (Can pay up to 71 rings)
12th group 72 rings. (Can pay up to 143 rings)
13th group 144 rings. (Can pay up to 287 rings)
14th group 288 rings. (Can pay up to 575 rings)
15th group 576 rings. (Can pay up to 1151 rings)
16th group 1152 rings. (Can pay up to 2303 rings)
17th group 2304 rings. (Can pay up to 4607 rings)
.'. With Rs. 95 paid for cutting, Bhalla will have cut 8 times to produce 17 groups of rings, which can pay in any denomination from 1 to 4607 rings.
ALTERNATE SOLUTION:
The number of cuts= 8.
.'. Number of rings formed= 2^{(n+1)} x (n+1)  1= (2^{9} x 9)  1 = 46081 = 4607.
.'. With Rs. 95 paid for cutting, Bhalla will have cut 8 times to produce 17 groups of rings, which can pay in any denomination from 1 to 4607 rings.
Bhalla was a landlord who paid his servants using golden rings in a gold chain. To make a certain payment, he needs to cut the rings such that he can pay his servants any amount they ask. He hires Kattapa to cut the chain intelligently. Bhalla has to pay Kattapa Rs.10 for every cut up to a maximum of 5 cuts, post which he is charged Rs.15 for every additional cut after 5. Note: When chain of length 'n' (n>2) is cut once, you will get 3 pieces of length 1, k, nk1
Q. If Bhalla has a chain with 908 rings, how much minimum amount will he pay to ensure that he can pay his servant any amount of rings from 1 to 908?
For a chain based puzzles, we need to understand two things to solve any question.
1. Number of cuts Vs. Number of pieces:
When we cut a ring once, we will have 3 pieces formed The ring where the cut is made, opens up and the group of rings to the left and right of the ring where cut is made detaches itself.
Similarly, when 2 cuts are made on 2 different rings, we will have 5 groups of rings:
The two rings where cuts are not a part of any group, but rest 3 forms a group by detaching itself in the following way:
Therefore, we can say that in general, when 'n' cuts are made, n rings of 1 piece each are formed exactly where the cuts are made. The regions between the cuts (n1) groups of ring detach itself from the chain and finally 2 pieces from each of the two ends form two separate groups. In total, for 'n' cuts, we have a maximum of (n)+(n1)+(2)= 2n+1 groups of chain with n chains of unit rings.
2. Maximum payment of each denomination from a given number of cuts:
When we cut the ring, we must ensure that the rings or group of rings can add up to any natural number. So, when we have 1 cut, which gives us three pieces, we already have a chain with 1 ring. To count 2 rings, we will cut the chain such that one of the part have a group of 2 rings. Doing this will ensure that we have 1, 2 and 3( Adding groups with 1 and 2 rings together) separate rings.
For eg. if we have to make 2 cuts, we will have 5 groups of chain A, B, C, D and E. Since we made two cuts, we will have exactly 2 single rings. So, A=1 and B=1. We can pay up to 2 rings using them both. Therefore, C must be 3. With A, B and C, we can make payments up to (1+1+3) units= 5 units. So, D should be 6 and using A, B, C and D together will ensure payment of up to 11 units. And hence, the last part E should be of 12 rings so as to make every payment from 1 ring to 23 rings. We notice that the number of rings get doubled for every subsequent group when cut intelligently.
Using the above two concepts, we will make n cuts so as to divide 908 rings efficiently.
Let us assume that we make 7 cuts. We will thus have 2n+1= 15 groups of chains. Here 7 pieces are each of unit ring, which can make payments up to 7 rings together. So, the next group (8th) has to be of length 8 rings. The 9th group will have 16 rings because all the first 8 groups can make payments up to 7+8= 15 rings. The number of rings gets doubled for every subsequent group.
10th group= 32 rings. (Can pay any amount up to 63)11th group= 64 rings. (Can pay any amount up to 127)
12th group= 128 rings (Can pay any amount up to 255)
13th group= 256 rings (Can pay any amount up to 511)
14th group= 512 rings (Can pay any amount up to 1023)
15th group= 1024 rings. (Can pay any amount up to 2047)
In total, we can pay up to 7+8+16+32+64+128+256+512+1024= 2047 rings, which is more than what we need.
When we make 6 cuts, we will have 2n+1= 13 groups of rings, where 6 groups will have 1 ring each which can pay any amount up to 6 rings.
7th group= 7 rings. (Can pay any amount up to 13)
8th group= 14 rings. (Can pay any amount up to 63)
9th group= 28 rings. (Can pay any amount up to 55)
10th group= 56 rings (Can pay any amount up to 111)
11th group= 112 rings. (Can pay any amount up to 223)
12th group= 224 rings. (Can pay any amount up to 447)
13th group= 448 rings. (Can pay any amount up to 895).
'.' We cannot pay any amount from 896 to 908, we will have to make more cuts.
.'. 7 cuts is the least possible amount of cuts required to pay any amount from 1 to 908.
Money needed for 7 cuts= Rs.(10 x 5) + (15 x 2) = Rs. 80
ALTERNATE SOLUTION:
For n cuts, we have a general formula of forming 2^{(n+1)} x (n+1)  1 rings.
To pay 908 rings,
The RHS is greater than 2^{9 }and smaller than 2^{10}
When we put n=8, LHS= 2^{9}x 9 = 4608, which satisfies the equation but since LHS is a very bigger number, we can cut the cutting cost by minimising the number of cuts.
When n=6, LHS=2^{7} x 7 = = 896. Here LHS is not greater than the RHS.
.'. Minimum number of cuts must be either 7 or 8.
When n=7, LHS=2^{8} x8= 2048.
.'. 7 cuts is the least possible amount of cuts required to pay any amount from 1 to 908.
Money needed for 7 cuts= Rs.(10x5)+(15x2) = Rs. 80
Bhalla was a landlord who paid his servants using golden rings in a gold chain. To make a certain payment, he needs to cut the rings such that he can pay his servants any amount they ask. He hires Kattapa to cut the chain intelligently. Bhalla has to pay Kattapa Rs.10 for every cut up to a maximum of 5 cuts, post which he is charged Rs.15 for every additional cut after 5. Note: When chain of length 'n' (n>2) is cut once, you will get 3 pieces of length 1, k, nk1
Q. Bhalla has three servants.They have to be paid n rings each for the work done on the nth day. Each day Bhalla takes back all the rings that he had paid previously and pays the full amount again. He has 1 chain for each servant and he spends Rs. 120 in total for cutting the chains, then possibly for how many days did each of the servants work.
(Consider the fact that he did not overspend and each servant worked equally without being absent on any day after starting.)
For a chain based puzzles, we need to understand two things to solve any question.
1. Number of cuts Vs. Number of pieces:
When we cut a ring once, we will have 3 pieces formed The ring where the cut is made, opens up and the group of rings to the left and right of the ring where cut is made detaches itself.
Similarly, when 2 cuts are made on 2 different rings, we will have 5 groups of rings:
The two rings where cuts are not a part of any group, but rest 3 forms a group by detaching itself in the following way:
Therefore, we can say that in general, when 'n' cuts are made, n rings of 1 piece each are formed exactly where the cuts are made. The regions between the cuts (n1) groups of ring detach itself from the chain and finally 2 pieces from each of the two ends form two separate groups. In total, for 'n' cuts, we have a maximum of (n)+(n1)+(2)= 2n+1 groups of chain with n chains of unit rings.
