CAT Mock Test- 8


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Attempt CAT Mock Test- 8 | 66 questions in 120 minutes | Mock test for CAT preparation | Free important questions MCQ to study CAT Mock Test Series for CAT Exam | Download free PDF with solutions
QUESTION: 1

Read the passage carefully and answer the questions that follow:

The word “bias” commonly appears in conversations about mistaken judgments and unfortunate decisions. We use it when there is discrimination, for instance against women or in favor of Ivy League graduates. But the meaning of the word is broader: A bias is any predictable error that inclines your judgment in a particular direction. For instance, we speak of bias when forecasts of sales are consistently optimistic or investment decisions overly cautious.

Society has devoted a lot of attention to the problem of bias — and rightly so. But when it comes to mistaken judgments and unfortunate decisions, there is another type of error that attracts far less attention: noise. To see the difference between bias and noise, consider your bathroom scale. If on average the readings it gives are too high (or too low), the scale is biased. If it shows different readings when you step on it several times in quick succession, the scale is noisy. While bias is the average of errors, noise is their variability.

Although it is often ignored, noise is a large source of malfunction in society. In a 1981 study, for example, 208 federal judges were asked to determine the appropriate sentences for the same 16 cases. The cases were described by the characteristics of the offense (robbery or fraud, violent or not) and of the defendant (young or old, repeat or first-time offender, accomplice or principal). The average difference between the sentences that two randomly chosen judges gave for the same crime was more than 3.5 years. Considering that the mean sentence was seven years, that was a disconcerting amount of noise. Noise in real courtrooms is surely only worse, as actual cases are more complex and difficult to judge than stylized vignettes. It is hard to escape the conclusion that sentencing is in part a lottery, because the punishment can vary by many years depending on which judge is assigned to the case and on the judge’s state of mind on that day. The judicial system is unacceptably noisy.

Noise causes error, as does bias, but the two kinds of error are separate and independent. A company’s hiring decisions could be unbiased overall if some of its recruiters favor men and others favor women. However, its hiring decisions would be noisy, and the company would make many bad choices. Where does noise come from? There is much evidence that irrelevant circumstances can affect judgments. In the case of criminal sentencing, for instance, a judge’s mood, fatigue and even the weather can all have modest but detectable effects on judicial decisions. Another source of noise is that people can have different general tendencies. Judges often vary in the severity of the sentences they mete out: There are “hanging” judges and lenient ones.

A third source of noise is less intuitive, although it is usually the largest: People can have not only different general tendencies (say, whether they are harsh or lenient) but also different patterns of assessment (say, which types of cases they believe merit being harsh or lenient about). Underwriters differ in their views of what is risky, and doctors in their views of which ailments require treatment. We celebrate the uniqueness of individuals, but we tend to forget that, when we expect consistency, uniqueness becomes a liability.

Q. Which of the following statements is the author most likely to agree with?

Solution:

In the second paragraph, the author points out that noise gets far less attention than bias. However, the author does not assert that noise is a more serious error compared to bias. Option A can be eliminated.

{We celebrate the uniqueness of individuals, but we tend to forget that, when we expect consistency, uniqueness becomes a liability.} The author posits that when expecting consistency, the distinctness of each individual might be undesirable/burdensome. Option B echoes this view. 

{In the case of criminal sentencing, for instance, a judge’s mood, fatigue and even the weather can all have modest but detectable effects on judicial decisions} The author mentions that even small factors can have a "modest, but a detectable influence" on decisions. The author would have agreed if the option read that small factors influence decision making. But he does not say that the influence is huge/substantial, as mentioned in Option C. Hence, it is a distortion and can be eliminated.

{ Noise in real courtrooms is surely only worse, as actual cases are more complex and difficult to judge than stylized vignettes. It is hard to escape the conclusion that sentencing is in part a lottery, because the punishment can vary by many years depending on which judge is assigned to the case and on the judge’s state of mind on that day. The judicial system is unacceptably noisy.} While the author does discuss the complexity of courtroom cases causing noise in judgments (or punishments meted out), there is no mention of bias. Hence, Option D is a distortion.

Therefore, of the given choices, Option B is the correct answer.

QUESTION: 2

Read the passage carefully and answer the questions that follow:

The word “bias” commonly appears in conversations about mistaken judgments and unfortunate decisions. We use it when there is discrimination, for instance against women or in favor of Ivy League graduates. But the meaning of the word is broader: A bias is any predictable error that inclines your judgment in a particular direction. For instance, we speak of bias when forecasts of sales are consistently optimistic or investment decisions overly cautious.

Society has devoted a lot of attention to the problem of bias — and rightly so. But when it comes to mistaken judgments and unfortunate decisions, there is another type of error that attracts far less attention: noise. To see the difference between bias and noise, consider your bathroom scale. If on average the readings it gives are too high (or too low), the scale is biased. If it shows different readings when you step on it several times in quick succession, the scale is noisy. While bias is the average of errors, noise is their variability.

Although it is often ignored, noise is a large source of malfunction in society. In a 1981 study, for example, 208 federal judges were asked to determine the appropriate sentences for the same 16 cases. The cases were described by the characteristics of the offense (robbery or fraud, violent or not) and of the defendant (young or old, repeat or first-time offender, accomplice or principal). The average difference between the sentences that two randomly chosen judges gave for the same crime was more than 3.5 years. Considering that the mean sentence was seven years, that was a disconcerting amount of noise. Noise in real courtrooms is surely only worse, as actual cases are more complex and difficult to judge than stylized vignettes. It is hard to escape the conclusion that sentencing is in part a lottery, because the punishment can vary by many years depending on which judge is assigned to the case and on the judge’s state of mind on that day. The judicial system is unacceptably noisy.

Noise causes error, as does bias, but the two kinds of error are separate and independent. A company’s hiring decisions could be unbiased overall if some of its recruiters favor men and others favor women. However, its hiring decisions would be noisy, and the company would make many bad choices. Where does noise come from? There is much evidence that irrelevant circumstances can affect judgments. In the case of criminal sentencing, for instance, a judge’s mood, fatigue and even the weather can all have modest but detectable effects on judicial decisions. Another source of noise is that people can have different general tendencies. Judges often vary in the severity of the sentences they mete out: There are “hanging” judges and lenient ones.

A third source of noise is less intuitive, although it is usually the largest: People can have not only different general tendencies (say, whether they are harsh or lenient) but also different patterns of assessment (say, which types of cases they believe merit being harsh or lenient about). Underwriters differ in their views of what is risky, and doctors in their views of which ailments require treatment. We celebrate the uniqueness of individuals, but we tend to forget that, when we expect consistency, uniqueness becomes a liability.

Q. Which of the following can serve as an example of 'noise' as per the the passage?

Solution:

{While bias is the average of errors, noise is their variability.} Noise, hence, refers to variability in the outcomes predicted for the same event/case. The judicial system example exemplifies this.
Option A is a valid example, as it highlights the variance in judgements of people analysing the same risk. Hence it is our answer
The surgical decisions may have been taken in completely different circumstances, and the patients may have presented with distinct issues. Hence, it is not the same event/situation. Option B can be eliminated.
Option C is an incorrect example. The revisions may have been forced due to changing economic conditions. Hence there is a change in the situation.
Option D talks about the discrimination against a particular group of people, and it is not varied from person to person. This would be better classified as bias, as a mean error of judgement is being talked about. Hence D can be eliminated too.

QUESTION: 3

Read the passage carefully and answer the questions that follow:

The word “bias” commonly appears in conversations about mistaken judgments and unfortunate decisions. We use it when there is discrimination, for instance against women or in favor of Ivy League graduates. But the meaning of the word is broader: A bias is any predictable error that inclines your judgment in a particular direction. For instance, we speak of bias when forecasts of sales are consistently optimistic or investment decisions overly cautious.

Society has devoted a lot of attention to the problem of bias — and rightly so. But when it comes to mistaken judgments and unfortunate decisions, there is another type of error that attracts far less attention: noise. To see the difference between bias and noise, consider your bathroom scale. If on average the readings it gives are too high (or too low), the scale is biased. If it shows different readings when you step on it several times in quick succession, the scale is noisy. While bias is the average of errors, noise is their variability.

Although it is often ignored, noise is a large source of malfunction in society. In a 1981 study, for example, 208 federal judges were asked to determine the appropriate sentences for the same 16 cases. The cases were described by the characteristics of the offense (robbery or fraud, violent or not) and of the defendant (young or old, repeat or first-time offender, accomplice or principal). The average difference between the sentences that two randomly chosen judges gave for the same crime was more than 3.5 years. Considering that the mean sentence was seven years, that was a disconcerting amount of noise. Noise in real courtrooms is surely only worse, as actual cases are more complex and difficult to judge than stylized vignettes. It is hard to escape the conclusion that sentencing is in part a lottery, because the punishment can vary by many years depending on which judge is assigned to the case and on the judge’s state of mind on that day. The judicial system is unacceptably noisy.

Noise causes error, as does bias, but the two kinds of error are separate and independent. A company’s hiring decisions could be unbiased overall if some of its recruiters favor men and others favor women. However, its hiring decisions would be noisy, and the company would make many bad choices. Where does noise come from? There is much evidence that irrelevant circumstances can affect judgments. In the case of criminal sentencing, for instance, a judge’s mood, fatigue and even the weather can all have modest but detectable effects on judicial decisions. Another source of noise is that people can have different general tendencies. Judges often vary in the severity of the sentences they mete out: There are “hanging” judges and lenient ones.

A third source of noise is less intuitive, although it is usually the largest: People can have not only different general tendencies (say, whether they are harsh or lenient) but also different patterns of assessment (say, which types of cases they believe merit being harsh or lenient about). Underwriters differ in their views of what is risky, and doctors in their views of which ailments require treatment. We celebrate the uniqueness of individuals, but we tend to forget that, when we expect consistency, uniqueness becomes a liability.

Q. According to the passage, noise in a judicial system could lead to which of the following consequences?

Solution:

In the third paragraph, the author discusses the pervasiveness of noise in the judicial system and how it may cause the judges the dish out different sentences for a similar crime. ("...because the punishment can vary by many years depending on which judge is assigned to the case and on the judge’s state of mind on that day")
Option A can be safely eliminated. The author discusses the difference in sentences of convicted persons, not wrongful convictions.
Option B is out of scope. The length of judicial proceedings has not been expanded upon in the passage.
Option C is in line with the idea elucidated above. When different sentences are meted out for the same offence, we can discern that the judgments are noisy.  

Option D is too extreme. The author gives an example where noise error leads to a difference of a few years of his sentence. This does not mean that an irrelevant factor like mood will lead to the complete overturn of a verdict. It can only increase/decrease the sentence to an extent. Hence Option D can be eliminated too.

QUESTION: 4

Read the passage carefully and answer the questions that follow:

The word “bias” commonly appears in conversations about mistaken judgments and unfortunate decisions. We use it when there is discrimination, for instance against women or in favor of Ivy League graduates. But the meaning of the word is broader: A bias is any predictable error that inclines your judgment in a particular direction. For instance, we speak of bias when forecasts of sales are consistently optimistic or investment decisions overly cautious.

Society has devoted a lot of attention to the problem of bias — and rightly so. But when it comes to mistaken judgments and unfortunate decisions, there is another type of error that attracts far less attention: noise. To see the difference between bias and noise, consider your bathroom scale. If on average the readings it gives are too high (or too low), the scale is biased. If it shows different readings when you step on it several times in quick succession, the scale is noisy. While bias is the average of errors, noise is their variability.

Although it is often ignored, noise is a large source of malfunction in society. In a 1981 study, for example, 208 federal judges were asked to determine the appropriate sentences for the same 16 cases. The cases were described by the characteristics of the offense (robbery or fraud, violent or not) and of the defendant (young or old, repeat or first-time offender, accomplice or principal). The average difference between the sentences that two randomly chosen judges gave for the same crime was more than 3.5 years. Considering that the mean sentence was seven years, that was a disconcerting amount of noise. Noise in real courtrooms is surely only worse, as actual cases are more complex and difficult to judge than stylized vignettes. It is hard to escape the conclusion that sentencing is in part a lottery, because the punishment can vary by many years depending on which judge is assigned to the case and on the judge’s state of mind on that day. The judicial system is unacceptably noisy.

Noise causes error, as does bias, but the two kinds of error are separate and independent. A company’s hiring decisions could be unbiased overall if some of its recruiters favor men and others favor women. However, its hiring decisions would be noisy, and the company would make many bad choices. Where does noise come from? There is much evidence that irrelevant circumstances can affect judgments. In the case of criminal sentencing, for instance, a judge’s mood, fatigue and even the weather can all have modest but detectable effects on judicial decisions. Another source of noise is that people can have different general tendencies. Judges often vary in the severity of the sentences they mete out: There are “hanging” judges and lenient ones.

A third source of noise is less intuitive, although it is usually the largest: People can have not only different general tendencies (say, whether they are harsh or lenient) but also different patterns of assessment (say, which types of cases they believe merit being harsh or lenient about). Underwriters differ in their views of what is risky, and doctors in their views of which ailments require treatment. We celebrate the uniqueness of individuals, but we tend to forget that, when we expect consistency, uniqueness becomes a liability.

Q. According to the passage, noise and bias differ in which of the following ways?

Solution:

In the first paragraph, the author states the following-{ A bias is any predictable error that inclines your judgment in a particular direction. For instance, we speak of bias when forecasts of sales are consistently optimistic or investment decisions overly cautious.}  Hence, although it is an error, bias reflects an element of consistency, that most of the values are consistently above or below the correct value. The 'bathroom scale' example discussed in the second paragraph strengthens this idea. The values displayed by the scale are too low or too high consistently.
On the other hand, noise, which reflects variability and where individual values are consistently different from one another, lacks an element of consistency.
Option A captures the above idea correctly. Option A is the answer.
Option B cannot be validated. Bias is any predictable error that inclines your judgment in a particular direction. This inclination could be of an individual or of a group of individuals. 
Option C can be eliminated. The author does not assert that noise is an unpredictable error. 
Option D has not been implied in the passage and can be eliminated. 

QUESTION: 5

Read the passage carefully and answer the questions that follow:

Information has never been more accessible or less reliable. So we are advised to check our sources carefully. There is so much talk of “fake news” that the term has entirely lost meaning. At school, we are taught to avoid Wikipedia, or at the very least never admit to using it in our citations. And most sources on the world wide web have been built without the standardized attributions that scaffold other forms of knowledge dissemination; they are therefore seen as degraded, even as they illuminate.

But it was only relatively recently that academic disciplines designed rigid systems for categorizing and organizing source material at all. Historian Anthony Grafton traces the genealogy of the footnote in an excellent book, which reveals many origin stories. It turns out that footnotes are related to early systems of marginalia, glosses, and annotation that existed in theology, early histories, and Medieval law. The footnote in something like its modern form seems to have been devised in the seventeenth century, and has proliferated since, with increasing standardization and rigor. And yet, Grafton writes, “appearances of uniformity are deceptive. To the inexpert, footnotes look like deep root systems, solid and fixed; to the connoisseur, however, they reveal themselves as anthills, swarming with constructive and combative activity.”

The purpose of citation, broadly speaking, is to give others credit, but it does much more than that. Famously, citations can be the sources of great enmity — a quick dismissal of a rival argument with a “cf.” They can serve a social purpose, as sly thank-yous to friends and mentors. They can perform a kind of box-checking of requisite major works. (As Grafton points out, the omission of these works can itself be a statement.) Attribution, significantly, allows others to check your work, or at least gives the illusion that they could, following a web of sources back to the origins. But perhaps above all else, citations serve a dual purpose that seems at once complementary and conflicting; they acknowledge a debt to a larger body of work while also conferring on oneself a certain kind of erudition and expertise.

Like many systems that appear meticulous, the writing of citations is a subjective art. Never more so than in fiction, where citation is an entirely other kind of animal, not required or even expected, except in the “acknowledgments” page, which is often a who’s who of the publishing world. But in the last two decades, bibliographies and sources cited pages have increasingly cropped up in the backs of novels. “It’s terribly off-putting,” James Wood said of this fad in 2006. “It would be very odd if Thomas Hardy had put at the end of all his books, ‘I’m thankful to the Dorset County Chronicle for dialect books from the 18th century.’ We expect authors to do that work, and I don’t see why we should praise them for that work.” Wood has a point, or had one — at their worst, citations in fiction are annoying, driven by an author’s anxiety to show off what he has read, to check the right boxes.

Q. Which of the following is a reason why citation is done?

Solution:

The author does not mention the improvement in the credibility of the author's work. Citations merely allow others to check the work and decide for themselves whether the work has any weight. Hence, Option A is beyond the scope of the passage and can be eliminated.
"They can perform a kind of box-checking of requisite major works." 
Option B can be inferred from this line. By citing major works, the author alludes to his erudition and familiarity on the topic, which means that he has referred to the mandatory amount of previous works in the field.
Famously, citations can be the sources of great enmity — a quick dismissal of a rival argument with a “cf.” 
Here, the author talks about negating an argument that is contrary to the author's. But the option reads 'rival's argument' which means argument put forward by his rival, which may not be contrary to the author's. Hence, Option C is a distortion and can be eliminated.
Attribution, significantly, allows others to check your work or at least gives the illusion that they could, following a web of sources back to the origins.
Option D talks about a significant increase in the visibility of the author's work. Whereas, in the passage, the adverb significantly talks about a significant role of attribution being allowing others to check the author's work. This means that the people who are viewing the author's work can check the credibility (or have an illusion of the same) through the attributions. This is different from more people checking out the work, as suggested in the option. Hence Option D can be eliminated.

QUESTION: 6

Read the passage carefully and answer the questions that follow:

Information has never been more accessible or less reliable. So we are advised to check our sources carefully. There is so much talk of “fake news” that the term has entirely lost meaning. At school, we are taught to avoid Wikipedia, or at the very least never admit to using it in our citations. And most sources on the world wide web have been built without the standardized attributions that scaffold other forms of knowledge dissemination; they are therefore seen as degraded, even as they illuminate.

But it was only relatively recently that academic disciplines designed rigid systems for categorizing and organizing source material at all. Historian Anthony Grafton traces the genealogy of the footnote in an excellent book, which reveals many origin stories. It turns out that footnotes are related to early systems of marginalia, glosses, and annotation that existed in theology, early histories, and Medieval law. The footnote in something like its modern form seems to have been devised in the seventeenth century, and has proliferated since, with increasing standardization and rigor. And yet, Grafton writes, “appearances of uniformity are deceptive. To the inexpert, footnotes look like deep root systems, solid and fixed; to the connoisseur, however, they reveal themselves as anthills, swarming with constructive and combative activity.”

The purpose of citation, broadly speaking, is to give others credit, but it does much more than that. Famously, citations can be the sources of great enmity — a quick dismissal of a rival argument with a “cf.” They can serve a social purpose, as sly thank-yous to friends and mentors. They can perform a kind of box-checking of requisite major works. (As Grafton points out, the omission of these works can itself be a statement.) Attribution, significantly, allows others to check your work, or at least gives the illusion that they could, following a web of sources back to the origins. But perhaps above all else, citations serve a dual purpose that seems at once complementary and conflicting; they acknowledge a debt to a larger body of work while also conferring on oneself a certain kind of erudition and expertise.

Like many systems that appear meticulous, the writing of citations is a subjective art. Never more so than in fiction, where citation is an entirely other kind of animal, not required or even expected, except in the “acknowledgments” page, which is often a who’s who of the publishing world. But in the last two decades, bibliographies and sources cited pages have increasingly cropped up in the backs of novels. “It’s terribly off-putting,” James Wood said of this fad in 2006. “It would be very odd if Thomas Hardy had put at the end of all his books, ‘I’m thankful to the Dorset County Chronicle for dialect books from the 18th century.’ We expect authors to do that work, and I don’t see why we should praise them for that work.” Wood has a point, or had one — at their worst, citations in fiction are annoying, driven by an author’s anxiety to show off what he has read, to check the right boxes.

Q. What can be inferred about the author's stance on including citations in works of fiction from the passage?

Solution:

The author mentions in the last paragraph that citations are not required or expected outside of the acknowledgements page. Overall, their purpose seems to be self-aggrandisement and showing that they have done some research, which is already expected of them.
Option A does not reflect the author's view, because the author has taken a complaining tone while mentioning the checking of boxes, which means that he does not approve of the same. Hence, A cannot be the answer.
Option B is covered above and can be the answer.
The term 'off-putting' has been introduced by James Wood and not necessarily defines the author's stance. Hence, Option C can be eliminated too.
The author mentions that citations are subjective to allow himself to criticize their usage in some areas. Though he calls it a 'different kind of animal', he clarifies his stance in the subsequent line indicating that this metaphor has a negative connotation, and he does not approve of the use. Option D defines the use as uniquely appealing, which is contrary in spirit to what the author is arguing. Hence it can be eliminated.

QUESTION: 7

Read the passage carefully and answer the questions that follow:

Information has never been more accessible or less reliable. So we are advised to check our sources carefully. There is so much talk of “fake news” that the term has entirely lost meaning. At school, we are taught to avoid Wikipedia, or at the very least never admit to using it in our citations. And most sources on the world wide web have been built without the standardized attributions that scaffold other forms of knowledge dissemination; they are therefore seen as degraded, even as they illuminate.

But it was only relatively recently that academic disciplines designed rigid systems for categorizing and organizing source material at all. Historian Anthony Grafton traces the genealogy of the footnote in an excellent book, which reveals many origin stories. It turns out that footnotes are related to early systems of marginalia, glosses, and annotation that existed in theology, early histories, and Medieval law. The footnote in something like its modern form seems to have been devised in the seventeenth century, and has proliferated since, with increasing standardization and rigor. And yet, Grafton writes, “appearances of uniformity are deceptive. To the inexpert, footnotes look like deep root systems, solid and fixed; to the connoisseur, however, they reveal themselves as anthills, swarming with constructive and combative activity.”

The purpose of citation, broadly speaking, is to give others credit, but it does much more than that. Famously, citations can be the sources of great enmity — a quick dismissal of a rival argument with a “cf.” They can serve a social purpose, as sly thank-yous to friends and mentors. They can perform a kind of box-checking of requisite major works. (As Grafton points out, the omission of these works can itself be a statement.) Attribution, significantly, allows others to check your work, or at least gives the illusion that they could, following a web of sources back to the origins. But perhaps above all else, citations serve a dual purpose that seems at once complementary and conflicting; they acknowledge a debt to a larger body of work while also conferring on oneself a certain kind of erudition and expertise.

Like many systems that appear meticulous, the writing of citations is a subjective art. Never more so than in fiction, where citation is an entirely other kind of animal, not required or even expected, except in the “acknowledgments” page, which is often a who’s who of the publishing world. But in the last two decades, bibliographies and sources cited pages have increasingly cropped up in the backs of novels. “It’s terribly off-putting,” James Wood said of this fad in 2006. “It would be very odd if Thomas Hardy had put at the end of all his books, ‘I’m thankful to the Dorset County Chronicle for dialect books from the 18th century.’ We expect authors to do that work, and I don’t see why we should praise them for that work.” Wood has a point, or had one — at their worst, citations in fiction are annoying, driven by an author’s anxiety to show off what he has read, to check the right boxes.

Q. "Citations serve a dual purpose that seems at once complementary and conflicting." Which of the following best captures the reason why the author makes this statement?

Solution:

"But perhaps above all else, citations serve a dual purpose that seems at once complementary and conflicting; they acknowledge a debt to a larger body of work while also conferring on oneself a certain kind of erudition and expertise."
Citations are complementary and conflicting because they acknowledge all the work that has been done by others, and at the same time. they indirectly imply that the author has knowledge that is additional to the existing work. So, citations, help acknowledge a debt to a larger body of work and the influence it has had on the author. But these citations also, in a way, convey the fact that the author has improved upon the credited body of work through his effort. 
Option A captures this viewpoint of the author correctly. Option A is the answer.
Option B, about promoting a superior image vis-a-vis peers is out of the scope of the passage.
Option D completely misses the point being made in the passage through those lines. Hence, it can be eliminated.
Option C has not been implied in the passage and can be safely eliminated.

QUESTION: 8

Read the passage carefully and answer the questions that follow:

Information has never been more accessible or less reliable. So we are advised to check our sources carefully. There is so much talk of “fake news” that the term has entirely lost meaning. At school, we are taught to avoid Wikipedia, or at the very least never admit to using it in our citations. And most sources on the world wide web have been built without the standardized attributions that scaffold other forms of knowledge dissemination; they are therefore seen as degraded, even as they illuminate.

But it was only relatively recently that academic disciplines designed rigid systems for categorizing and organizing source material at all. Historian Anthony Grafton traces the genealogy of the footnote in an excellent book, which reveals many origin stories. It turns out that footnotes are related to early systems of marginalia, glosses, and annotation that existed in theology, early histories, and Medieval law. The footnote in something like its modern form seems to have been devised in the seventeenth century, and has proliferated since, with increasing standardization and rigor. And yet, Grafton writes, “appearances of uniformity are deceptive. To the inexpert, footnotes look like deep root systems, solid and fixed; to the connoisseur, however, they reveal themselves as anthills, swarming with constructive and combative activity.”

The purpose of citation, broadly speaking, is to give others credit, but it does much more than that. Famously, citations can be the sources of great enmity — a quick dismissal of a rival argument with a “cf.” They can serve a social purpose, as sly thank-yous to friends and mentors. They can perform a kind of box-checking of requisite major works. (As Grafton points out, the omission of these works can itself be a statement.) Attribution, significantly, allows others to check your work, or at least gives the illusion that they could, following a web of sources back to the origins. But perhaps above all else, citations serve a dual purpose that seems at once complementary and conflicting; they acknowledge a debt to a larger body of work while also conferring on oneself a certain kind of erudition and expertise.

Like many systems that appear meticulous, the writing of citations is a subjective art. Never more so than in fiction, where citation is an entirely other kind of animal, not required or even expected, except in the “acknowledgments” page, which is often a who’s who of the publishing world. But in the last two decades, bibliographies and sources cited pages have increasingly cropped up in the backs of novels. “It’s terribly off-putting,” James Wood said of this fad in 2006. “It would be very odd if Thomas Hardy had put at the end of all his books, ‘I’m thankful to the Dorset County Chronicle for dialect books from the 18th century.’ We expect authors to do that work, and I don’t see why we should praise them for that work.” Wood has a point, or had one — at their worst, citations in fiction are annoying, driven by an author’s anxiety to show off what he has read, to check the right boxes.

Q. Which of the following statements about footnotes can be inferred from the second paragraph?
I. According to Grafton, inexperts view footnotes as an immutable system with a singular purpose.
II. Footnotes, in their modern form, have attained a higher degree of standardization and rigour.
III. According to Grafton, experts view footnotes as a system that brews both beneficial and confrontational activities.
IV. Footnotes were an integral feature of Medieval literature, albeit in a form different from modern forms.

Solution:

Statement I is only partially true. While inexperts view it as a fixed and solid system, their view on the purpose it serves has not been discussed in the second paragraph. Hence, statement I cannot be inferred.
{The footnote in something like its modern form seems to have been devised in the seventeenth century and has proliferated since, with increasing standardization and rigor.} Statement II is a direct inference from this line.
{...to the connoisseur, however, they reveal themselves as anthills, swarming with constructive and combative activity.} Statement III can be inferred as well. Here, the phrase 'constructive and combative activity' is the key, so footnotes can sometimes be beneficial, whereas, on other occasions, it can be an avenue for academic confrontation. The author further expounds on these aspects of citations in the penultimate paragraph, where he says that they can brew enmity as well as prove to be very effective.
Statement IV is an incorrect generalization. In the passage, the author only talks about Medieval Law and not Medieval literature in general. Hence, statement IV cannot be inferred.
Hence, only statements II and III can be inferred; Option A is the answer.

QUESTION: 9

Read the passage carefully and answer the questions that follow:

Humiliation is more than an individual and subjective feeling. It is an instrument of political power, wielded with intent. In the late 1930s, Soviet show trials used every means to degrade anyone whom Stalin considered a potentially dangerous opponent. National Socialism copied this practice whenever it put ‘enemies of the people’ on trial. On the streets of Vienna in 1938, officials forced Jews to kneel on the pavement and scrub off anti-Nazi graffiti to the laughter of non-Jewish men, women and children. During the Cultural Revolution in China, young activists went out of their way to relentlessly humiliate senior functionaries - a common practice that, to this day, hasn’t been officially reprimanded or rectified.

Liberal democracies, especially after the Second World War, have taken issue with these practices. We like to believe that we have largely eradicated such politics from our societies. Compared with totalitarian regimes of the 20th century, this belief might seem justified. Yet we’re still a far cry from being ‘decent societies’ whose members and institutions, in the philosopher Avishai Margalit’s terms, ‘do not humiliate people’, but respect their dignity. Although construction of the road to decency began as early as around 1800, it was - and remains - paved with obstacles and exceptions.

Mass opposition to the politics of humiliation began from the early 19th century in Europe, as lower-class people increasingly objected to disrespectful treatment. Servants, journeymen and factory workers alike used the language of honour and concepts of personal and social self-worth - previously monopolised by the nobility and upper-middle classes - to demand that they not be verbally and physically insulted by employers and overseers.