2. Maximum payment of each denomination from a given number of cuts:
When we cut the ring, we must ensure that the rings or group of rings can add up to any natural number. So, when we have 1 cut, which gives us three pieces, we already have a chain with 1 ring. To count 2 rings, we will cut the chain such that one of the part have a group of 2 rings. Doing this will ensure that we have 1, 2 and 3( Adding groups with 1 and 2 rings together) separate rings.
For eg. if we have to make 2 cuts, we will have 5 groups of chain A, B, C, D and E. Since we made two cuts, we will have exactly 2 single rings. So, A=1 and B=1. We can pay up to 2 rings using them both. Therefore, C must be 3. With A, B and C, we can make payments up to (1+1+3) units= 5 units. So, D should be 6 and using A, B, C and D together will ensure payment of up to 11 units. And hence, the last part E should be of 12 rings so as to make every payment from 1 ring to 23 rings. We notice that the number of rings get doubled for every subsequent group when cut intelligently.
So, here he spent Rs. 120 to cut the chain and he did not overspend. This means that he necessarily had to spend Rs. 40 for each chain. And hence, 4 cuts were required. For the first day, a servant is paid 1 ring. For the second day, he/she is paid 2 rings. So, for n days he/she will be paid 1+2+3+4+....n= rings.
In 3 cuts, a chain is cut into 7 groups. Maximum that can be paid in 3 cuts= 1+1+1+4+8+16+32= 63 rings.
In 4 cuts, a chain is cut into 9 groups. Maximum that can be paid in 4 cuts= 1+1+1+1+5+10+20+40+80= 159 rings.
So, the payment for each servant for n days lie between 64 and 159 including both. (Not 63 because had that been the case, Bhalla would have paid for 3 cuts only.)
.'. We can say that
By plugging in values, we get 11 ≤ n ≤ 17
Only 1 value, i.e. 15 in option C satisfies the inequality and hence is our answer.
The following table records the scores of 6 students in 5 subjects S1, S2, S3, S4, and S5 in their semester exams. However, some data is missing. The following information is known:
1.The scores are out of 10.
2.The maximum score is 10 and the minimum score is 4.
3.A student never scores the same in more than 1 subject.
4.Also, no 2 students score the same marks in any subject.
5.The marks scored by E in S5 is neither his highest nor his secondhighest score.
Based on the information given above, answer the questions that follow.
Q. How much did C score in S4?
The table has been provided to us as follows:
Step 1: The marks scored by E in S5, which is 7, is not his highest or secondhighest marks. Hence, he must have scored at least 2 out of 8, 9 and 10 in the remaining subjects. Now, E cannot score 8 in S1, S2 or S3 because other students have already scored 8 in the respective subjects. Hence, E must have scored 9 and 10 in 2 of the remaining 3 subjects. Now, he has to score 10 in S2, since other students have already scored 10 in S1 and S3. Now out of S1 and S3, he needs to score a 9. How do we know which of the 2 subjects he gets a 9 in? Let us assume the sum of all scores in S1. 42 = 4 + 5 + 6 + 8 + 9 + 10. Let us assume the sum of salaries in S2 to S5 all of which is 40. 40 = 4 + 5 + 6 + 7 + 8 + 10. SO, a score of 9 is possible only in S1. So, we can conclude that E scores 9 in S1. Also, since the total score of E is 35, his score in S3 is 35  9  10  4  7 = 5.
Step 2: The total score in S1 is 42, and as we have already seen in Step 1 that the different scores are (4,5,6,8,9,10). So, A and B should score among 4 and 6 in S1. Since B has already scored 4 in S2, he cannot score 4 anywhere else. So he scores 6 and A scores 4 in S1.
Step 3: The total score in S3 is 40, and we have seen in Step 1 that the different scores are (4,5,6,7,8,10). 8, 5 and 10 have already been scored by B, E and F respectively, the others must score among 4, 6 and 7. Since 4 cannot be scored by A and C as they have scored 4 in other subjects, 4 must be scored by D.
Step 4: Since the total score of B is 30, the sum of B's scores in S4 and S5 is 30  6  4  8 = 12. 12 can be written as 4 + 8, 5 + 7 or 6 + 6, 4 + 8 is not possible since they have already bn scored by B. 6 + 6 is also not possible since 2 students cannot score the same marks. Hence, it is 5 + 7. Since there is already a 5 in S4 and 7 in S5, B's scores in S4 and S5 are 7 and 5 respectively.
Step 5: Since the sum of scores in S5 is 40, the sum of the remaining scores = 40  5  4 7 = 24. The remaining scores in S5 are 6, 8 and 10. Now 10 cannot b scored by D or F. So, it is scored by A.
Step 6: Since the total score of A is 33, marks scored by him in S3 = 33  4  8  5  10 = 6. Also, in that case, marks scored by C in s3 will be 7, because that is the only number left among (4,5,6,7,8,10).
Step 7: The remaining marks in S4 are 6, 8 and 10. Now 10 can only be scored by C since other students have already scored 10 in different subjects.
Step 8: Since C scores a total of 35, his scores in S2 are 35  4  10  7  8 = 6.
Step 9: Since the scores remaining in S2 are 5 and 7, and F has already scored a 5 in S1, D scores a 5 in S2 and F scores a 7 in S2.
The remaining scores can be 6 or 8 since they are the only remaining possibilities. So we can make 2 arrangements as follows:
We cannot deduce any further information.
In both cases, C scores 10 in S4.
The following table records the scores of 6 students in 5 subjects S1, S2, S3, S4, and S5 in their semester exams. However, some data is missing. The following information is known:
1.The scores are out of 10.
2.The maximum score is 10 and the minimum score is 4.
3.A student never scores the same in more than 1 subject.
4.Also, no 2 students score the same marks in any subject.
5.The marks scored by E in S5 is neither his highest nor his secondhighest score.
Based on the information given above, answer the questions that follow.
Q. Which score appears for the least number of times in the table?
The table has been provided to us as follows:
Step 1: The marks scored by E in S5, which is 7, is not his highest or secondhighest marks. Hence, he must have scored at least 2 out of 8, 9 and 10 in the remaining subjects. Now, E cannot score 8 in S1, S2 or S3 because other students have already scored 8 in the respective subjects. Hence, E must have scored 9 and 10 in 2 of the remaining 3 subjects. Now, he has to score 10 in S2, since other students have already scored 10 in S1 and S3. Now out of S1 and S3, he needs to score a 9. How do we know which of the 2 subjects he gets a 9 in? Let us assume the sum of all scores in S1. 42 = 4 + 5 + 6 + 8 + 9 + 10. Let us assume the sum of salaries in S2 to S5 all of which is 40. 40 = 4 + 5 + 6 + 7 + 8 + 10. SO, a score of 9 is possible only in S1. So, we can conclude that E scores 9 in S1. Also, since the total score of E is 35, his score in S3 is 35  9  10  4  7 = 5.
Step 2: The total score in S1 is 42, and as we have already seen in Step 1 that the different scores are (4,5,6,8,9,10). So, A and B should score among 4 and 6 in S1. Since B has already scored 4 in S2, he cannot score 4 anywhere else. So he scores 6 and A scores 4 in S1.
Step 3: The total score in S3 is 40, and we have seen in Step 1 that the different scores are (4,5,6,7,8,10). 8, 5 and 10 have already been scored by B, E and F respectively, the others must score among 4, 6 and 7. Since 4 cannot be scored by A and C as they have scored 4 in other subjects, 4 must be scored by D.
Step 4: Since the total score of B is 30, the sum of B's scores in S4 and S5 is 30  6  4  8 = 12. 12 can be written as 4 + 8, 5 + 7 or 6 + 6, 4 + 8 is not possible since they have already bn scored by B. 6 + 6 is also not possible since 2 students cannot score the same marks. Hence, it is 5 + 7. Since there is already a 5 in S4 and 7 in S5, B's scores in S4 and S5 are 7 and 5 respectively.
Step 5: Since the sum of scores in S5 is 40, the sum of the remaining scores = 40  5  4 7 = 24. The remaining scores in S5 are 6, 8 and 10. Now 10 cannot b scored by D or F. So, it is scored by A.
Step 6: Since the total score of A is 33, marks scored by him in S3 = 33  4  8  5  10 = 6. Also, in that case, marks scored by C in s3 will be 7, because that is the only number left among (4,5,6,7,8,10).
Step 7: The remaining marks in S4 are 6, 8 and 10. Now 10 can only be scored by C since other students have already scored 10 in different subjects.
Step 8: Since C scores a total of 35, his scores in S2 are 35  4  10  7  8 = 6.
Step 9: Since the scores remaining in S2 are 5 and 7, and F has already scored a 5 in S1, D scores a 5 in S2 and F scores a 7 in S2.
The remaining scores can be 6 or 8 since they are the only remaining possibilities. So we can make 2 arrangements as follows:
We cannot deduce any further information.
9 appears only once, which is the least.
The following table records the scores of 6 students in 5 subjects S1, S2, S3, S4, and S5 in their semester exams. However, some data is missing. The following information is known:
1.The scores are out of 10.
2.The maximum score is 10 and the minimum score is 4.
3.A student never scores the same in more than 1 subject.
4.Also, no 2 students score the same marks in any subject.
5.The marks scored by E in S5 is neither his highest nor his secondhighest score.
Based on the information given above, answer the questions that follow.
Q. How many times does the score 8 appear in the list of all the marks scored by the students in each subject?
The table has been provided to us as follows:
Step 1: The marks scored by E in S5, which is 7, is not his highest or secondhighest marks. Hence, he must have scored at least 2 out of 8, 9 and 10 in the remaining subjects. Now, E cannot score 8 in S1, S2 or S3 because other students have already scored 8 in the respective subjects. Hence, E must have scored 9 and 10 in 2 of the remaining 3 subjects. Now, he has to score 10 in S2, since other students have already scored 10 in S1 and S3. Now out of S1 and S3, he needs to score a 9. How do we know which of the 2 subjects he gets a 9 in? Let us assume the sum of all scores in S1. 42 = 4 + 5 + 6 + 8 + 9 + 10. Let us assume the sum of salaries in S2 to S5 all of which is 40. 40 = 4 + 5 + 6 + 7 + 8 + 10. SO, a score of 9 is possible only in S1. So, we can conclude that E scores 9 in S1. Also, since the total score of E is 35, his score in S3 is 35  9  10  4  7 = 5.
Step 2: The total score in S1 is 42, and as we have already seen in Step 1 that the different scores are (4,5,6,8,9,10). So, A and B should score among 4 and 6 in S1. Since B has already scored 4 in S2, he cannot score 4 anywhere else. So he scores 6 and A scores 4 in S1.
Step 3: The total score in S3 is 40, and we have seen in Step 1 that the different scores are (4,5,6,7,8,10). 8, 5 and 10 have already been scored by B, E and F respectively, the others must score among 4, 6 and 7. Since 4 cannot be scored by A and C as they have scored 4 in other subjects, 4 must be scored by D.
Step 4: Since the total score of B is 30, the sum of B's scores in S4 and S5 is 30  6  4  8 = 12. 12 can be written as 4 + 8, 5 + 7 or 6 + 6, 4 + 8 is not possible since they have already bn scored by B. 6 + 6 is also not possible since 2 students cannot score the same marks. Hence, it is 5 + 7. Since there is already a 5 in S4 and 7 in S5, B's scores in S4 and S5 are 7 and 5 respectively.
Step 5: Since the sum of scores in S5 is 40, the sum of the remaining scores = 40  5  4 7 = 24. The remaining scores in S5 are 6, 8 and 10. Now 10 cannot b scored by D or F. So, it is scored by A.
Step 6: Since the total score of A is 33, marks scored by him in S3 = 33  4  8  5  10 = 6. Also, in that case, marks scored by C in s3 will be 7, because that is the only number left among (4,5,6,7,8,10).
Step 7: The remaining marks in S4 are 6, 8 and 10. Now 10 can only be scored by C since other students have already scored 10 in different subjects.
Step 8: Since C scores a total of 35, his scores in S2 are 35  4  10  7  8 = 6.
Step 9: Since the scores remaining in S2 are 5 and 7, and F has already scored a 5 in S1, D scores a 5 in S2 and F scores a 7 in S2.
The remaining scores can be 6 or 8 since they are the only remaining possibilities. So we can make 2 arrangements as follows:
We cannot deduce any further information.
In both cases, 8 appears 5 times.
The following table records the scores of 6 students in 5 subjects S1, S2, S3, S4, and S5 in their semester exams. However, some data is missing. The following information is known:
1.The scores are out of 10.
2.The maximum score is 10 and the minimum score is 4.
3.A student never scores the same in more than 1 subject.
4.Also, no 2 students score the same marks in any subject.
5.The marks scored by E in S5 is neither his highest nor his secondhighest score.
Based on the information given above, answer the questions that follow.
Q. What is the absolute difference between the total scores of E and F?
The table has been provided to us as follows:
Step 1: The marks scored by E in S5, which is 7, is not his highest or secondhighest marks. Hence, he must have scored at least 2 out of 8, 9 and 10 in the remaining subjects. Now, E cannot score 8 in S1, S2 or S3 because other students have already scored 8 in the respective subjects. Hence, E must have scored 9 and 10 in 2 of the remaining 3 subjects. Now, he has to score 10 in S2, since other students have already scored 10 in S1 and S3. Now out of S1 and S3, he needs to score a 9. How do we know which of the 2 subjects he gets a 9 in? Let us assume the sum of all scores in S1. 42 = 4 + 5 + 6 + 8 + 9 + 10. Let us assume the sum of salaries in S2 to S5 all of which is 40. 40 = 4 + 5 + 6 + 7 + 8 + 10. SO, a score of 9 is possible only in S1. So, we can conclude that E scores 9 in S1. Also, since the total score of E is 35, his score in S3 is 35  9  10  4  7 = 5.
Step 2: The total score in S1 is 42, and as we have already seen in Step 1 that the different scores are (4,5,6,8,9,10). So, A and B should score among 4 and 6 in S1. Since B has already scored 4 in S2, he cannot score 4 anywhere else. So he scores 6 and A scores 4 in S1.
Step 3: The total score in S3 is 40, and we have seen in Step 1 that the different scores are (4,5,6,7,8,10). 8, 5 and 10 have already been scored by B, E and F respectively, the others must score among 4, 6 and 7. Since 4 cannot be scored by A and C as they have scored 4 in other subjects, 4 must be scored by D.
Step 4: Since the total score of B is 30, the sum of B's scores in S4 and S5 is 30  6  4  8 = 12. 12 can be written as 4 + 8, 5 + 7 or 6 + 6, 4 + 8 is not possible since they have already bn scored by B. 6 + 6 is also not possible since 2 students cannot score the same marks. Hence, it is 5 + 7. Since there is already a 5 in S4 and 7 in S5, B's scores in S4 and S5 are 7 and 5 respectively.