This social change was enabled and supported by a new type of honour that followed the invention of ‘citizens’ (rather than subjects) in democratising societies. Citizens who carried political rights and duties were also seen as possessing civic honour. Traditionally, social honour had been stratified according to status and rank, but now civic honour pertained to each and every citizen, and this helped to raise their self-esteem and self-consciousness. Consequently, humiliation, and other demonstrations of the alleged inferiority of others, was no longer considered a legitimate means by which to exert power over one’s fellow citizens.

Historically then, humiliation could be felt - and objected to - only once the notion of equal citizenship and human dignity entered political discourse and practice. As long as society subscribed to the notion that some individuals are fundamentally superior to others, people had a hard time feeling humiliated. They might feel treated unfairly, and rebel. But they wouldn’t perceive such treatment as humiliating, per se. Humiliation can be experienced only when the victims consider themselves on a par with the perpetrator - not in terms of actual power, but in terms of rights and dignity. This explains the surge of libel suits in Europe during the 19th century: they reflected the democratised sense of honour in societies that had granted and institutionalised equal rights after the French Revolution (even in countries that didn’t have a revolution).

The evolution of the legal system in Western nations serves as both a gauge of, and an active participant in, these developments. From the Middle Ages to the early 19th century, public shaming was used widely as a supplementary punishment for men and women sentenced for unlawful acts.

Q. Which of the following is true based on the passage?

Solution:

Option A: "...Liberal democracies, especially after the Second World War, have taken issue with these practices. We like to believe that we have largely eradicated such politics from our societies. Compared with totalitarian regimes of the 20th century, this belief might seem justified. Yet we’re still a far cry from being ‘decent societies’ whose members and institutions, in the philosopher Avishai Margalit’s terms, ‘do not humiliate people’, but respect their dignity...". The use of the term 'completely' in the option appears to be extreme; additionally, the author adds that we are a 'far cry' from transforming into a society devoid of any mechanisms involving humiliation. Hence, Option A can be eliminated. 

Option B: "...Mass opposition to the politics of humiliation began from the early 19th century in Europe, as lower-class people increasingly objected to disrespectful treatment. Servants, journeymen and factory workers alike used the language of honour and concepts of personal and social self-worth - previously monopolised by the nobility and upper-middle classes - to demand that they not be verbally and physically insulted by employers and overseers...". The statement here is distorted since the author evidently specifies that the antagonism against the politics of humiliation began from the bottom up - servants, journeymen and factory workers. Thus, Option B can be discarded.

Option C: "...Traditionally, social honour had been stratified according to status and rank, but now civic honour pertained to each and every citizen, and this helped to raise their self-esteem and self-consciousness...". We notice that the statement in C aligns with the information presented in this excerpt and is, therefore, true.

Option D: There is no evidence to substantiate this claim, since the term 'totalitarian' has not been ascribed to the entities mentioned in the passage.

Hence, the correct answer is Option C.

QUESTION: 10

Read the passage carefully and answer the questions that follow:

Humiliation is more than an individual and subjective feeling. It is an instrument of political power, wielded with intent. In the late 1930s, Soviet show trials used every means to degrade anyone whom Stalin considered a potentially dangerous opponent. National Socialism copied this practice whenever it put ‘enemies of the people’ on trial. On the streets of Vienna in 1938, officials forced Jews to kneel on the pavement and scrub off anti-Nazi graffiti to the laughter of non-Jewish men, women and children. During the Cultural Revolution in China, young activists went out of their way to relentlessly humiliate senior functionaries - a common practice that, to this day, hasn’t been officially reprimanded or rectified.

Liberal democracies, especially after the Second World War, have taken issue with these practices. We like to believe that we have largely eradicated such politics from our societies. Compared with totalitarian regimes of the 20th century, this belief might seem justified. Yet we’re still a far cry from being ‘decent societies’ whose members and institutions, in the philosopher Avishai Margalit’s terms, ‘do not humiliate people’, but respect their dignity. Although construction of the road to decency began as early as around 1800, it was - and remains - paved with obstacles and exceptions.

Mass opposition to the politics of humiliation began from the early 19th century in Europe, as lower-class people increasingly objected to disrespectful treatment. Servants, journeymen and factory workers alike used the language of honour and concepts of personal and social self-worth - previously monopolised by the nobility and upper-middle classes - to demand that they not be verbally and physically insulted by employers and overseers.

This social change was enabled and supported by a new type of honour that followed the invention of ‘citizens’ (rather than subjects) in democratising societies. Citizens who carried political rights and duties were also seen as possessing civic honour. Traditionally, social honour had been stratified according to status and rank, but now civic honour pertained to each and every citizen, and this helped to raise their self-esteem and self-consciousness. Consequently, humiliation, and other demonstrations of the alleged inferiority of others, was no longer considered a legitimate means by which to exert power over one’s fellow citizens.

Historically then, humiliation could be felt - and objected to - only once the notion of equal citizenship and human dignity entered political discourse and practice. As long as society subscribed to the notion that some individuals are fundamentally superior to others, people had a hard time feeling humiliated. They might feel treated unfairly, and rebel. But they wouldn’t perceive such treatment as humiliating, per se. Humiliation can be experienced only when the victims consider themselves on a par with the perpetrator - not in terms of actual power, but in terms of rights and dignity. This explains the surge of libel suits in Europe during the 19th century: they reflected the democratised sense of honour in societies that had granted and institutionalised equal rights after the French Revolution (even in countries that didn’t have a revolution).

The evolution of the legal system in Western nations serves as both a gauge of, and an active participant in, these developments. From the Middle Ages to the early 19th century, public shaming was used widely as a supplementary punishment for men and women sentenced for unlawful acts.

Q. Why does the author feel that humiliation could be felt only after the entrance of the notion of equal citizenship and human dignity in political discourse?

Solution:

Let us pay heed to the following excerpt from the penultimate paragraph: "...As long as society subscribed to the notion that some individuals are fundamentally superior to others, people had a hard time feeling humiliated. They might feel treated unfairly, and rebel. But they wouldn’t perceive such treatment as humiliating, per se. Humiliation can be experienced only when the victims consider themselves on a par with the perpetrator - not in terms of actual power, but in terms of rights and dignity..." The author believes that the introduction of rights in the sociopolitical domain evinced the perception of humiliation and the wrongdoing associated with it. If people inherently believe that social stratification exists, wherein some individuals qualify as being inferior to others, this might not elicit a feeling of humiliation. Individuals might find this system/treatment unjust, but that feeling can not necessarily be tagged as humiliation. However, the presence of civic rights induces the feeling of individual dignity. It fosters the idea that every person within the civic society is equal, and therefore, at par with the group/subset that humiliates another. The author adds that this distinction that every individual is equal in terms of rights and dignity (perhaps not in terms of social status) is what allows the presence of the feeling of humiliation. Option B correctly captures this reason.

Option A: The focus here is neither on the presence of social stratification nor on the increase in self-esteem. Instead, the realization concerning equality in rights and dignity is presented as the reason why humiliation could be experienced only post the entrance of these two notions. Therefore, Option A fails to answer the question. 

Option C: The presence of legal systems is not the primary focal point here. The following is stated in this regard: "...The evolution of the legal system in Western nations serves as both a gauge of, and an active participant in, these developments..." Although the author does call it an "active participant" in changing the status quo, he does not attach it to the "entrance of the notion of equal citizenship and human dignity in political discourse" directly (as demanded by the question). hence, Option C can be eliminated.

Option D: The author says that the perception of superiority might have made people feel mistreated but not humiliated. The issue was not with 'objecting' to humiliation (as presented in Option D) but with feeling humiliated in the first place. This difference in interpretation helps us eliminate Option D.

Hence, Option B is the correct answer.

QUESTION: 11

Read the passage carefully and answer the questions that follow:

Humiliation is more than an individual and subjective feeling. It is an instrument of political power, wielded with intent. In the late 1930s, Soviet show trials used every means to degrade anyone whom Stalin considered a potentially dangerous opponent. National Socialism copied this practice whenever it put ‘enemies of the people’ on trial. On the streets of Vienna in 1938, officials forced Jews to kneel on the pavement and scrub off anti-Nazi graffiti to the laughter of non-Jewish men, women and children. During the Cultural Revolution in China, young activists went out of their way to relentlessly humiliate senior functionaries - a common practice that, to this day, hasn’t been officially reprimanded or rectified.

Liberal democracies, especially after the Second World War, have taken issue with these practices. We like to believe that we have largely eradicated such politics from our societies. Compared with totalitarian regimes of the 20th century, this belief might seem justified. Yet we’re still a far cry from being ‘decent societies’ whose members and institutions, in the philosopher Avishai Margalit’s terms, ‘do not humiliate people’, but respect their dignity. Although construction of the road to decency began as early as around 1800, it was - and remains - paved with obstacles and exceptions.

Mass opposition to the politics of humiliation began from the early 19th century in Europe, as lower-class people increasingly objected to disrespectful treatment. Servants, journeymen and factory workers alike used the language of honour and concepts of personal and social self-worth - previously monopolised by the nobility and upper-middle classes - to demand that they not be verbally and physically insulted by employers and overseers.

This social change was enabled and supported by a new type of honour that followed the invention of ‘citizens’ (rather than subjects) in democratising societies. Citizens who carried political rights and duties were also seen as possessing civic honour. Traditionally, social honour had been stratified according to status and rank, but now civic honour pertained to each and every citizen, and this helped to raise their self-esteem and self-consciousness. Consequently, humiliation, and other demonstrations of the alleged inferiority of others, was no longer considered a legitimate means by which to exert power over one’s fellow citizens.

Historically then, humiliation could be felt - and objected to - only once the notion of equal citizenship and human dignity entered political discourse and practice. As long as society subscribed to the notion that some individuals are fundamentally superior to others, people had a hard time feeling humiliated. They might feel treated unfairly, and rebel. But they wouldn’t perceive such treatment as humiliating, per se. Humiliation can be experienced only when the victims consider themselves on a par with the perpetrator - not in terms of actual power, but in terms of rights and dignity. This explains the surge of libel suits in Europe during the 19th century: they reflected the democratised sense of honour in societies that had granted and institutionalised equal rights after the French Revolution (even in countries that didn’t have a revolution).

The evolution of the legal system in Western nations serves as both a gauge of, and an active participant in, these developments. From the Middle Ages to the early 19th century, public shaming was used widely as a supplementary punishment for men and women sentenced for unlawful acts.

Q. Which of the following topics would be a likely continuation of the given discussion?

Solution:

Towards the end of the passage, the author delves into how public shaming was used as a 'supplementary punishment'. The next course of discussion should be in line with this and further elucidate what the author intends to convey via this claim. Option D serves as an apt continuation in this regard.
Option A: We notice multiple information skips here - both with regard to time as well as the subject under discussion. The author has not supplemented the claim made towards the end and is yet to steer the discourse towards present-day affairs. Hence, Option A is an unlikely continuation.  
Option B: The information would not continue the chain of thought. Statistics to supplement a tangential claim is of little importance and hence, can be discarded.
Option C: The main themes of the concluding paragraph and the stated option do not coincide. The author has not focused on the social transformation or the removal of societal hierarchies; instead, the perception associated with humiliation is discussed. In this regard, Option C is irrelevant. 
Hence, of the given choices, Option D is the correct answer.

QUESTION: 12

Read the passage carefully and answer the questions that follow:

Humiliation is more than an individual and subjective feeling. It is an instrument of political power, wielded with intent. In the late 1930s, Soviet show trials used every means to degrade anyone whom Stalin considered a potentially dangerous opponent. National Socialism copied this practice whenever it put ‘enemies of the people’ on trial. On the streets of Vienna in 1938, officials forced Jews to kneel on the pavement and scrub off anti-Nazi graffiti to the laughter of non-Jewish men, women and children. During the Cultural Revolution in China, young activists went out of their way to relentlessly humiliate senior functionaries - a common practice that, to this day, hasn’t been officially reprimanded or rectified.

Liberal democracies, especially after the Second World War, have taken issue with these practices. We like to believe that we have largely eradicated such politics from our societies. Compared with totalitarian regimes of the 20th century, this belief might seem justified. Yet we’re still a far cry from being ‘decent societies’ whose members and institutions, in the philosopher Avishai Margalit’s terms, ‘do not humiliate people’, but respect their dignity. Although construction of the road to decency began as early as around 1800, it was - and remains - paved with obstacles and exceptions.

Mass opposition to the politics of humiliation began from the early 19th century in Europe, as lower-class people increasingly objected to disrespectful treatment. Servants, journeymen and factory workers alike used the language of honour and concepts of personal and social self-worth - previously monopolised by the nobility and upper-middle classes - to demand that they not be verbally and physically insulted by employers and overseers.

This social change was enabled and supported by a new type of honour that followed the invention of ‘citizens’ (rather than subjects) in democratising societies. Citizens who carried political rights and duties were also seen as possessing civic honour. Traditionally, social honour had been stratified according to status and rank, but now civic honour pertained to each and every citizen, and this helped to raise their self-esteem and self-consciousness. Consequently, humiliation, and other demonstrations of the alleged inferiority of others, was no longer considered a legitimate means by which to exert power over one’s fellow citizens.

Historically then, humiliation could be felt - and objected to - only once the notion of equal citizenship and human dignity entered political discourse and practice. As long as society subscribed to the notion that some individuals are fundamentally superior to others, people had a hard time feeling humiliated. They might feel treated unfairly, and rebel. But they wouldn’t perceive such treatment as humiliating, per se. Humiliation can be experienced only when the victims consider themselves on a par with the perpetrator - not in terms of actual power, but in terms of rights and dignity. This explains the surge of libel suits in Europe during the 19th century: they reflected the democratised sense of honour in societies that had granted and institutionalised equal rights after the French Revolution (even in countries that didn’t have a revolution).

The evolution of the legal system in Western nations serves as both a gauge of, and an active participant in, these developments. From the Middle Ages to the early 19th century, public shaming was used widely as a supplementary punishment for men and women sentenced for unlawful acts.

Q. Why does the author cite the example of the Soviet, National Socialism and the Cultural Revolution in China?

Solution:

The author makes the following comment: "...Humiliation is more than an individual and subjective feeling. It is an instrument of political power, wielded with intent..." After this, he proceeds to cite examples/historical occurrences that reinforce his claim - humiliation has been used as an instrument to meet political ends. Option A correctly captures this intention.
Option B: The topic does not include an emphasis on totalitarian regimes. The author lists out instances wherein humiliation was used as a mechanism for political ends. The statement here is far off the target and hence, can be eliminated.
Option C: The passage focuses on humiliation and its history. The focus is not on how far we have come but on tracing the history of humiliation. Hence, option C is not in line with the objective of the passage.
Option D: The passage does not highlight the use of humiliation for maintaining "social order". This is a misinterpretation and, therefore, can be discarded as incorrect choice.
Hence, Option A is the correct answer.

QUESTION: 13

Read the passage carefully and answer the questions that follow:

Humiliation is more than an individual and subjective feeling. It is an instrument of political power, wielded with intent. In the late 1930s, Soviet show trials used every means to degrade anyone whom Stalin considered a potentially dangerous opponent. National Socialism copied this practice whenever it put ‘enemies of the people’ on trial. On the streets of Vienna in 1938, officials forced Jews to kneel on the pavement and scrub off anti-Nazi graffiti to the laughter of non-Jewish men, women and children. During the Cultural Revolution in China, young activists went out of their way to relentlessly humiliate senior functionaries - a common practice that, to this day, hasn’t been officially reprimanded or rectified.

Liberal democracies, especially after the Second World War, have taken issue with these practices. We like to believe that we have largely eradicated such politics from our societies. Compared with totalitarian regimes of the 20th century, this belief might seem justified. Yet we’re still a far cry from being ‘decent societies’ whose members and institutions, in the philosopher Avishai Margalit’s terms, ‘do not humiliate people’, but respect their dignity. Although construction of the road to decency began as early as around 1800, it was - and remains - paved with obstacles and exceptions.

Mass opposition to the politics of humiliation began from the early 19th century in Europe, as lower-class people increasingly objected to disrespectful treatment. Servants, journeymen and factory workers alike used the language of honour and concepts of personal and social self-worth - previously monopolised by the nobility and upper-middle classes - to demand that they not be verbally and physically insulted by employers and overseers.

This social change was enabled and supported by a new type of honour that followed the invention of ‘citizens’ (rather than subjects) in democratising societies. Citizens who carried political rights and duties were also seen as possessing civic honour. Traditionally, social honour had been stratified according to status and rank, but now civic honour pertained to each and every citizen, and this helped to raise their self-esteem and self-consciousness. Consequently, humiliation, and other demonstrations of the alleged inferiority of others, was no longer considered a legitimate means by which to exert power over one’s fellow citizens.

Historically then, humiliation could be felt - and objected to - only once the notion of equal citizenship and human dignity entered political discourse and practice. As long as society subscribed to the notion that some individuals are fundamentally superior to others, people had a hard time feeling humiliated. They might feel treated unfairly, and rebel. But they wouldn’t perceive such treatment as humiliating, per se. Humiliation can be experienced only when the victims consider themselves on a par with the perpetrator - not in terms of actual power, but in terms of rights and dignity. This explains the surge of libel suits in Europe during the 19th century: they reflected the democratised sense of honour in societies that had granted and institutionalised equal rights after the French Revolution (even in countries that didn’t have a revolution).

The evolution of the legal system in Western nations serves as both a gauge of, and an active participant in, these developments. From the Middle Ages to the early 19th century, public shaming was used widely as a supplementary punishment for men and women sentenced for unlawful acts.

Q. Which of the following captures the main point of the antepenultimate paragraph?

Solution:

{This social change was enabled and supported by a new type of honour that followed the invention of ‘citizens’ (rather than subjects) in democratising societies. Citizens who carried political rights and duties were also seen as possessing civic honour.
{Consequently, humiliation, and other demonstrations of the alleged inferiority of others, was no longer considered a legitimate means by which to exert power over one’s fellow citizens.}
The above excerpts from the antepenultimate para indicate how the introduction of civic honour put a stop to the use of humiliation as an instrument to exert power over fellow citizens. Option D aptly captures this point and is, hence, the correct choice.
Option A: While true, the Option misses out on the source of the increased sense of 'self-esteem and self-consciousness' - civic honour. Thus, we can reject A as the potential answer.
Option B: Option B captures the discussion in the antepenultimate paragraph partially. The consequence highlighted in the para is completely missed out.  
Option C: The author does not intend to highlight the differences in the two forms of honour; instead, the impact of civic honour on humiliation is emphasised. Hence, Option C can be eliminated.

QUESTION: 14

Read the passage carefully and answer the questions that follow:

Humans are strange. For a global species, we’re not particularly genetically diverse, thanks in part to how our ancient roaming explorations caused “founder effects” and “bottleneck events” that restricted our ancestral gene pool. We also have a truly outsize impact on the planetary environment without much in the way of natural attrition to trim our influence.

But the strangest thing of all is how we generate, exploit, and propagate information that is not encoded in our heritable genetic material, yet travels with us through time and space. Not only is much of that information represented in purely symbolic forms—alphabets, languages, binary codes—it is also represented in each brick, alloy, machine, and structure we build from the materials around us. Even the symbolic stuff is instantiated in some material form or the other, whether as ink on pages or electrical charges in nanoscale pieces of silicon. Altogether, this “dataome” has become an integral part of our existence. In fact, it may have always been an integral, and essential, part of our existence since our species of hominins became more and more distinct some 200,000 years ago.

For example, let’s consider our planetary impact. Today we can look at our species’ energy use and see that of the roughly six to seven terawatts of average global electricity production, about 3 percent to 4 percent is gobbled up by our digital electronics, in computing, storing and moving information. That might not sound too bad—except the growth trend of our digitized informational world is such that it requires approximately 40 percent more power every year. Even allowing for improvements in computational efficiency and power generation, this points to a world in some 20 years where all of the energy we currently generate in electricity will be consumed by digital electronics alone.

And that’s just one facet of the energy demands of the human dataome. We still print onto paper, and the energy cost of a single page is the equivalent of burning five grams of high-quality coal. Digital devices, from microprocessors to hard drives, are also extraordinarily demanding in terms of their production, owing to the deep repurposing of matter that is required. We literally fight against the second law of thermodynamics to forge these exquisitely ordered, restricted, low-entropy structures out of raw materials that are decidedly high-entropy in their messy natural states. It is hard to see where this informational tsunami slows or ends.

Our dataome looks like a distinct, although entirely symbiotic phenomenon. Homo sapiens arguably only exists as a truly unique species because of our coevolution with a wealth of externalized information; starting from languages held only in neuronal structures through many generations, to our tools and abstractions on pottery and cave walls, all the way to today’s online world.

But symbiosis implies that all parties have their own interests to consider as well. Seeing ourselves this way opens the door to asking whether we’re calling all the shots. After all, in a gene-centered view of biology, all living things are simply temporary vehicles for the propagation and survival of information. In that sense the dataome is no different, and exactly how information survives is less important than the fact that it can do so. Once that information and its algorithmic underpinnings are in place in the world, it will keep going forever if it can.

Q. The author calls humans 'strange' for all of the following reasons, EXCEPT

Solution:

The author highlights the reasons in the first and second paragraph-
-"For a global species, we’re not particularly genetically diverse"
-"We also have a truly outsize impact on the planetary environment without much in the way of natural attrition to trim our influence."
-"But the strangest thing of all is how we generate, exploit, and propagate information that is not encoded in our heritable genetic material, yet travels with us through time and space."
Options B, C, and D can be inferred from the above lines. 
Option A cannot be concluded. Though "founder effects" and "bottleneck events" have reduced the genetic diversity, the author does not assert that these events were manageable/controllable. Option A is the answer.

QUESTION: 15

Read the passage carefully and answer the questions that follow:

Humans are strange. For a global species, we’re not particularly genetically diverse, thanks in part to how our ancient roaming explorations caused “founder effects” and “bottleneck events” that restricted our ancestral gene pool. We also have a truly outsize impact on the planetary environment without much in the way of natural attrition to trim our influence.

But the strangest thing of all is how we generate, exploit, and propagate information that is not encoded in our heritable genetic material, yet travels with us through time and space. Not only is much of that information represented in purely symbolic forms—alphabets, languages, binary codes—it is also represented in each brick, alloy, machine, and structure we build from the materials around us. Even the symbolic stuff is instantiated in some material form or the other, whether as ink on pages or electrical charges in nanoscale pieces of silicon. Altogether, this “dataome” has become an integral part of our existence. In fact, it may have always been an integral, and essential, part of our existence since our species of hominins became more and more distinct some 200,000 years ago.

For example, let’s consider our planetary impact. Today we can look at our species’ energy use and see that of the roughly six to seven terawatts of average global electricity production, about 3 percent to 4 percent is gobbled up by our digital electronics, in computing, storing and moving information. That might not sound too bad—except the growth trend of our digitized informational world is such that it requires approximately 40 percent more power every year. Even allowing for improvements in computational efficiency and power generation, this points to a world in some 20 years where all of the energy we currently generate in electricity will be consumed by digital electronics alone.

And that’s just one facet of the energy demands of the human dataome. We still print onto paper, and the energy cost of a single page is the equivalent of burning five grams of high-quality coal. Digital devices, from microprocessors to hard drives, are also extraordinarily demanding in terms of their production, owing to the deep repurposing of matter that is required. We literally fight against the second law of thermodynamics to forge these exquisitely ordered, restricted, low-entropy structures out of raw materials that are decidedly high-entropy in their messy natural states. It is hard to see where this informational tsunami slows or ends.

Our dataome looks like a distinct, although entirely symbiotic phenomenon. Homo sapiens arguably only exists as a truly unique species because of our coevolution with a wealth of externalized information; starting from languages held only in neuronal structures through many generations, to our tools and abstractions on pottery and cave walls, all the way to today’s online world.

But symbiosis implies that all parties have their own interests to consider as well. Seeing ourselves this way opens the door to asking whether we’re calling all the shots. After all, in a gene-centered view of biology, all living things are simply temporary vehicles for the propagation and survival of information. In that sense the dataome is no different, and exactly how information survives is less important than the fact that it can do so. Once that information and its algorithmic underpinnings are in place in the world, it will keep going forever if it can.

Q. According to the author, which of the following reason makes humans a truly unique species?

Solution:

" Altogether, this “dataome” has become an integral part of our existence. In fact, it may have always been an integral, and essential, part of our existence since our species of hominins became more and more distinct some 200,000 years ago."
" Homo sapiens arguably only exists as a truly unique species because of our coevolution with a wealth of externalized information;."
From the above lines, it is clear that humans coevolved with a growing wealth of information and this symbiotic relationship is the reason for the uniqueness of our species.
Option B conveys this idea precisely and is the answer.
Option A is wrong. A symbiotic relationship need not necessarily be synergistic. Where symbiosis refers to a relationship where both the parties are there to fulfill their individual interests, synergy is combination of the parties to yield a greater total sum. Hence both are different and the option can be eliminated.
Options C and D may be true but do not reflect the reason cited by the author. They are merely excerpts taken from the passage which are tangent to the current discussion, hence can be eliminated.

QUESTION: 16

Read the passage carefully and answer the questions that follow:

Humans are strange. For a global species, we’re not particularly genetically diverse, thanks in part to how our ancient roaming explorations caused “founder effects” and “bottleneck events” that restricted our ancestral gene pool. We also have a truly outsize impact on the planetary environment without much in the way of natural attrition to trim our influence.

But the strangest thing of all is how we generate, exploit, and propagate information that is not encoded in our heritable genetic material, yet travels with us through time and space. Not only is much of that information represented in purely symbolic forms—alphabets, languages, binary codes—it is also represented in each brick, alloy, machine, and structure we build from the materials around us. Even the symbolic stuff is instantiated in some material form or the other, whether as ink on pages or electrical charges in nanoscale pieces of silicon. Altogether, this “dataome” has become an integral part of our existence. In fact, it may have always been an integral, and essential, part of our existence since our species of hominins became more and more distinct some 200,000 years ago.

For example, let’s consider our planetary impact. Today we can look at our species’ energy use and see that of the roughly six to seven terawatts of average global electricity production, about 3 percent to 4 percent is gobbled up by our digital electronics, in computing, storing and moving information. That might not sound too bad—except the growth trend of our digitized informational world is such that it requires approximately 40 percent more power every year. Even allowing for improvements in computational efficiency and power generation, this points to a world in some 20 years where all of the energy we currently generate in electricity will be consumed by digital electronics alone.

And that’s just one facet of the energy demands of the human dataome. We still print onto paper, and the energy cost of a single page is the equivalent of burning five grams of high-quality coal. Digital devices, from microprocessors to hard drives, are also extraordinarily demanding in terms of their production, owing to the deep repurposing of matter that is required. We literally fight against the second law of thermodynamics to forge these exquisitely ordered, restricted, low-entropy structures out of raw materials that are decidedly high-entropy in their messy natural states. It is hard to see where this informational tsunami slows or ends.

Our dataome looks like a distinct, although entirely symbiotic phenomenon. Homo sapiens arguably only exists as a truly unique species because of our coevolution with a wealth of externalized information; starting from languages held only in neuronal structures through many generations, to our tools and abstractions on pottery and cave walls, all the way to today’s online world.

But symbiosis implies that all parties have their own interests to consider as well. Seeing ourselves this way opens the door to asking whether we’re calling all the shots. After all, in a gene-centered view of biology, all living things are simply temporary vehicles for the propagation and survival of information. In that sense the dataome is no different, and exactly how information survives is less important than the fact that it can do so. Once that information and its algorithmic underpinnings are in place in the world, it will keep going forever if it can.

Q. Which of the following best captures the central idea discussed in the last paragraph?

Solution:

In the penultimate paragraph, the author discusses a symbiotic relationship between humans and the information ecosystem. In the final paragraph, he says that it is important to view the relationship as a symbiotic one so that people realise that the dataome will try ensure the survival of its information irrespective of how it is done. Thus, once the dataome is able to ensure the survival of its information, it will do so irrespective of the decisions made by humans. 
Option A can be eliminated. The author highlights the importance of all living things, and not just the genetically gifted species.
Option B can be eliminated as well. The author does not claim that all physical processes are complicit in information propagation.
Option C is wrong. In the penultimate paragraph, the author clearly points out the symbiotic benefits for humans, including the uniqueness of the species. 
Option D best captures the author's view outlined above. Option D is the answer.

QUESTION: 17

Read the passage carefully and answer the questions that follow:

Humans are strange. For a global species, we’re not particularly genetically diverse, thanks in part to how our ancient roaming explorations caused “founder effects” and “bottleneck events” that restricted our ancestral gene pool. We also have a truly outsize impact on the planetary environment without much in the way of natural attrition to trim our influence.

But the strangest thing of all is how we generate, exploit, and propagate information that is not encoded in our heritable genetic material, yet travels with us through time and space. Not only is much of that information represented in purely symbolic forms—alphabets, languages, binary codes—it is also represented in each brick, alloy, machine, and structure we build from the materials around us. Even the symbolic stuff is instantiated in some material form or the other, whether as ink on pages or electrical charges in nanoscale pieces of silicon. Altogether, this “dataome” has become an integral part of our existence. In fact, it may have always been an integral, and essential, part of our existence since our species of hominins became more and more distinct some 200,000 years ago.