Step 5: Since the sum of scores in S5 is 40, the sum of the remaining scores = 40  5  4 7 = 24. The remaining scores in S5 are 6, 8 and 10. Now 10 cannot b scored by D or F. So, it is scored by A.
Step 6: Since the total score of A is 33, marks scored by him in S3 = 33  4  8  5  10 = 6. Also, in that case, marks scored by C in s3 will be 7, because that is the only number left among (4,5,6,7,8,10).
Step 7: The remaining marks in S4 are 6, 8 and 10. Now 10 can only be scored by C since other students have already scored 10 in different subjects.
Step 8: Since C scores a total of 35, his scores in S2 are 35  4  10  7  8 = 6.
Step 9: Since the scores remaining in S2 are 5 and 7, and F has already scored a 5 in S1, D scores a 5 in S2 and F scores a 7 in S2.
The remaining scores can be 6 or 8 since they are the only remaining possibilities. So we can make 2 arrangements as follows:
We cannot deduce any further information.
In both cases, sum of scores of E = 9 + 10 + 5 + 4 + 7 = 35.
In both cases, sum of scores of F = 5 + 7 + 10 + 8 + 6 = 36.
Hence, absolute difference = 1.
10 people are sitting around a circular table, each facing the table. They are numbered 1 to 10 and are sitting in the following manner.
They sit in the same arrangement for some time, till there is a transition. In a transition, one person moves out of the table, and a different person moves in, although not in the same seat. It happens in the following manner. In the first transition, a particular person(say A) moves out of the table, the person sitting diametrically opposite to A(say B) replaces him(A), and a new person(say C) enters the position where B sat initially. Every new person coming into the table is numbered in a successive way. So, the first person joining the table when one person leaves will be numbered 11, the next person joining the table will be numbered 12 and so on. In the second transition, the person to the immediate right of the person who joined last(say X), moves away. The person diametrically opposite to him(say Y) replaces him, and a new person(say Z) replaces Y. And this goes on. For example, suppose, in the first transition, 1 moves out of the table and 6 replaces him. A new person numbered 11 enters the position where 6 sat initially. In the second transition, the person to the immediate right of 11, that is 5, moves out of the table and 10 replaces him, and a new person 12 enters the position where 10 sat initially and it continues.
Based on the above information, answer the questions that follow.
Q. The person numbered 1 moves out of the table in the first transition. Which of the following persons move out of the table in the 4th transition?
Initially, the arrangement is as follows.
Now, in the first transition, 1 moves out, 6 replaces 1 and 11 replaces 6.
Now in the second transition, 5 moves out, 10 replaces 5, and 12 replaces 10.
Now, in the third transition, 9 moves out, 4 replaces 9, and 13 replaces 4.
In the fourth transition, 3 moves out, 8 replaces 3, and 14 replaces 8.
Hence, 3 moves out of the table in the 4th transition.
10 people are sitting around a circular table, each facing the table. They are numbered 1 to 10 and are sitting in the following manner.
They sit in the same arrangement for some time, till there is a transition. In a transition, one person moves out of the table, and a different person moves in, although not in the same seat. It happens in the following manner. In the first transition, a particular person(say A) moves out of the table, the person sitting diametrically opposite to A(say B) replaces him(A), and a new person(say C) enters the position where B sat initially. Every new person coming into the table is numbered in a successive way. So, the first person joining the table when one person leaves will be numbered 11, the next person joining the table will be numbered 12 and so on. In the second transition, the person to the immediate right of the person who joined last(say X), moves away. The person diametrically opposite to him(say Y) replaces him, and a new person(say Z) replaces Y. And this goes on. For example, suppose, in the first transition, 1 moves out of the table and 6 replaces him. A new person numbered 11 enters the position where 6 sat initially. In the second transition, the person to the immediate right of 11, that is 5, moves out of the table and 10 replaces him, and a new person 12 enters the position where 10 sat initially and it continues.
Based on the above information, answer the questions that follow.
Q. The person numbered 1 moves out of the table in the first transition. Which of the following represents all the people who remain seated after the 6th transition?
Initially, the arrangement is as follows.
Now, in the first transition, 1 moves out, 6 replaces 1 and 11 replaces 6.
Now in the second transition, 5 moves out, 10 replaces 5, and 12 replaces 10.
Now, in the third transition, 9 moves out, 4 replaces 9, and 13 replaces 4.
In the fourth transition, 3 moves out, 8 replaces 3, and 14 replaces 8.
In the fifth transition, 7 moves out, 2 replaces 7 and 15 replaces 2.
In the sixth transition, 6 moves out, 11 replaces 6 and 16 replaces 11.
So, after the 6th transition, 2, 4, 8, 10, 11, 12,13, 14, 15 and 16 remain seated.
10 people are sitting around a circular table, each facing the table. They are numbered 1 to 10 and are sitting in the following manner.
They sit in the same arrangement for some time, till there is a transition. In a transition, one person moves out of the table, and a different person moves in, although not in the same seat. It happens in the following manner. In the first transition, a particular person(say A) moves out of the table, the person sitting diametrically opposite to A(say B) replaces him(A), and a new person(say C) enters the position where B sat initially. Every new person coming into the table is numbered in a successive way. So, the first person joining the table when one person leaves will be numbered 11, the next person joining the table will be numbered 12 and so on. In the second transition, the person to the immediate right of the person who joined last(say X), moves away. The person diametrically opposite to him(say Y) replaces him, and a new person(say Z) replaces Y. And this goes on. For example, suppose, in the first transition, 1 moves out of the table and 6 replaces him. A new person numbered 11 enters the position where 6 sat initially. In the second transition, the person to the immediate right of 11, that is 5, moves out of the table and 10 replaces him, and a new person 12 enters the position where 10 sat initially and it continues.
Based on the above information, answer the questions that follow.
Q. The person numbered 1 moves out of the table in the first transition. Which of the following persons remain on the table after the 15th transition?
Initially, the arrangement is as follows.
Now, in the first transition, 1 moves out, 6 replaces 1 and 11 replaces 6.
Now in the second transition, 5 moves out, 10 replaces 5, and 12 replaces 10.
Now, in the third transition, 9 moves out, 4 replaces 9, and 13 replaces 4.
In the fourth transition, 3 moves out, 8 replaces 3, and 14 replaces 8.
In the fifth transition, 7 moves out, 2 replaces 7 and 15 replaces 2.
In the sixth transition, 6 moves out, 11 replaces 6 and 16 replaces 11.
In the sixth transition, 6 moves out, 11 replaces 6 and 16 replaces 11.
So if we observe now, in the sixth transition, a person again moves out of seat A. This is similar to that of 1st transition, so we can assume a set of 5 transitions because, after each set of 5 transitions, the pattern repeats itself.
Now we need to see who is seating where initially and after the 5th transition so that we can use that information to deduce who is sitting where after each 5n transition.
So, after 5 transitions, 6, who sits at F replaces 1, hence after 10 transitions, 11 who sits at F replaces 6.
After 5 transitions, 15, who is the 5th person to enter the table replaces 1, hence after 10 transitions, 20 who is the 5th person to enter in the second 5 rounds replaces 15.
After 5 transitions, 8, who sits at H replaces 1, hence after 10 transitions, 14 who sits at H replaces 8.
After 5 transitions, 13, who is the 3rd person to enter the table replaces 4, hence after 10 transitions, 18 who is the 3rd person to enter in the second 5 rounds replaces 13.
Similarly, we can calculate for the remaining people, as to who would be seating where after the 10 transitions, and we get this.