For example, let’s consider our planetary impact. Today we can look at our species’ energy use and see that of the roughly six to seven terawatts of average global electricity production, about 3 percent to 4 percent is gobbled up by our digital electronics, in computing, storing and moving information. That might not sound too bad—except the growth trend of our digitized informational world is such that it requires approximately 40 percent more power every year. Even allowing for improvements in computational efficiency and power generation, this points to a world in some 20 years where all of the energy we currently generate in electricity will be consumed by digital electronics alone.

And that’s just one facet of the energy demands of the human dataome. We still print onto paper, and the energy cost of a single page is the equivalent of burning five grams of high-quality coal. Digital devices, from microprocessors to hard drives, are also extraordinarily demanding in terms of their production, owing to the deep repurposing of matter that is required. We literally fight against the second law of thermodynamics to forge these exquisitely ordered, restricted, low-entropy structures out of raw materials that are decidedly high-entropy in their messy natural states. It is hard to see where this informational tsunami slows or ends.

Our dataome looks like a distinct, although entirely symbiotic phenomenon. Homo sapiens arguably only exists as a truly unique species because of our coevolution with a wealth of externalized information; starting from languages held only in neuronal structures through many generations, to our tools and abstractions on pottery and cave walls, all the way to today’s online world.

But symbiosis implies that all parties have their own interests to consider as well. Seeing ourselves this way opens the door to asking whether we’re calling all the shots. After all, in a gene-centered view of biology, all living things are simply temporary vehicles for the propagation and survival of information. In that sense the dataome is no different, and exactly how information survives is less important than the fact that it can do so. Once that information and its algorithmic underpinnings are in place in the world, it will keep going forever if it can.

Q. Which of the following can be inferred from the passage?

Solution:

"Not only is much of that information represented in purely symbolic forms—alphabets, languages, binary codes—it is also represented in each brick, alloy, machine, and structure we build from the materials around us. Even the symbolic stuff is instantiated in some material form or the other, whether as ink on pages or electrical charges in nanoscale pieces of silicon." 
The above excerpt shows that the materials present in the human environment have played a major role in the propagation of information. Each method of propagation mentioned above employs a material medium of representation. Hence Option A can be inferred.
"For a global species, we’re not particularly genetically diverse, thanks in part to how our ancient roaming explorations caused “founder effects” and “bottleneck events” that restricted our ancestral gene pool." 
The above lines mention roaming exploration, which is not the same as migration, which is defined as moving to settle in another place. Hence Option B is incorrect.
In the fourth paragraph, the author points out that digitized information is only one facet of the energy demand. There are other factors too which have contributed to the rising energy use. Hence, controlling one facet may not necessarily help avert the crisis. Option C can be eliminated.
Option D is a distortion. In the last paragraph, the author highlights the following about the gene-centered view of biology-" After all, in a gene-centered view of biology, all living things are simply temporary vehicles for the propagation and survival of information. In that sense, the dataome is no different, and exactly how information survives is less important than the fact that it can do so." 
It is quite evident that, though the mechanism is not as important as the survival of the information itself, the independence relation described in Option D has not been implied by the author. Hence it can be eliminated.

QUESTION: 18

Read the passage carefully and answer the questions that follow:

Humans are strange. For a global species, we’re not particularly genetically diverse, thanks in part to how our ancient roaming explorations caused “founder effects” and “bottleneck events” that restricted our ancestral gene pool. We also have a truly outsize impact on the planetary environment without much in the way of natural attrition to trim our influence.

But the strangest thing of all is how we generate, exploit, and propagate information that is not encoded in our heritable genetic material, yet travels with us through time and space. Not only is much of that information represented in purely symbolic forms—alphabets, languages, binary codes—it is also represented in each brick, alloy, machine, and structure we build from the materials around us. Even the symbolic stuff is instantiated in some material form or the other, whether as ink on pages or electrical charges in nanoscale pieces of silicon. Altogether, this “dataome” has become an integral part of our existence. In fact, it may have always been an integral, and essential, part of our existence since our species of hominins became more and more distinct some 200,000 years ago.

For example, let’s consider our planetary impact. Today we can look at our species’ energy use and see that of the roughly six to seven terawatts of average global electricity production, about 3 percent to 4 percent is gobbled up by our digital electronics, in computing, storing and moving information. That might not sound too bad—except the growth trend of our digitized informational world is such that it requires approximately 40 percent more power every year. Even allowing for improvements in computational efficiency and power generation, this points to a world in some 20 years where all of the energy we currently generate in electricity will be consumed by digital electronics alone.

And that’s just one facet of the energy demands of the human dataome. We still print onto paper, and the energy cost of a single page is the equivalent of burning five grams of high-quality coal. Digital devices, from microprocessors to hard drives, are also extraordinarily demanding in terms of their production, owing to the deep repurposing of matter that is required. We literally fight against the second law of thermodynamics to forge these exquisitely ordered, restricted, low-entropy structures out of raw materials that are decidedly high-entropy in their messy natural states. It is hard to see where this informational tsunami slows or ends.

Our dataome looks like a distinct, although entirely symbiotic phenomenon. Homo sapiens arguably only exists as a truly unique species because of our coevolution with a wealth of externalized information; starting from languages held only in neuronal structures through many generations, to our tools and abstractions on pottery and cave walls, all the way to today’s online world.

But symbiosis implies that all parties have their own interests to consider as well. Seeing ourselves this way opens the door to asking whether we’re calling all the shots. After all, in a gene-centered view of biology, all living things are simply temporary vehicles for the propagation and survival of information. In that sense the dataome is no different, and exactly how information survives is less important than the fact that it can do so. Once that information and its algorithmic underpinnings are in place in the world, it will keep going forever if it can.

Q. Production of digital devices require large amounts of energy because

Solution:

The following reason is presented in the passage: {Digital devices, from microprocessors to hard drives, are also extraordinarily demanding in terms of their production, owing to the deep repurposing of matter that is required. We literally fight against the second law of thermodynamics to forge these exquisitely ordered, restricted, low-entropy structures out of raw materials that are decidedly high-entropy in their messy natural states.} The author highlights how repurposing the materials into low-entropy structures necessitates high amounts of energy. Thus, processing the materials to be different from their inherently 'messy' natural states is the reason behind the massive energy consumption. Option A conveys this idea correctly.
Option B can be eliminated. Repurposing may not necessarily involve restructuring the materials. 
Option C has not been implied in the passage.
Option D is extreme. The author does not state that the natural behaviour of the materials is inhibited, but only altered to suit our needs. 

QUESTION: 19

The passage given below is followed by four summaries. Choose the option that best captures the author’s position.

What is beauty? Beauty is that which gives aesthetic pleasure. Beauty is both subjective and objective—subjective because it is “in the eye of the beholder” but objective in that “pleasure” is something you either experience or you do not. If a building isn’t giving people pleasure to look at, then it is not beautiful, because beautiful things are things that you want to keep looking at because seeing them brings joy. The fact that beauty is both subjective and objective means that a thing can be beautiful to some people and not to others. For instance, contemporary buildings are beautiful to architects, who clearly receive pleasure from looking at them. However, majority of people get more pleasure out of looking at the ancient buildings than the contemporary buildings.

Solution:

In the passage, the author talks about the subjective and objective nature of beauty- a subjective nature depends on the personal views of a person, whereas the objective facet is independent of personal influences. Beauty is subjective as it is perceived differently by different individuals, but this difference arises from the fact that pleasure is 'objective,' i.e., it is generated sans personal influences. Hence, the combined effect is unique, where beauty wields both of these contrasting characteristics.
Option D captures the idea correctly and is the answer.
Options A and B do not elaborate on the objective nature and can be easily eliminated.
Option C is distorted. Beauty lends aesthetic pleasure. To say that beauty depends on the generation of pleasure, hence, is wrong. Hence C can be eliminated too.

*Answer can only contain numeric values
QUESTION: 20

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. These observations are informative but do not address fundamental questions about how social-cognitive brain systems develop or why their development might be different for autistic people.
  2. Accordingly, differences in the development and/or transmissions of information across this distributed social-cognitive brain network may contribute to differences in mentalizing among autistic people.
  3. Social-cognitive neuroscience tells us that brain systems of the medial frontal cortex, temporal cortex and parietal cortex, as well as reward centres of the brain, enable mentalizing.
  4. These differences can lead to a range of outcomes, from problems in the capacity to mentalize to alterations in the spontaneous use of mentalizing or the motivation and effort involved in mentalizing during social interactions.

Solution:

Sentence 3 will be the starting sentence because it is not dependant on any other sentence. Sentence 2 will follow 3 because 3 talks about the different parts of the brain that enable mentalizing, and 2 talks about the differences in transmission of information and signals in this network that contributes to the difference in mentalizing among autistic people. Sentence 4 will follow 2 because the "differences" mentioned in 4 refer to the ones discussed in 2, and 4 tells us what kind of problems do autistic people face because of these differences. Finally, 1 will follow 4 because the "observations" mentioned in 1 refer to the challenges faced by autistic people as mentioned in 4, and it further tells us that those observations do not tell us how and why the developments are different for autistic people. Hence, the sequence 3241.

*Answer can only contain numeric values
QUESTION: 21

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. As a matter of fact, many of the tools and resources that I used on my missions, such as solar panels and rechargeable storage batteries, are also the answer to our problems here on Earth.
  2. After seeing the Earth dramatically change from this unique perspective, I firmly believe that solving climate change is the moonshot of the 21st century.
  3. On my last mission in 2016, only 17 years later, burning and clear-cutting were clearly evident in the region.
  4. During my first mission, in 1999, to fix the Hubble Space Telescope, I remember passing over South America and being awed by the sheer size of the Amazon rainforest.

Solution:

Sentence 4 will be the starting sentence as it is not dependant on any other sentence. Sentence 3 will follow 4 because of the reference '17 years later' which is the span between 1999 and 2016. Also, 3 describes the change the author witnessed from space which is also mentioned in 2. So, sentence 2 will follow 3. Sentence 1 will follow 2 because it is where the author discusses some possible solutions to our problems on earth regarding climate change. Hence, the sequence 4321.
We can identify the thought flow here. 4 and 3 make a bloc that talks about the author's experience and perspective. 2 and 1 derive conclusions and solutions from that. Arranging these, we get the correct answer.

*Answer can only contain numeric values
QUESTION: 22

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. Most of it isn’t thrown off ships, she and her colleagues say, but is dumped carelessly on land or in rivers, mostly in Asia.
  2. It’s unclear how long it will take for that plastic to completely biodegrade into its constituent molecules.
  3. No one knows how much unrecycled plastic waste ends up in the ocean, Earth’s last sink.
  4. It is then blown or washed into the sea.
  5. But in 2015, Jenna Jambeck, a University of Georgia engineering professor, caught everyone’s attention with a rough estimate: between 5.3 million and 14 million tons each year just from coastal regions.

Solution:

Sentence 3 will be the starting sentence because it introduces the topic i.e. how much unrecycled plastic ends up in the ocean. Sentence 5 will follow 3 as it somehow is able to give us a rough estimation contrary to what is said in 3. Sentence 1 will follow 5 because it provides us with a bit more details of the estimation. Sentence 4 will follow 1 because it is just an extension of what is mentioned in 1. Hence, the sequence 3514. Sentence 2 is the odd one out because it talks about how long would it take to biodegrade that plastic, and not about the estimation of the plastic dumped.

*Answer can only contain numeric values
QUESTION: 23

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. Instead, it was three beluga whales from Marineland, an aquatic park in Ontario, Canada, that were sitting aboard, in special water-filled transport containers.
  2. Kharabali, Havana and Jetta, three females, were loaded onto flatbed trucks and driven seven miles east on I-95 to Mystic Aquarium in southeast Connecticut.
  3. There, a crane gently lowered them, one by one, into the medical pool, a separate but connected body of water within the aquarium’s 750,000-gallon beluga pool, called Arctic Coast.
  4. Two more whales, Havok and Sahara, a male and a female, were sent back to Ontario as part of the exchange agreement.
  5. A dusty grey C-130 rolled to a stop just as the sun was going down over the tarmac of the Air National Guard Station at the Groton-New London Airport in Connecticut on Friday, and the plane wasn’t carrying its usual haul of utility helicopters or jeeps.

Solution:

Four out of the five sentences talk about the transportation of 3 Beluga Whales. Sentence 5 will be the starting sentence as it initiates the transportation sequence. Sentence 1 will follow sentence 5 because it reveals what the plane was actually carrying instead of the utility helicopters or jeeps as mentioned in 5. Sentence 3 will follow 2 because 'the aquarium' mentioned 3 refers to the Mystic Aquarium, first introduced in 2. So, 2-3 form a pair. And this pair will follow 1 as it fits the sequence of transportation. Hence, the sequence 5123.
Sentence 4 talks about 'the exchange agreement'. However, no such agreement is mentioned in any of the other sentences. Hence, sentence 4 with its missing antecedent is the odd one out.

*Answer can only contain numeric values
QUESTION: 24

Which of the following will be the odd one out.
"Dollar, Peso, Ounce, Euro".


Solution:

All except Ounce are names of currencies, while Ounce is a unit of weight.
So, Ounce will be the perfect odd one out. 

QUESTION: 25

Seven metropolitan cities A, B, C, D, E, F and G are connected by means of several roads as follows. Each road is bidirectional and has 2 parameters associated with it:
(a) Length (in km) d
(b) Traffic Index ti
The time t(in minutes) taken to travel from a source city to a destination city through a road is given by:
time t(in mins) = a x d + b x (ti - 50) , where a = 2 and b = 2.

Based on the information given above, answer the questions that follow.

Q. In how many ways can one travel to A from F if one cannot travel through the same city twice?

Solution:

We need to construct the given network of cities and connecting roads.


The blue numbers denote the length of the roads and the red ones denote the traffic index. Calculating the time required in minutes between the cities, we get,

Hence, plotting the figure with the lengths of the roads and the time constraints, we will get the following diagram.

Here, the red numbers denote the time taken in minutes and the blue numbers denote the length in kilometres. 
The different routes are:
FDBCA
FDCA
FDECA
FDEGCA
FGCA
FGECA
FGEDCA
FGEDBCA
FDBA
FDECBA
FDEGCBA
FGEDBA
FGECBA
FGCBA
FDCBA
FGEDCBA
FGCEDBA
FGECDBA
FGCDBA
Hence, there are a total of 19 routes.