In a similar way, we can calculate, who would be sitting where after the 15th transition.
Hence, out of the given options, 17 remain.
10 people are sitting around a circular table, each facing the table. They are numbered 1 to 10 and are sitting in the following manner.
They sit in the same arrangement for some time, till there is a transition. In a transition, one person moves out of the table, and a different person moves in, although not in the same seat. It happens in the following manner. In the first transition, a particular person(say A) moves out of the table, the person sitting diametrically opposite to A(say B) replaces him(A), and a new person(say C) enters the position where B sat initially. Every new person coming into the table is numbered in a successive way. So, the first person joining the table when one person leaves will be numbered 11, the next person joining the table will be numbered 12 and so on. In the second transition, the person to the immediate right of the person who joined last(say X), moves away. The person diametrically opposite to him(say Y) replaces him, and a new person(say Z) replaces Y. And this goes on. For example, suppose, in the first transition, 1 moves out of the table and 6 replaces him. A new person numbered 11 enters the position where 6 sat initially. In the second transition, the person to the immediate right of 11, that is 5, moves out of the table and 10 replaces him, and a new person 12 enters the position where 10 sat initially and it continues.
Based on the above information, answer the questions that follow.
Q. The person numbered 4 moves out of the table in the first transition. Let X_{n} be the initial position of the person numbered n, and let Y_{m} be the position of the person numbered m after the 5th transition. Which of the following pairs represent the same position?
Initially, the arrangement is as follows.
Now, in the first transition, 1 moves out, 6 replaces 1 and 11 replaces 6.
Now in the second transition, 5 moves out, 10 replaces 5, and 12 replaces 10.
Now, in the third transition, 9 moves out, 4 replaces 9, and 13 replaces 4.
In the fourth transition, 3 moves out, 8 replaces 3, and 14 replaces 8.
In the fifth transition, 7 moves out, 2 replaces 7 and 15 replaces 2.
But in this question, we have been given that 4 moves out in the first transition.
Now we can take 2 approaches. First, we can repeat what we did when 1 moved out in the first transition to the case when 4 moved out in the first transition, and follow similar steps to find out who sits where after the fifth transition.
The second and better approach is that since we have already worked out who sits where after the fifth transition (when 1 moves out first), we can simply apply the final results, adjusting them in a way that 4 is the first one to move. This approach follows the logic that irrespective of the person, the one who is sitting on A moves out first, so we can adjust in a way that 4 sits on A in the initial arrangement.
Now, in the first table, we see that 6 who was sitting on F is replacing 1, who was sitting on A. SImilarly, in table 2, 9 who is sitting on F will replace 4 who is sitting on A.
In the first table, 15(the person joining in the fifth transition) is replacing the one sitting at B. Similarly in table 2, 15 will be replacing 5.
In the first table, we see that 8 who was sitting on H is replacing 3, who was sitting on C. SImilarly, in table 2, 1 who is sitting on H will replace 6 who is sitting on C.
In the first table, 13(the person joining in th 3rd transition) is replacing the one sitting on D. Similarly in table 2, 13 will be replacing 7.
We can continue in a similar fashion to find out the positions of all people after the 5th transition.
Hence the initial position of 2 and the final position of 7 are the same.
2 friends Virat and Sourav are playing a game that involves a dice. In each round, Virat rolls the dice twice, and then Sourav rolls the dice twice. If the sum of the numbers that Virat gets exceeds the sum of numbers that Sourav gets, Virat wins the round, else Sourav wins the round. In case the sum is the same, Sourav is given the advantage and he wins the round. The game ends when any one of them wins three consecutive rounds, and he is declared the winner. Based on the information given, answer the questions that follow.
Q. In a particular game, Sourav and Virat decide that either of them can start the first round, but whoever starts the first round has to start all subsequent rounds. Following is the sequence of numbers that come up starting from the first roll of dice in round 1. It is known that the game ends after the 12th throw of the dice (with the last roll of 2) as shown in the pattern.
3 6 5 4 2 5 A 1 B C 1 2
By varying the values of A, B and C, what is the total number of ways Sourav and Virat can throw the dice in the above pattern?
Since the total number of rolls = 12, the number of rounds in the game = 12/4 = 3
This implies that in all 3 rounds, the same player wins, in order to complete the game in round 3.
Let us suppose Virat starts the first round.
Now, in the first round, Virat's sum = 3 + 6 = 9, and Sourav's sum = 5 + 4 = 9.
In case the sum is the same, Sourav wins. Hence in Round 2 and Round 3 also, Sourav wins.
For Sourav to win in Round 2, he must roll a minimum sum of 7 so that he can match the sum of Virat and win the round. Hence, A can only be 6.
For Sourav to win the third round as well, Virat cannot exceed the sum of Sourav.
Sourav's sum = 1 + 2 = 3.
Hence, Virat can roll (1,1), (1,2) or (2,1). Hence B and C can together take 3 different ordered pairs as values.
Hence, the required count = 1 x 3 = 3
Let us suppose Sourav starts the first round.
Now, in the first round, Sourav's sum = 3 + 6 = 9, and Virat's sum = 5 + 4 = 9.
In case the sum is the same, Sourav wins. Hence in Round 2 and Round 3 also, Sourav wins.
Sourav rolls a sum of 2 + 5 = 7 in the second round. So Virat has to roll a sum less than or equal to 7. So, A can take 1 to 6. Hence, 6 values.
In round 3, Virat rolls a sum of 3. Sourav has to throw a minimum of a total of 3. So he can roll anything except (1,1). Hence number of possibilities = 36  1 = 35.
Hence, the required count = 35 x 6 = 210.
Hence, total count = 210 + 3 = 213.
2 friends Virat and Sourav are playing a game that involves a dice. In each round, Virat rolls the dice twice, and then Sourav rolls the dice twice. If the sum of the numbers that Virat gets exceeds the sum of numbers that Sourav gets, Virat wins the round, else Sourav wins the round. In case the sum is the same, Sourav is given the advantage and he wins the round. The game ends when any one of them wins three consecutive rounds, and he is declared the winner. Based on the information given, answer the questions that follow.
Q. It is known that the game ends after the 8th round. The numbers rolled in the 8th round are successively 4, 5, 1, 6. How many of the choices given below can represent the successive numbers rolled in the 5th round?
(4,3,2,6), (4,1,1,5), (2,3,1,4), (5,6,5,5), (2,3,1,2), (1,2,3,4)
The question says that the game ends after the 8th round. So, firstly the winner of the 8th round is the winner of the game. Secondly, the winner of the 5th round should be different from the winner of the game, because, to win, a player must win for the third consecutive time in the eighth round, so he should win in the 6th, 7th and 8th round. Suppose he wins in the 5th round, now if we win in the 6th and 7th round as well, the game ends after the 7th round, and if he loses any of the 6th or 7th rounds, the game goes beyond 8 rounds. In the question, Virat win the final round since 4 + 5 > 1 + 6. Hence, Virat must lose round 5 by all possible means.
4 + 3 < 2 + 6, Hence Sourav wins
4 + 1 < 1 + 5, Hence Sourav wins
2 + 3 = 1 + 4, Hence Sourav wins
5 + 6 > 5 + 5, Hence Virat wins
2 + 3 > 1 + 2, Hence Virat wins
1 + 2 < 3 + 4, Hence Sourav wins
Hence, in 4 possible scenarios, Virat loses. Hence 4 is the correct answer.
2 friends Virat and Sourav are playing a game that involves a dice. In each round, Virat rolls the dice twice, and then Sourav rolls the dice twice. If the sum of the numbers that Virat gets exceeds the sum of numbers that Sourav gets, Virat wins the round, else Sourav wins the round. In case the sum is the same, Sourav is given the advantage and he wins the round. The game ends when any one of them wins three consecutive rounds, and he is declared the winner. Based on the information given, answer the questions that follow.
Q. Sourav has a special tool at his disposal, that allows him to always roll a 6, but he does not use it always. He only uses it in the final roll of a round only if the same player wins in both of the consecutive rounds preceding that round. He won't use it under any other circumstance.
In a particular game, Sourav uses this tool thrice, once in the 3rd round, once in the 6th round and once in the 10th round to win the game. How many rounds did Virat win?
Sourav uses the tool in the third round, and he does not win after that round, which means he saved himself from losing the game by using this tool, hence Virat was the winner of Rund 1 and Round 2, and Sourav used the tool to win Round 3.
Sourav again uses this tool in the sixth round, and he does not win after the round, which means he saved himself from losing the game by using the tool, hence Virat was the winner of Round 4 and Round 5, and Sourav is the winner in Round 6.
Sourav again uses the tool in the tenth round, but this time to win, so Sourav must have won the 8th and 9th rounds already. Hence he cannot win round 7.
Hence Virat won Round 7.
Hence, Virat won a total of 5 rounds.
Direction: Study the following table carefully to answer these question:
Production (in core units) of six companies over the years
Which company has less average production in the last three years compared to that of first three years?
Sum of the productions of the companies in first three years and the last three years is as follows:
AB and CD are 2 parallel chords of a circle which has a radius of 10 units. Parallel chords are 14 units apart such that one of the chords has a length of 12 units. What is the length of nonparallel side of trapezium ABCD
Since the radius of the circle is 10 and the chords are 14 units apart, both of them have to be on the opposite side of the centre, let CD = 12. It can be shown as
E and F are the midpoint of respective chords.
From the properties of the circle, we know that OF is the perpendicular bisector of DC. Thus DF = 6 and OD =10(radius). It gives OF = 8 (from Pythagoras theorem)
Since it is given that EF = 14, it implies that EO = 14OF =148 = 6
EOB is also a righttriangle such that EO = 6 and OB = 10. This gives EB = 8 or AB = 16.
Since they are symmetrical the trapezium will look like this
From pythogoras we find that AD^{2} = 14^{2} + 2^{2} = 196 + 4 = 200
AD = 10√2
A rectangle ABCD exists such that AB = 6 units and BC = 12 units. E and F trisect the diagonal AC in 3 equal parts. G is centroid of the triangle formed by DEF. What is the area of DGBC?
Let us draw a rectangle on the coordinate axis. With (0,0) be one of the edge A. B can be (6,0), C(6,12) and D(0,12). E and F divide the AC in 3 equal part. E has to be (2,4) and F (4,8)
G is centroid of DEF, Coordinates of G will be
Upon finding G the required diagram looks like this
Area DGBC = Area GBC + Area DCG
Area DGBC =
Area DGBC = 24+12 = 36 sq units
What is the ratio of the shaded region to nonshaded region in the following diagram
ABC is an equilateral triangle and D, E and F are the midpoint of the sides.
Since ABC is an equilateral triangle and DEF is the midpoint. Thus they will divide the ABC in 4 equilateral triangle of side half of that of ABC
Let side of ABC = 2a units. Then the side of the smaller triangle is a unit.
Shaded region = Area of 3 small circles + Area DEF  Area of 1 small circle
Shaded region = Area of 2 small circles + Area DEF
Circles are an incircle of equilateral triangle of side "a"
Radius of this incircle
Area of 1 small circle =
Area of 2 small circle
Area of triangle DEF =
Shaded area =
Unshaded area = Total area  Shaded area
Unshaded area =  Shaded area
Unshaded area =
Unshaded area =
Ratio =
Among all the possible permutation of the word " VENKATESHAN" What is the probability that a word is chosen such that both the "A"s are before both the "E"s?
There are a total of 11 alphabets in VENKATESHAN which when arranged in ascending order are A, A, E, E, H K, N, N, S, T and V.
Total possible permutation are =
Now we need to find the cases where all the "A"s are before "E"s. There are total of 2 A and 2 E. If we pick places for A and E, they can be placed in one way. 4 places can be picked in ^{11}C_{4} ways.
Remaining 7 alphabets can be arranged in 7!/2! ways.
The number of ways possible =
Probability =
Probability =
How many 4digit numbers exist which is divisible by 3 or 8?
The divisibility rule of 3 states that the sum of digits has to be divisible by 3 in order to be divisible by 3.
Such numbers are 1002,1005,1008.....9999 : 3000 numbers.
The divisibility rules of 8 imply that the last 3 digits have to be divisible by 8: Thus "dcba" has to be divisible by 8. Such number are : 1000,1008,..9992 : 1125.
We have included the number which are divisible by 24 twice. Thus we have to remove those extra numbers.
Such number are : 1008,1032,...9984: 375 numbers.
The numbers of 4digit number which are divisible by 3 or 8: 3000+1125375 = 3750.
An absentminded shopkeeper interchanged the markup of m% and discount d% of a product. So, instead of making a profit of 8%, he made a loss of 12% on the product. What is the value of d^{2} + m^{2}?
Let the cost price be x
When markup percent is m% and discount given is d% then (1+m%)(1−d%)x=1.08x
Upon expanding we get
When markup percent is d% and discount given is m% then
(1+d%)(1−m%)x = 0.88x
Upon expanding we get
Adding (I) and (II) we get,
Substracting (I) and (II) we get,
or md =10
Squaring both sides, m^{2} + d^{2}  2md = 100
m^{2} + d^{2}  400 = 100
m^{2} + d^{2} = 500
A cunning rice merchant uses a faulty weighing machine to cheat. While buying the rice from the whole seller he uses a faulty machine which shows the quantity 20% less than actually on the scale. While selling the rice, he uses another faulty scale which shows 10% extra weight than that on the scale. He marks up the price of rice by 20% on the rate he bought from the wholesaler. Sherlock found out about this scam and asked the rice seller to give approximately a d% discount on the current marked price so that the rice seller doesn't make a profit or a loss. What is the value of [d]?
[X] represents the largest integer less than or equal to X.
Let the rate at which the whole seller sells the rice be Rs x per kg.
But the cunning merchant uses the faulty scale to trick the wholesaler. When the wholeseller puts in 1kg of rice, the machine will show 0.8kg of rice. Thus merchant will get 1 kg of rice for the price of 0.8x0.8x and thus Actual selling price for the wholeseller = Actual costprice for the merchant = Rs0.8x = 4x/5 per kg.
The rate at which he sells the rice = Rs 1.2x per kg.
When the merchant puts 1 kg of rice on the weighing machine, the machine will show 1.1 kg.
As per the rate the customer has to pay 1.2x x 1.1 = 1.32x for 1 kg of rice.
Actual selling price for the merchant= Rs 1.32x per kg
Let Sherlock by y kgs of rice.
Cost price to the merchant = 0.8xy
Actual selling price for the merchant = 1.32 xy
Discount = d
In order to be noprofit no loss
Siddhart is a penseller. He sells a pen such that the profit earned by selling 10 pens is equal to the cost price of 1 pen. The discount he gave on the marked price of the pen is 3 times the profit he earned by selling the pen. What approximate discount % should he offer the customer if he wishes to have a profit of 20%
Let the profit be P and cost price be C.P
Then 10 P = C.P ....(I)
Selling Price = Cost Price + Profit = 10 P +P = 11P
Discount given = 3P.