*Answer can only contain numeric values
QUESTION: 26

Seven metropolitan cities A, B, C, D, E, F and G are connected by means of several roads as follows. Each road is bidirectional and has 2 parameters associated with it:
(a) Length (in km) d
(b) Traffic Index ti
The time t(in minutes) taken to travel from a source city to a destination city through a road is given by:
time t(in mins) = a x d + b x (ti - 50) , where a = 2 and b = 2.

Based on the information given above, answer the questions that follow.

Q. What is the time taken(in minutes) to travel from B to F through the shortest route possible?


Solution:

We need to construct the given network of cities and connecting roads.


The blue numbers denote the length of the roads and the red ones denote the traffic index. Calculating the time required in minutes between the cities, we get,

Hence, plotting the figure with the lengths of the roads and the time constraints, we will get the following diagram.

Here, the red numbers denote the time taken in minutes and the blue numbers denote the length in kilometres.
Since the distances are very close to each other, the route which has a minimum number of connecting cities will be the shortest route.
Hence, the shortest route is BDF.
Time taken = 94 + 102 = 196.

QUESTION: 27

Seven metropolitan cities A, B, C, D, E, F and G are connected by means of several roads as follows. Each road is bidirectional and has 2 parameters associated with it:
(a) Length (in km) d
(b) Traffic Index ti
The time t(in minutes) taken to travel from a source city to a destination city through a road is given by:
time t(in mins) = a x d + b x (ti - 50) , where a = 2 and b = 2.

Based on the information given above, answer the questions that follow.

Q. How many cities are within a reach of 196 minutes from A?

Solution:

We need to construct the given network of cities and connecting roads.


The blue numbers denote the length of the roads and the red ones denote the traffic index. Calculating the time required in minutes between the cities, we get,

Hence, plotting the figure with the lengths of the roads and the time constraints, we will get the following diagram.

Here, the red numbers denote the time taken in minutes and the blue numbers denote the length in kilometres.
We can reach both B and C directly from A in less than 196 minutes. Also. if we travel from A to B and B to D or if we travel from A to C and C to D, we can reach D in less than 196 minutes.
Hence, there are only 3 cities that can be reached from A in less than 196 minutes.

*Answer can only contain numeric values
QUESTION: 28

Seven metropolitan cities A, B, C, D, E, F and G are connected by means of several roads as follows. Each road is bidirectional and has 2 parameters associated with it:
(a) Length (in km) d
(b) Traffic Index ti
The time t(in minutes) taken to travel from a source city to a destination city through a road is given by:
time t(in mins) = a x d + b x (ti - 50) , where a = 2 and b = 2.

Based on the information given above, answer the questions that follow.

Q. What is the longest distance(in km) that a person can travel to reach A from F if he/she cannot travel through the same city twice?


Solution:

We need to construct the given network of cities and connecting roads.


The blue numbers denote the length of the roads and the red ones denote the traffic index. Calculating the time required in minutes between the cities, we get,

Hence, plotting the figure with the lengths of the roads and the time constraints, we will get the following diagram.

Here, the red numbers denote the time taken in minutes and the blue numbers denote the length in kilometres.
The different routes are:
FDBCA
FDCA
FDECA
FDEGCA
FGCA
FGECA
FGEDCA
FGEDBCA
FDBA
FDECBA
FDEGCBA
FGEDBA
FGECBA
FGCBA
FDCBA
FGEDCBA
FGCEDBA
FGECDBA
FGCDBA 

Since the lengths are very similar to each other, the route containing the maximum number of cities will be the longest route.
There are 5 such routes, FGEDBCA, FDEGCBA, FGEDCBA and FGCEDBA, FGECDBA
FGEDBCA = 47 + 44 + 45 + 46 + 45 + 47 = 274
FDEGCBA = 46 + 45 + 44 + 48 + 45 + 47 = 275
FGEDCBA = 47 + 44 + 45 + 44 + 45 + 47 = 272
FGCEDBA = 47 + 48 + 47 + 45 + 46 + 47 = 280
FGECDBA = 47 + 44 + 47 + 44 + 46 + 47 = 275
the longest length among the 5 is of FGCEDBA.
Length = 280 km.

*Answer can only contain numeric values
QUESTION: 29

Jehindra wanted to open up a driving school in Bilekahalli. Before starting his school he wanted to conduct a survey to understand the need of local people in order to give attractive offers. For this purpose, he tasked his cousin Siddhart to go house to house and gather information on whether the residents knew riding a bike, scooty or car. Siddhart went house to house to gather the driving knowledge of adults and came back with the following details:

  1. Number of females driving all 3 types of vehicles is half the number of males driving all 3 types of vehicle. The number of females driving only scooty and the car is 80 which is double the number of males driving only scooty and car
  2. Total of 120 adults don't know how to drive any type of vehicles
  3. Number of males who don't know to drive any of the vehicles is equal to the number of males who know how to drive only cars
  4. The total number of car drivers in society is equal to the total number of male adults in society
  5. Out of 180 males who do not know how to drive a bike, 130 of them know how to drive at least one type of vehicle
  6. 250 males know how to drive a bike and 210 males know how to drive a car
  7. 185 females know how to drive a scooty out of which 125 of them drives at least 1 more type of vehicle
  8. 1/4th  of the female car drivers do not know how to drive other types of vehicles
  9. Number of females not knowing to drive any of the vehicles is equal to the number of females who know how to drive only bike and car
  10. 60 males know how to drive only bike which is three times the number of females who know how to drive only bike

Q. How many adults were surveyed


Solution:

Since adult can be either male or female but not both we can divide the adults into 2 different sets.  It is given that the survey is done for 3 types of vehicles. It can be represented as 

 

Let us start by filling in the known details
> Out of 180 males who do not know how to drive a bike, 130 of them know how to drive at least one type of vehicle. It implies that 180-130 = 50 males don't know how to drive any vehicles. Thus h = 50. Total 120 adults don't know how to ride any type of vehicles hence h+p = 120 or p = 70
> 250 males know how to drive a bike, thus d+b+g+f = 250
> 210 males know how to drive a car, thus e+f+g+c = 210
> 185 females know how to drive a scooty out of which 125 of them drives at least 1 more type of vehicle. Thus the number of females who drive only scooty= i  = 185 -125 = 60
These all can be updated as follows

> Number of males who don't know to drive any of the vehicles is equal to the number of males who know how to drive only cars. Thus c = 50
> Number of the male members in society = number of men who don't drive bike + number of men who drive bike = 180 + 250 = 430
>The total number of car drivers in society is equal to the total number of male adults in society = 430. Thus number of female car drivers = 430-210 = 220
> 1/4th of the female car drivers do not know how to drive other types of vehicles thus k = 220/4 = 55
> Number of females not knowing to drive any of the vehicles is equal to the number of females who know how to drive only bike and car thus n = 70

> 60 males know how to drive only bike which is three times the number of females who know how to drive only bike. Thus b = 60 and j = 60/3 = 20
> the number of females driving only scooty and the car is 80 which is double the number of males driving only scooty and car. Thus m = 80 and e  = 80/2 = 40

We can say that 80+70+55+o = 220 or o = 15
Looking at female scooty drivers, 60+80+o+l = 60+80+15+l = 185 or l = 30
> Number of females driving all 3 types of vehicles is half the number of males driving all 3 types of vehicle. Thus g = 30
Number of male car drivers = 40+50+g+f = 40+50+30+f = 210 or f = 90
Number of male bike drivers = d+g+f+60 = d+30+90+60= 250 or d = 70


Total male in the society = a+70+60+30+40+90+50 = 430 or a+ 390 = 430 , thus a = 40
Male who know ow to ride scooty = 40+40+70+30 = 180
Number of females who know how to ride bike = 30+15+70+20 = 135
Number of adult females in society  = 60+30+20+80+15+70+55 = 400

Total adults surveyed = 430+400 = 830

*Answer can only contain numeric values
QUESTION: 30

Jehindra wanted to open up a driving school in Bilekahalli. Before starting his school he wanted to conduct a survey to understand the need of local people in order to give attractive offers. For this purpose, he tasked his cousin Siddhart to go house to house and gather information on whether the residents knew riding a bike, scooty or car. Siddhart went house to house to gather the driving knowledge of adults and came back with the following details:

  1. Number of females driving all 3 types of vehicles is half the number of males driving all 3 types of vehicle. The number of females driving only scooty and the car is 80 which is double the number of males driving only scooty and car
  2. Total of 120 adults don't know how to drive any type of vehicles
  3. Number of males who don't know to drive any of the vehicles is equal to the number of males who know how to drive only cars
  4. The total number of car drivers in society is equal to the total number of male adults in society
  5. Out of 180 males who do not know how to drive a bike, 130 of them know how to drive at least one type of vehicle
  6. 250 males know how to drive a bike and 210 males know how to drive a car
  7. 185 females know how to drive a scooty out of which 125 of them drives at least 1 more type of vehicle
  8. 1/4th of the female car drivers do not know how to drive other types of vehicles
  9. Number of females not knowing to drive any of the vehicles is equal to the number of females who know how to drive only bike and car
  10. 60 males know how to drive only bike which is three times the number of females who know how to drive only bike

Q. What is the number of adults who know how to drive a bike and car?


Solution:

Since adult can be either male or female but not both we can divide the adults into 2 different sets.  It is given that the survey is done for 3 types of vehicles. It can be represented as 

Let us start by filling in the known details
> Out of 180 males who do not know how to drive a bike, 130 of them know how to drive at least one type of vehicle. It implies that 180-130 = 50 males don't know how to drive any vehicles. Thus h = 50. Total 120 adults don't know how to ride any type of vehicles hence h+p = 120 or p = 70
> 250 males know how to drive a bike, thus d+b+g+f = 250
> 210 males know how to drive a car, thus e+f+g+c = 210
> 185 females know how to drive a scooty out of which 125 of them drives at least 1 more type of vehicle. Thus the number of females who drive only scooty= i  = 185 -125 = 60
These all can be updated as follows

> Number of males who don't know to drive any of the vehicles is equal to the number of males who know how to drive only cars. Thus c = 50
> Number of the male members in society = number of men who don't drive bike + number of men who drive bike = 180 + 250 = 430
> The total number of car drivers in society is equal to the total number of male adults in society = 430. Thus number of female car drivers = 430-210 = 220
> 1/4th of the female car drivers do not know how to drive other types of vehicles thus k = 220/4 = 55
> Number of females not knowing to drive any of the vehicles is equal to the number of females who know how to drive only bike and car thus n = 70

> 60 males know how to drive only bike which is three times the number of females who know how to drive only bike. Thus b = 60 and j = 60/3 = 20
> the number of females driving only scooty and the car is 80 which is double the number of males driving only scooty and car. Thus m = 80 and e  = 80/2 = 40

We can say that 80+70+55+o = 220 or o = 15
Looking at female scooty drivers, 60+80+o+l = 60+80+15+l = 185 or l = 30
> Number of females driving all 3 types of vehicles is half the number of males driving all 3 types of vehicle. Thus g = 30
Number of male car drivers = 40+50+g+f = 40+50+30+f = 210 or f = 90
Number of male bike drivers = d+g+f+60 = d+30+90+60= 250 or d = 70


Total male in the society = a+70+60+30+40+90+50 = 430 or a+ 390 = 430 , thus a = 40
Male who know ow to ride scooty = 40+40+70+30 = 180
Number of females who know how to ride bike = 30+15+70+20 = 135
Number of adult females in society  = 60+30+20+80+15+70+55 = 400

Number of adult knowing how to drive = 30+90+15+70 = 205

QUESTION: 31

Jehindra wanted to open up a driving school in Bilekahalli. Before starting his school he wanted to conduct a survey to understand the need of local people in order to give attractive offers. For this purpose, he tasked his cousin Siddhart to go house to house and gather information on whether the residents knew riding a bike, scooty or car. Siddhart went house to house to gather the driving knowledge of adults and came back with the following details:

  1. Number of females driving all 3 types of vehicles is half the number of males driving all 3 types of vehicle. The number of females driving only scooty and the car is 80 which is double the number of males driving only scooty and car
  2. Total of 120 adults don't know how to drive any type of vehicles
  3. Number of males who don't know to drive any of the vehicles is equal to the number of males who know how to drive only cars
  4. The total number of car drivers in society is equal to the total number of male adults in society
  5. Out of 180 males who do not know how to drive a bike, 130 of them know how to drive at least one type of vehicle
  6. 250 males know how to drive a bike and 210 males know how to drive a car
  7. 185 females know how to drive a scooty out of which 125 of them drives at least 1 more type of vehicle
  8. 1/4th of the female car drivers do not know how to drive other types of vehicles
  9. Number of females not knowing to drive any of the vehicles is equal to the number of females who know how to drive only bike and car
  10. 60 males know how to drive only bike which is three times the number of females who know how to drive only bike

Q. What is the number of males who drive scooty?

Solution:

Since adult can be either male or female but not both we can divide the adults into 2 different sets.  It is given that the survey is done for 3 types of vehicles. It can be represented as 

Let us start by filling in the known details
> Out of 180 males who do not know how to drive a bike, 130 of them know how to drive at least one type of vehicle. It implies that 180-130 = 50 males don't know how to drive any vehicles. Thus h = 50. Total 120 adults don't know how to ride any type of vehicles hence h+p = 120 or p = 70
> 250 males know how to drive a bike, thus d+b+g+f = 250
> 210 males know how to drive a car, thus e+f+g+c = 210
> 185 females know how to drive a scooty out of which 125 of them drives at least 1 more type of vehicle. Thus the number of females who drive only scooty= i  = 185 -125 = 60
These all can be updated as follows

> Number of males who don't know to drive any of the vehicles is equal to the number of males who know how to drive only cars. Thus c = 50
> Number of the male members in society = number of men who don't drive bike + number of men who drive bike = 180 + 250 = 430
> The total number of car drivers in society is equal to the total number of male adults in society = 430. Thus number of female car drivers = 430-210 = 220
> 1/4th of the female car drivers do not know how to drive other types of vehicles thus k = 220/4 = 55
> Number of females not knowing to drive any of the vehicles is equal to the number of females who know how to drive only bike and car thus n = 70

> 60 males know how to drive only bike which is three times the number of females who know how to drive only bike. Thus b = 60 and j = 60/3 = 20
> the number of females driving only scooty and the car is 80 which is double the number of males driving only scooty and car. Thus m = 80 and e  = 80/2 = 40

We can say that 80+70+55+o = 220 or o = 15
Looking at female scooty drivers, 60+80+o+l = 60+80+15+l = 185 or l = 30
> Number of females driving all 3 types of vehicles is half the number of males driving all 3 types of vehicle. Thus g = 30
Number of male car drivers = 40+50+g+f = 40+50+30+f = 210 or f = 90
Number of male bike drivers = d+g+f+60 = d+30+90+60= 250 or d = 70