Marked price = Selling Price + Discount = 11P+3P = 14P.
Let the discount given to ensure profit of 20% be d%.
Ram invests a total of Rs 1,50,000 into two schemes in the ratio 2:1. Both of the schemes have interest rates which are integers. After 2 years, Ram received a total of 1,93,000 in return. If one of the interest rates is 20%, and the interest rate of the other is R%, what is the value of R? Assume the interest to be compounded annually
Let the scheme be Scheme I and Scheme II. Money spent on scheme I =
Money on scheme II = 50,000
We don't know which of the scheme has an interest rate of 20%. Thus there will be 2 cases
Case I: Scheme I has a 20% return rate, In this case, let r be return rate for scheme II
Here we can see that the RHS is less than 1, the value of rr has to be negative. Which is not possible. Thus this case is rejected
Case II: Scheme II has a 20% return rate, In this case, let r be return rate for scheme I
Therefore r = 10. Which is an integer
A number N is given by = 2^{5} x 3^{8} x 4^{2} x 5^{3} x 6 x 7^{2}
If a certain factor of N is not divisible by 9, the probability that the factor is an odd number is m/n where 'n' is a natural number less than 20. Find the value of m+n.
Let us start by writing the N in empirical form which is 2^{5} x 3^{8} x 2^{4} x 5^{3 }x 2 x 3 x 7^{2}
Which equals 2^{10} x 3^{9 }x 5^{3} x 7^{2}
Let A = number of factors not divisible by 9
B = Number of Factors which are odd
We have to find
(A∩B) = Number of factors not divisible by 9 and are odd. It implies it does not have 2 as a factor and the highest power of 3 can be 1. Such type of factors are = (1+1)(3+1)(2+1) = 24
A = Number of factors that are not divisible by 9. Thus the maximum power of 3 they can have is 1. Such number are = (10+1)(1+1)(3+1)(2+1) = 264
Probability = 24/264 = 1/11
m+n = 12.
Let N be a natural number < 1500 exist such that when N divided by 7 has the same remainder when N^{3} is divided by 7. How many such values of N are there?
We have to find values of N such that N and N^{3 }both have the same remainder when divided by 7
Thus (N mod 7) =(N^{3} mod 7)
It can be written as
(N mod 7) = (N x N x N) mod7 = (Nmod7) x (Nmod7) x (Nmod7).
Thus it can be implied that
(N mod 7) = (N mod 7)^{3}
When N = 1 then (Nmod7) = (Nmod7)^{3} = 1 so N =1 is a solution
When N = 2 then (Nmod7) = 2 and (Nmod7)^{3} = 1 so N ≠ 2
When N = 7 then the remainder is 0. Thus N has to be of form 7k, 7k+1 and 7k+6 to meet the required criteria
N< 1500 of from 7k = 7,14, .... 1498 which is 214 terms
N<1500 of from 7k+1 = 1, 8,15, .... 1499 which is again 215 terms
N<1500 of from 7k+6 = 6,15, .... 1497 which is again 214 terms
Total terms = 214+215+214 = 643.
A man was driving from city X to city Y. After travelling for 3 hours, his car develops a fault and his speed reduced to 1/3^{rd} of his original speed. He was originally supposed to complete the journey in 17 hours. What was % increase in his overall travelling time?
t/3 = 14 Let the original speed of the car be xx km/hr
Since he was originally supposed to cover the distance in 17 hours, The total distance of the journey is 17x km.
After the malfunction, his speed will be x/3. Let him take time "t" hours to complete after the vehicle malfunction. Equating the distances we get
3x + (x/3)t = 17x
Cancelling x from both sides
We get t/3 = 14
t = 42 hours.
Initial travelling time = 17 hours.
Final travelling time = 3+42 = 45 hours.
% increase in time =
In a race. A beats B by 120m or 20 seconds. B beats C by 50m or 10 seconds. What is the sum of the speeds of A, B and C? (in m/sec)
300m race A=10m/s. B = 6m/s C = 5m/s
Let the distance of the race be x meters. Let the speed of A, B and C be V_{a}, V_{b }and V_{c} (in m/sec)
A beats B by 120m or 20 seconds
Thus
Putting the value of x/V_{a} from (I) to (II)
It gives V_{b }= 6 m/s
Now coming to B beats C by 50m or 10 seconds
From (III) and (IV) we get
or V_{c }= 5m/sec
From (III)
Cross multiplying
5x=6(x−50) or x= 300 meters.
Sum = 10+6+5 = 21
A, B and C are 3 friends who have to go to another city Z. A has a bike that has an average speed of 40 km/hr. B and C both can walk with an average speed of 5km/hr. To minimise the time taken for them to reach the other city it was decided that C will start walking towards the city Z while A will gives a lift to B for a certain distance after which A will dropoff B and B will start walking towards Z. A will go back to pick up C and then will start moving towards city Z. They all reach the destination at the same time. What percentage of the overall journey time, did B spend walking?
A and B start on bike and A drops B at R. The time taken is T_{1}. Hence , PR 40T_{1}.
At the same time, C walks from P to Q. Distance covered = 5T_{1}.
Distance between A and C = 40T_{1}  5T_{1} = 35T_{1}.
Relative speed between A and C = 40 + 5 = 45.
Time taken to meet = 35/45T_{1} = 7/9T_{1}
Now, in the meantime, B also walks from R to T. His speed is same as C, so distance travelled is same, i.e, 5 x 7/9T_{1} = 35/9T_{1}.
Hence, the distnce between the bike and B when the bike starts from S is ST, i.e, 35T_{1}.
Now, let they meet at Z after time T_{2}.
Relative speed = 40  5 = 35.
Hence, 35 T_{2} = 35T_{1}
T_{2} = T_{1}
Hence, time taken by the overall journey = T_{1} + 7/9T_{1} + T_{1} = 25/9T_{1}
Time spent by B walking = Toatl time  T_{1} = 25/9T_{1}T_{1} = 16/9T_{1}.
Hence, percentage time = 16/25 x 100 = 64%.
Alternate solution:
Let us divide all the activities into certain time periods for simplification. Let all of them start at time t = 0.
(1) From time t = 0 to t_{1}. A and B will move towards Z on bike and C will walk towards Z. At exactly t_{1}, A will drop B and start moving back to pick up C. Distance covered by A = 40t_{1}, Distance covered by B = 40t_{1} and Distance covered by C = 5(t_{2}  t_{1}) and distance by A in this time period =  40(t_{2}  t_{1}). We have taken"" as A is moving in opposite direction 3) From time t = t_{2} to t_{3}. A has picked up C and now both are on bike moving towards city Z. 0. B is walking towards city Z. They all reach at city Z at same time t_{3} Distance travelled by A = 40(t_{3}  t_{2}). Distance covered by B = 5(t_{3}  t_{2}). Distance travelled by C = 40 (t_{3}  t_{2})
Let the overall distance be d
Distance travelled by A = 40t_{1}  40 (t_{2}  t_{1}) + 40(t_{3}  t_{2}) = d
Thus 40(2t_{1} + t_{3}  2t_{2}) = d ...(I)
Distance travelled by B = 40t_{1} + 5(t_{2}  t_{1})+5(t_{3}t_{2})
35t_{1} + 5t_{3} = d ...(II)
Distance travelled by C = 5t_{1} + 5(t_{2}  t_{1}) + 40(t_{3}  t_{2}) = d
40t_{3}  35t_{2} = d ...(III)
Equating (II) and (III)
35t_{1} + 5t_{3} = 40t_{3}  35t_{2}
t_{1} = t_{3}  t_{2} ...(IV)
Equating (I) and (III)
80t_{1} + 40t_{3}  80t_{2} = 40t_{3}  35t_{2}
⇒ 80t_{1} = 45t_{2}
Or t_{2} = (16/9)t_{1} ...(V)
Putting (V) in(IV)
From time t_{1} to t_{3} B was walking and total journey time was t_{3}
% time on walking =
% time on walking =
% time walking =
2 men and a woman can complete a task in a certain number of days. If 13 men and 12 women work on the same task they can complete it in 1/8^{th }of days required earlier. The number of days taken by 13 men and 12 women is equal to the number of days taken by 4 men and 27 children to finish the same task.
If 2 children and a man can complete another task in 12 days. What is the minimum number of days required by 3 women and 1 child to do the same task?
Even if they have to work for a fraction of a day, it will be counted as a whole day.
Let the amount of work done by a man in 1 day be "m" units and the amount of work done by a woman in 1 day be "w" units. Let's assume they take N days to complete
As per the first line we can say that
(2m + w) x N = (N/8)(13m + 12w)
On cancelling the common factors and rearranging we get
(2m + w) x 8 = (13 m + 12w)
Which implies 16m + 8w = (13m + 12w)
or 3m = 4w ...(I)
It is also given that it is equal to 4 men and 27 children. Let a child to "c" units of work in a day
Then
(N/8) (13m + 12w) = (N/8)(4m +27c)
Or, 13m + 12w = 4m + 27c
Putting value of w from (I)
13m+9m=4m+27c
or, 18m=27c or 2m = 3c...(II)
Given that another task takes 12 days to be completed by 2 children and a man. Let us assume that it takes x days to be completed by 3 women and 1 child. Equating the amount of work done
Cancelling m and cross multiplying
9.6 days is needed. 10 is the next biggest number .
There are 3 types of sugar, type A, type B and type C. The cost of each of the is Rs 35/kg, Rs, 40/kg and Rs 42/kg. The shopkeeper mixes them in a fixed ratio. He sold 40 kg of the mixture for Rs 1900 and had a profit of 25%. If the ratio of type A, type B and type C in the ratio x:y:z where x,y,z are integers. What is the minimum value of x+y+z?
Shopkeeper sold 40 kg of mixed sugar for Rs 1900. Selling price per kg = 1900/40 = Rs 1900/40 = Rs 47.5/kg
Cost price per kg = Rs 38/kg
SInce 35 < 38 < 40.
We have to find the ratio of sugar of mixture I containing type A and B and mixture 2 containing A and C
For mixture 1 let the quantity of type A and type B be a:b
Then 35a + 40b = 38(a+b) or 3a = 2b. Thus a:b = 2:3....(I)
For mixture 2 let the quantity of type A and type C be a:c
35a + 42c = 38(a+c) or 3a = 4c or a:c = 4:3 ...(II)
(I)+(II) gives a:b:c = 6:3:3. Which can be simplified to 2:1:1
Fresh grapes have 75% water and the remaining 25% as fruit pulp. A shopkeeper bought a certain quantity of fresh grapes and let it dry so that the fraction of pulp in the grapes increase by 1/3^{rd} of the original quantity. If the ratio of the evaporated water to the pulp is m:n where m and n are the lowest possible integers. Which of the following is the has maximum absolute value?
Let 100kg of fresh grapes be there. Then 25 kgs is the pulp and 75 kg is the weight of water,
Initial fraction of pulp = 25% = 1/4
FInal fraction of pulp =
SInce the weight of pulp will not change
Putting pulp = 25kgs
This gives updated weight of water as 50 kgs.
Evaporated water = 7550 = 25
Ratio = 25:25 = 1:1 = m:n
a) n5m =15 = 4
b) n+m = 1+1 =2
c) 6m3n = 63 = 3
d) m3n = 13 = 2
A has the greatest value
What is the sum of the first 20 numbers in the series 8,24,62,122, 204
Let us look at the series 8, 24, 62, 122
Their first level difference = 248 = 16, 6224= 38 and 12262= 60
Their second level difference = 3816 = 22, 6038 = 22 which are same. So this series varies with power of 2
Let T_{n} represent the term of series. Then T_{n} can be assumed as an^{2} + bn + c
From (III)(II) we get 5a+b = 38
From (II)(I) we get 3a+b =16
Eliminating b we get 2a = 22 or a=11. Thus b = 17 and c = 14
Sum = 315703570+280 = 28280
f(x) and g(x) are 2 polynomial functions such that f(g(x)) = x^{2} + 12x + 33 and g(f(x)) = x2 + 4x + 5. it is given that f(26) = 46. What is maximum possible value of f(3)?
We know that f(g(x)) =x^{2} + 12x +33
Thus f(g(f(x))) = f(x^{2}) + 12f(x) + 33
Putting g(f(x)) = x^{2} + 4x + 5
Thus f(x^{2} + 4x + 5) = f(x)^{2} + 12f(x) + 33
Given f(26) = 46
putting x^{2} + 4x + 5 = 26
Or x^{2} + 4x  21 = 0
Or (x+7)(x3) =0.
Putting x = 3 in f(x^{2} + 4x + 5) = f(x)^{2} + 12f(x) + 33
f(26) = 46 = f(3)^{2}+12f(3)+33
Or f(3)^{2} + 12f(3)  13 = 0
(f(3)+13)(f(3)1) = 0 Thus f(3) = 1 or 13
1 > 13 so it is the answer
Let aa be the value of the common area bounded by the following 2 equations:
What is the value of 4a?
Since both the terms of x and y have modulus, it will be symmetric in all 4 quadrants. We can find the value in the first quadrant and multiply t by 4 to get the desired result
Thus, y  x ≥ 5 and y + x ≤ 10
Area shaded in red shows the feasible region in quadrant 1. Its area = (1/2)5x2.5=6.25
Overall area = a = 4 x 6.25 = 25
4a = 4 x 25 = 100
At how many points do the following curves C1 and C2 intersect?
From curve C_{1} we can see that x ≥ 0 and y can be either positive or negative. Thus either intersection happens in the first quadrant or fourth quadrant.
x^{1/2} = y or x = y^{2} ...(I)) from C_{1}
Putting this in the C_{2} equation
y^{2}(y) = 4y^{2} + y
On rearranging we get y^{3} + 4y^{2 } y = 0
y(y^{2} + 4y  1) = 0
Discriminate of (y^{2} + 4y  1) is positive so it must have 2 distinct roots ≠ 0
y(y^{2} + 4y  1) = 0 has 3 distinct roots.
For each value of y there will be unique x such that x^{1/2} = Y.
Rajesh is 10 years younger to Baskar. 10 years back, Rajesh's age was twothirds that of Baskar's. How old is Baskar now?
Let the present age of Baskar be 'b' and that of Rajesh be "r". So, r=b−10 ...(1)
10 years back Rajesh was ( r−10) years old. 10 years back Baskar was (b−10) years old.
The question states that 10 years back Rajesh was two thirds as old as Baskar was. i.e., (r−10)=(2/3)×(b−10) ...(2)
Cross multiplying, we get 3(r−10)=2(b−10) or 3r−30=2b−20 ..(2)
From eqn (1) we can substitute r as (b−10) in eqn ( 2) So, 3(b−10)−30=2b−20
or 3b−30−30=2b−20
or b=40
The present age of Baskar is 40 years.
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