Total male in the society = a+70+60+30+40+90+50 = 430 or a+ 390 = 430 , thus a = 40
Male who know ow to ride scooty = 40+40+70+30 = 180
Number of females who know how to ride bike = 30+15+70+20 = 135
Number of adult females in society  = 60+30+20+80+15+70+55 = 400

Number of males driving scooty = 180

QUESTION: 32

Jehindra wanted to open up a driving school in Bilekahalli. Before starting his school he wanted to conduct a survey to understand the need of local people in order to give attractive offers. For this purpose, he tasked his cousin Siddhart to go house to house and gather information on whether the residents knew riding a bike, scooty or car.  Siddhart went house to house to gather the driving knowledge of adults and came back with the following details:

  1. Number of females driving all 3 types of vehicles is half the number of males driving all 3 types of vehicle. The number of females driving only scooty and the car is 80 which is double the number of males driving only scooty and car
  2. Total of 120 adults don't know how to drive any type of vehicles
  3. Number of males who don't know to drive any of the vehicles is equal to the number of males who know how to drive only cars
  4. The total number of car drivers in society is equal to the total number of male adults in society
  5. Out of 180 males who do not know how to drive a bike, 130 of them know how to drive at least one type of vehicle
  6. 250 males know how to drive a bike and 210 males know how to drive a car
  7. 185 females know how to drive a scooty out of which 125 of them drives at least 1 more type of vehicle
  8. 1/4th of the female car drivers do not know how to drive other types of vehicles
  9. Number of females not knowing to drive any of the vehicles is equal to the number of females who know how to drive only bike and car
  10. 60 males know how to drive only bike which is three times the number of females who know how to drive only bike

Q. How many of the adults drive exactly 2 types of vehicles

Solution:

Since adult can be either male or female but not both we can divide the adults into 2 different sets. It is given that the survey is done for 3 types of vehicles. It can be represented as 

Let us start by filling in the known details
> Out of 180 males who do not know how to drive a bike, 130 of them know how to drive at least one type of vehicle. It implies that 180-130 = 50 males don't know how to drive any vehicles. Thus h = 50. Total 120 adults don't know how to ride any type of vehicles hence h+p = 120 or p = 70
> 250 males know how to drive a bike, thus d+b+g+f = 250
> 210 males know how to drive a car, thus e+f+g+c = 210
> 185 females know how to drive a scooty out of which 125 of them drives at least 1 more type of vehicle. Thus the number of females who drive only scooty= i  = 185 -125 = 60
These all can be updated as follows

> Number of males who don't know to drive any of the vehicles is equal to the number of males who know how to drive only cars. Thus c = 50
> Number of the male members in society = number of men who don't drive bike + number of men who drive bike = 180 + 250 = 430
> The total number of car drivers in society is equal to the total number of male adults in society = 430. Thus number of female car drivers = 430-210 = 220
> 1/4th of the female car drivers do not know how to drive other types of vehicles thus k = 220/4 = 55
> Number of females not knowing to drive any of the vehicles is equal to the number of females who know how to drive only bike and car thus n = 70

> 60 males know how to drive only bike which is three times the number of females who know how to drive only bike. Thus b = 60 and j = 60/3 = 20
> the number of females driving only scooty and the car is 80 which is double the number of males driving only scooty and car. Thus m = 80 and e  = 80/2 = 40

We can say that 80+70+55+o = 220 or o = 15
Looking at female scooty drivers, 60+80+o+l = 60+80+15+l = 185 or l = 30
> Number of females driving all 3 types of vehicles is half the number of males driving all 3 types of vehicle. Thus g = 30
Number of male car drivers = 40+50+g+f = 40+50+30+f = 210 or f = 90
Number of male bike drivers = d+g+f+60 = d+30+90+60= 250 or d = 70


Total male in the society = a+70+60+30+40+90+50 = 430 or a+ 390 = 430 , thus a = 40
Male who know ow to ride scooty = 40+40+70+30 = 180
Number of females who know how to ride bike = 30+15+70+20 = 135
Number of adult females in society  = 60+30+20+80+15+70+55 = 400

Number of adults driving exactly 2 types of vehicles = 70+40+90+80+30+70 = 380

*Answer can only contain numeric values
QUESTION: 33

Messi, Neymar and Suarez are three players playing for a football team together. They played for three seasons together and scored some goals when they were playing for the team. Given below is a chart that shows the proportion of goals scored by the three players among them. They together scored 80%, 90% and 60% of the goals scored by their teams in the 2012-13, 2013-14 and 2014-15 season respectively.

Q. If Messi, Neymar and Suarez scored 120, 73 and 82 goals respectively in the three seasons combined, then the team for which they played scored how many goals in the 2014-2015 season?


Solution:

Let us assume that the total goals scored by the 3 players in the year 2012-13, 2013-14, 2014-15 be A, B and C respectively.
Using the information given in the question, we can form a table as below


 

It is given that Messi scored 120 goals in total.
So, 0.6A+0.4B+ 0.3C = 120
⇒ 6A+4B+3C=1200 .....(1)
Suarez scored 82 goals in all the seasons combined.
So, 0.2A+0.4B+0.2C = 82
⇒ A+2B+C= 410 .....(2)
Neymar scored 73 goals in all the seasons combined.
So, 0.2A+0.2B+0.5C= 73
⇒ 2A+2B+5C=730 .....(3)
Subtracting 3 times equation (2) from (1), we get:
6A+4B+3C-(3A+6B+3C)= 1200- 1230
⇒ 3A-2B= -30 ....(4)
Subtracting equation (3) from 5 times equation (2), we get:
5A+10B+5C-(2A+2B+5C)= 2050- 730
⇒ 3A+8B=1320 ...(5)
Subtracting equation (4) from equation (5), we get:
3A+8B-3A+2B= 1320+30
⇒ 10B= 1350
⇒ B = 135.
Using B= 135 in equation (4), 3A= 2B-30
⇒ 3A= 270-30= 240
∴ A = 80
Using A=80 and B= 135 in equation (2), we get:
80 + 270 + C = 410.
⇒ C = 60.
Let the total goals scored by the entire team in the year 2012-13, 2013-14 and 2014-15 be X, Y and Z.
0.8X = A = 80. So, X = 100
0.9Y = B = 135. So, Y= 150
and 0.6C = 60. So, C = 100.

QUESTION: 34

The letters inside the circles given in the figure below represent digits from 1 to 9, such that the sum of any three numbers which are connected in a straight line is equal.
It is also known that-

  1. For any pair of two numbers, diametrically opposite to one another, the number represented by the alphabet which appears before the other one in the English dictionary is smaller than its pair.
  2. Each one of E and F does not represent 4.
  3. A, B and G are prime numbers and X is not a perfect square.

Q. What is the number represented by G?

Solution:

It is given that each set of 3 numbers forming a straight line gives the same sum, let's say 'K'.
∵ A, B, C, D, E, F, G, H and X represents numbers from 1 to 9.
Sum of all the numbers 

A+B+X = K   .... (1)
C+D+X = K .... (2)
E+F+X = K .... (3)
G+H+X = K .... (4)
Adding all four above equations, we get:
A+B+C+D+E+F+G+H+X+3X= 4K
⇒ 45+ 3X= 4K
⇒ 3(15+X) = 4K.
∴ K should be a multiple of 3 and 4K should be greater than 45.
When K= 12, we have:
45 + 3X = 48
⇒ X = 1---- Case 1(Not Possible because X is not a perfect square)
When K= 15, we have 45+3X= 60 and X = 5---- Case 2.
When K=18, we have 45+3X= 72 and X = 9----- Case 3 (Not possible because X is not a perfect square)
We can see from equations (1), (2), (3) and (4) that A+B= C+D= E+F= G+H
Only Possibility X=5 and Sum =15
When sum= 15 and X=5.
A+B= C+D= E+F= G+H= 15-5= 10.
And hence any pair of diametrically opposite letters can represent pairs- (1,9), (2,8), (3,7) and (4,6)
Using the extra information given in the question, we can say that the pair that contains two prime numbers are (A,B)
∵ Only (3,7) forms such a pair, A=3 and B= 7 (A takes the lower number of the two because of the 1st point mentioned in the question).
Also, the only other prime number left is 2, which is taken up by G. If G=2, H=8
We are now left with pairs (E,F) and (C,D) which can take either (1,9) or (4,6).
∵ Neither E nor F is 4, E and F must represent 1 and 9 respectively and therefore C and D takes the values 4 and 6 respectively.
So, A= 3, B=7, C=4, D=6, E=1, F=9, G=2, H=8 and X=5.

QUESTION: 35

The letters inside the circles given in the figure below represent digits from 1 to 9, such that the sum of any three numbers which are connected in a straight line is equal.
It is also known that-

  1. For any pair of two numbers, diametrically opposite to one another, the number represented by the alphabet which appears before the other one in the English dictionary is smaller than its pair.
  2. Each one of E and F does not represent 4.
  3. A, B and G are prime numbers and X is not a perfect square.

Q. Suppose that we rule out the condition given in statement 3 of the question, how many values are possible for X?

Solution:

It is given that each set of 3 numbers forming a straight line gives the same sum, let's say 'K'.
∵ A, B, C, D, E, F, G, H and X represents numbers from 1 to 9.
Sum of all the numbers 

A+B+X = K   .... (1)
C+D+X = K .... (2)
E+F+X = K .... (3)
G+H+X = K .... (4)
Adding all four above equations, we get:
A+B+C+D+E+F+G+H+X+3X= 4K
⇒ 45+ 3X= 4K
⇒ 3(15+X) = 4K.
∴ K should be a multiple of 3 and 4K should be greater than 45.
When K= 12, we have:
45 + 3X = 48
⇒ X = 1---- Case 1
When K= 15, we have 45+3X= 60 and X= 5---- Case 2.
When K=18, we have 45+3X= 72 and X= 9----- Case 3 
∴ There are 3 possible values for X.

QUESTION: 36

The letters inside the circles given in the figure below represent digits from 1 to 9, such that the sum of any three numbers which are connected in a straight line is equal.
It is also known that-

  1. For any pair of two numbers, diametrically opposite to one another, the number represented by the alphabet which appears before the other one in the English dictionary is smaller than its pair.
  2. Each one of E and F does not represent 4.
  3. A, B and G are prime numbers and X is not a perfect square.

Q. What is the value of B?

Solution:

It is given that each set of 3 numbers forming a straight line gives the same sum, let's say 'K'.
∵ A, B, C, D, E, F, G, H and X represents numbers from 1 to 9.
Sum of all the numbers 

A+B+X = K   .... (1)
C+D+X = K .... (2)
E+F+X = K .... (3)
G+H+X = K .... (4)
Adding all four above equations, we get:
A+B+C+D+E+F+G+H+X+3X= 4K
⇒ 45+ 3X= 4K
⇒ 3(15+X) = 4K.
∴ K should be a multiple of 3 and 4K should be greater than 45.
When K= 12, we have:
45 + 3X = 48
⇒  X= 1---- Case 1 (Not Possible because X is not a perfect square)
When K= 15, we have 45+3X= 60 and X= 5---- Case 2.
When K=18, we have 45+3X= 72 and X= 9----- Case 3 (Not possible because X is not a perfect square)
We can see from equations (1), (2), (3) and (4) that A+B= C+D= E+F= G+H
CASE 2 is the only possibility.
When sum= 15 and X=5.
A+B= C+D= E+F= G+H= 15-5= 10.
And hence any pair of diametrically opposite letters can represent pairs- (1,9), (2,8), (3,7) and (4,6)
Using the extra information given in the question, we can say that the pair that contains two prime numbers are (A,B)
∵ Only (3,7) forms such a pair, A=3 and B= 7 (A takes the lower number of the two because of the 1st point mentioned in the question).
Also, the only other prime number left is 2, which is taken up by G. If G=2, H=8
We are now left with pairs (E,F) and (C,D) which can take either (1,9) or (4,6).
∵ Neither E nor F is 4, E and F must represent 1 and 9 respectively and therefore C and D takes the values 4 and 6 respectively.
So, A= 3, B=7, C=4, D=6, E=1, F=9, G=2, H=8 and X=5.

QUESTION: 37

There were 35 logical friends who were trying to get tickets for a session held by a famous Mathematician- Mr X. But Mr X put in a challenge for all 35 of the friends to get into the session. He gave a cap each to the 35 enthusiastic friends, the colour of which could not be seen by the person wearing it. However, a person was able to see the colours of the caps worn by the remaining 34 friends. Given below are some rules put in by Mr X for the 35 friends-

RULES:

  1. A person is allowed to enter the session if he/she can tell his/her own cap's colour. Mr X gives 1 minute time for them to think, at the end of which he opens the door. He repeats this process till everyone gets in.
  2. No person is allowed to speak anything until he gets inside the session.
  3. The friends do not know the total varieties of colours of caps.
  4. The caps are distributed in such a way that it will eventually be possible for everyone to logically deduce their cap's colour and everyone is aware of this.
  5. All the 35 friends played the game perfectly and gained the entry eventually after multiple rounds.
  6. The following events took place at the end of every minute.

EVENTS:

  1. 6 of the friends gained entry after the 1st time the gate was opened.
  2. The friends wearing blue and green caps entered the gate when it was opened for the second time.
  3. 4 persons entered the gate when it was opened for the third time. 
  4. No one could enter the gate when it was opened for the fourth time.
  5. Friends wearing multiple cap colours entered the gate when it was opened for the fifth time.

Q. How many different colours of caps were given to the 35 friends in total?

Solution:

It is given that the 35 friends were able to figure out themselves the colour of the cap they were wearing. If this is the case, there should not be any cap colour present in a quantity of 1. Because then the person wearing it will never know the colour of his cap. 
Therefore, it is necessary that the minimum number of caps of a particular colour is 2. Now, since the 35 friends are logical, the ones who see only 1 cap of a particular colour can understand that the colour of his cap is the same. It is given that after the gate was opened for the first time, 6 friends went inside. This suggests that 3 pairs of friends moved inside. So, 3 colours were present in numbers of 2.
Next up, out of the 29 friends left, everyone knows that the ones wearing 2 caps are gone. They cannot comment anything on their cap's colour watching 3 or more caps of the same colour. Because they cannot surely know if they are the ones with the fourth cap of the same colour. So, the ones who see only 2 caps of the same colour can understand that they are the ones wearing the cap with the same colour as the ones who were in pairs already left. The group of friends wearing blue and green cap entered the session when the gate was opened for the second time. So, 6 people joined the session and 23 were left outside
We now see a pattern building up. After people with 2 and 3 same coloured caps left, the ones with 4 same coloured caps will enter the gate and since 4 people left when the gate was open for the third time indicates that there was only 1 such colour which had 4 caps. Now, only 19 friends were outside the gate.
Again, we see that there was no group of 5 caps having the same colour. Had there been a group of 5 of the same coloured caps, they would have left the group. 
The ones who could see that there are 5 other caps with same colour, understood that they are the ones wearing the 6th cap. But it is said that there were friends wearing multiple coloured caps who went inside for the session. So, either 2 or 3 groups of 6 people each must have left for the session. But, if there were 3 such groups, only 1 person would be left and we already saw that a single coloured cap is not possible. So, there were 2 such groups of caps which had 6 similar colour. So, 12 friends went inside leaving just 7 behind.
Now, each of the 7 fiends could see 6 caps of the same colour and thus conclude that they are the ones wearing the same coloured cap and go inside together. 
So, in total, after the first round- 3 colours went inside.
After the second round, 2 colours went inside.
After the third round, 1 colour went inside.
After the 4th round- 0 colour went inside.
After the 5th round, 2 colours went inside and after the 6th round, 1 colour went inside.
∴ There were 9 colours of the cap with the 35 friends.

QUESTION: 38

There were 35 logical friends who were trying to get tickets for a session held by a famous Mathematician- Mr X. But Mr X put in a challenge for all 35 of the friends to get into the session. He gave a cap each to the 35 enthusiastic friends, the colour of which could not be seen by the person wearing it. However, a person was able to see the colours of the caps worn by the remaining 34 friends. Given below are some rules put in by Mr X for the 35 friends-

RULES:

  1. A person is allowed to enter the session if he/she can tell his/her own cap's colour. Mr X gives 1 minute time for them to think, at the end of which he opens the door. He repeats this process till everyone gets in.
  2. No person is allowed to speak anything until he gets inside the session.
  3. The friends do not know the total varieties of colours of caps.
  4. The caps are distributed in such a way that it will eventually be possible for everyone to logically deduce their cap's colour and everyone is aware of this.
  5. All the 35 friends played the game perfectly and gained the entry eventually after multiple rounds.
  6. The following events took place at the end of every minute.

EVENTS:

  1. 6 of the friends gained entry after the 1st time the gate was opened.
  2. The friends wearing blue and green caps entered the gate when it was opened for the second time.
  3. 4 persons entered the gate when it was opened for the third time. 
  4. No one could enter the gate when it was opened for the fourth time.
  5. Friends wearing multiple cap colours entered the gate when it was opened for the fifth time.

Q. How many groups with the same colours of caps went inside when the gate was opened for the 5th time?

Solution:

It is given that the 35 friends were able to figure out themselves the colour of the cap they were wearing. If this is the case, there should not be any cap colour present in a quantity of 1. Because then the person wearing it will never know the colour of his cap.
Therefore, it is necessary that the minimum number of caps of a particular colour is 2. Now, since the 35 friends are logical, the ones who see only 1 cap of a particular colour can understand that the colour of his cap is the same. It is given that after the gate was opened for the first time, 6 friends went inside. This suggests that 3 pairs of friends moved inside. So, 3 colours were present in numbers of 2.
Next up, out of the 29 friends left, everyone knows that the ones wearing 2 caps are gone. They cannot comment anything on their cap's colour watching 3 or more caps of the same colour. Because they cannot surely know if they are the ones with the fourth cap of the same colour. So, the ones who see only 2 caps of the same colour can understand that they are the ones wearing the cap with the same colour as the ones who were in pairs already left. The group of friends wearing blue and green cap entered the session when the gate was opened for the second time. So, 6 people joined the session and 23 were left outside
We now see a pattern building up. After people with 2 and 3 same coloured caps left, the ones with 4 same coloured caps will enter the gate and since 4 people left when the gate was open for the third time indicates that there was only 1 such colour which had 4 caps. Now, only 19 friends were outside the gate.
Again, we see that there was no group of 5 caps having the same colour. Had there been a group of 5 of the same coloured caps, they would have left the group.
The ones who could see that there are 5 other caps with same colour, understood that they are the ones wearing the 6th cap. But it is said that there were friends wearing multiple coloured caps who went inside for the session. So, either 2 or 3 groups of 6 people each must have left for the session. But, if there were 3 such groups, only 1 person would be left and we already saw that a single coloured cap is not possible. So, there were 2 such groups of caps which had 6 similar colour. So, 12 friends went inside leaving just 7 behind.
Now, each of the 7 fiends could see 6 caps of the same colour and thus conclude that they are the ones wearing the same coloured cap and go inside together.
So, in total, after the first round- 3 colours went inside.
After the second round, 2 colours went inside.
After the third round, 1 colour went inside.
After the 4th round- 0 colour went inside.
After the 5th round, 2 colours went inside and after the 6th round, 1 colour went inside.
∴ 2 groups wearing the same coloured caps went inside when the gate was opened for the 5th time .

QUESTION: 39

There were 35 logical friends who were trying to get tickets for a session held by a famous Mathematician- Mr X. But Mr X put in a challenge for all 35 of the friends to get into the session. He gave a cap each to the 35 enthusiastic friends, the colour of which could not be seen by the person wearing it. However, a person was able to see the colours of the caps worn by the remaining 34 friends. Given below are some rules put in by Mr X for the 35 friends-

RULES:

  1. A person is allowed to enter the session if he/she can tell his/her own cap's colour. Mr X gives 1 minute time for them to think, at the end of which he opens the door. He repeats this process till everyone gets in.
  2. No person is allowed to speak anything until he gets inside the session.
  3. The friends do not know the total varieties of colours of caps.
  4. The caps are distributed in such a way that it will eventually be possible for everyone to logically deduce their cap's colour and everyone is aware of this.
  5. All the 35 friends played the game perfectly and gained the entry eventually after multiple rounds.
  6. The following events took place at the end of every minute.

EVENTS:

  1. 6 of the friends gained entry after the 1st time the gate was opened.
  2. The friends wearing blue and green caps entered the gate when it was opened for the second time.
  3. 4 persons entered the gate when it was opened for the third time. 
  4. No one could enter the gate when it was opened for the fourth time.
  5. Friends wearing multiple cap colours entered the gate when it was opened for the fifth time.

Q. Had there been 37 friends initially instead of 35 and all the rules and events remained the same as stated, then what would be the minimum number of times that gate was opened by Mr X to ensure that everyone went in?

Solution:

It is given that the 37 friends were able to figure out themselves the colour of the cap they were wearing. If this is the case, there should not be any cap colour present in a quantity of 1. Because then the person wearing it will never know the colour of his cap.
Therefore, it is necessary that the minimum number of caps of a particular colour is 2. Now, since the 37 friends are logical, the ones who see only 1 cap of a particular colour can understand that the colour of his cap is the same. It is given that after the gate was opened for the first time, 6 friends went inside. This suggests that 3 pairs of friends moved inside. So, 3 colours were present in numbers of 2.
Next up, out of the 31 friends left, everyone knows that the ones wearing 2 caps are gone. They cannot comment anything on their cap's colour watching 3 or more caps of the same colour. Because they cannot surely know if they are the ones with the fourth cap of the same colour. So, the ones who see only 2 caps of the same colour can understand that they are the ones wearing the cap with the same colour as the ones who were in pairs already left. The group of friends wearing blue and green cap entered the session when the gate was opened for the second time. So, 6 people joined the session and 25 were left outside
We now see a pattern building up. After people with 2 and 3 same coloured caps left, the ones with 4 same coloured caps will enter the gate and since 4 people left when the gate was open for the third time indicates that there was only 1 such colour which had 4 caps. Now, only 21 friends were outside the gate.
Again, we see that there was no group of 5 caps having the same colour. Had there been a group of 5 of the same coloured caps, they would have left the group.
The ones who could see that there are 5 other caps with same colour, understood that they are the ones wearing the 6th cap. But it is said that there were friends wearing multiple coloured caps who went inside for the session. So, either 2 or 3 groups of 6 people each must have left for the session. But, if there were 3 such groups, only 3 persons would be left and we already saw that three caps with the same colour left for the session. So, there were 2 such groups of caps which had 6 similar colours. So, 12 friends went inside leaving just 9 behind.
Now, the possibility of having a group of 7 or 8 same coloured caps is ruled out because that would leave behind 2 or 1 cap with the same colour. This cannot be possible when the friends are logical as the ones with 2 same coloured caps left when the gate was opened for the first time. 
Now, each of the 9 fiends could see 8 caps of the same colour and thus conclude that they are the ones wearing the same coloured cap and go inside together.
So, in total, after the first round- 3 colours went inside.
After the second round, 2 colours went inside.
After the third round, 1 colour went inside.
After the 4th round- 0 colour went inside.
After the 5th round, 2 colours went inside andafter the 6th round, 1 colour went inside.
∴ If there were 37 friends instead of 35 it would take 6 rounds to make sure everyone gets through to the session and hence it would require X to open the gate a minimum of 6 times .

QUESTION: 40

In a certain code Language
134 means good and tasty
478 means see good picture
729 means picture are faint
Which number has been used here for faint?

Solution:

4= good
7= Picture
and 2 and 9= are and faint respectively.

QUESTION: 41

Statement:
Anger is energy, in a more proactive way and how to channelize it is in itself a skill.
Assumptions:
I. Anger needs to be channelized.
II. Only skillful people can channelize anger to energy.

Solution:

In this the author has not clearly stated whether there is a need to channelize anger in to energy or not. So, I is irrelevant.
In the statement II it is given that channelizing anger to energy is a skill. Here the assumption of the author is that only those people who have the skill can channelize anger to energy.
Only II is implicit.

QUESTION: 42

Anger is energy, in a more proactive way and how to channelize it is in itself a skill.
Assumptions:
I. Anger needs to be channelized.
II. Only skillful people can channelize anger to energy.

Solution:

In this the author has not clearly stated whether there is a need to channelize anger in to energy or not. So, I is irrelevant.
In the statement II it is given that channelizing anger to energy is a skill. Here the assumption of the author is that only those people who have the skill can channelize anger to energy.
Only II is implicit.

QUESTION: 43

If South-East becomes North, North-East becomes West and so on. What will West become?

Solution:


 

It is clear from the diagrams that new name of West will become South-East.

QUESTION: 44

Which amongst the following is kept at the topmost position?

Solution:

Boxes: P, Q, R, S, T, U, V and W.
1) Only three boxes are kept above box R.
2) Two boxes are kept between box T and box R.
Here, we have two possible cases i.e. Case 1 and Case 2.
3) Box W is kept immediate below box T.


4) Four boxes are kept between box W and box U.
5) Box S is kept just above box Q but not at the topmost position.

6) Box V is kept above box P.
7) More than three boxes are kept between box V and box P.
Here, Case 1 will be eliminated hence, Case 2 will be our final arrangement:

Clearly, box T is kept at the topmost position.

*Answer can only contain numeric values
QUESTION: 45

3 friends started invested in the company. Friend A invested 60,000 for 4 months. After this, he additionally invested 20,000 extra for the rest of the year. Friend B invested in the company after 6 months and the amount he invested was 50,000. Friend C invested 1,00,000 for the first 7 months after which he took out 40,000. How much money will C receive at the end of a year if the total profit of the company is 1,09,00,000?


Solution:

Profit received is proportional to the money and time invested for the company.
For A the product of time and money for a year will be = (60,000 × 4) + (80, 000 × 8) = 240,000 + 6,40,000 = 8,80,000
For B the product of time and money for a year will be = (50,000 × 6) = 3,00,000
For C the product of time and money for a year will be = (1,00,000×7)+(60,000 × 5) = 10,00,000
Ratio of Profit for A:B:C will be = 8,80,000:3,00,000:10,00,000
Ratio of Profit for A:B:C will be = 44:15:50
Fraction of money recieved by C


Amount received 

QUESTION: 46

Ram is the father of Shyam. Currently, 3 times the age of Ram is 7 times the age of Shyam.  When Shyam was as old as Mohan's present age, The age of Ram then was 5 times that of Shyam's at that time. What is the ratio of age of current age of Ram to the current age of Mohan?

Solution:

Let the current age of Ram be RR, Shyam be SS, and Mohan is M.
As per the question, 3R = 7S ....(i)
Let the age difference of Shyam and Mohan be x. Thus x = S - M
x year ago, age of Ram was times that of Shyam
R − x = 5(S − x)
putting the value of x
R−(S−M)= 5(S−(S−M)).
R−S+M =5M or R - S = 4M.....(ii)
Putting the value of S from (i) in (ii)

QUESTION: 47

There are 2 containers of 1 L each which are exactly half filled. The first container named container A contains pure alcohol and the second container named container B contains pure water. A cup of volume 70 ml is used to transfer the contents among the containers. Initially, 2 cups of A is poured in B and was mixed thoroughly. After this 3 cups were taken from B and were put in A and mixed. After which 1 cup was taken and put in B. If the concentration of alcohol in A is P and the concentration of water in B is Q. Which of the following is true?

Solution:

A has 500ml of alcohol and B has 500ml of water.
We see that after all the transfer, both the container will have 500ml each.
Let A has x ml of alcohol in it. Thus it will have 500 - x ml of water.  
Since overall A+B has 500 ml each of water and alcohol. If A has x ml alcohol then B will have 500 − x ml of alcohol.
Therefore B will have x ml of water.
Concentration of alcohol in 

Concentration of water in

Thus P = Q

*Answer can only contain numeric values
QUESTION: 48

Find the sum of integer values of x (|x| <10) satisfying the following inequality:


Solution:


Factorising these terms we get,


 

Hence, possible values are -3, -2, 5, 6, 7, 8, 9.
Sum = 30.

QUESTION: 49

If x2 - √6x = 1, then the value of x10 - 61x6 - 62x2 is ?

Solution:


Dividing throughout by x, we get:

Squaring both sides, we get:

Squaring both the sides again, we get:

Now, we can re-write x10 - 61x6 - 62x2 as:

QUESTION: 50

In the figure given below, AB = 9 units, BC = 12 units, CD= 13 units, AD = 14 units and AC = 15 units. Perpendiculars from B and D are dropped to AC at P and Q respectively. What is the length of PQ?

Solution:

Considering triangle ACD, we can find its area by heron's formula using Area

where s is the semi-perimeter and a, b and c are its side. 
s = (13+14+15)/2 = 42/2 = 21 units.

So, when we drop a perpendicular from C to AD as:


⇒ 7EC = 84.
∴ EC = 12 units. Also, ED= 5 because 5, 12 and 13 are pythagorean triplets and ECD is a right angled triangle.
∴ AE = 9 units, EC= 12 units and AC = 15 units.
Δ ABC & Δ AEC are congruent.
In triangle ABC,  AC/AB = AB/AP
⇒ 15/9 = 9/AP
∴ AP = 27/5 units.
When BP is extended to E,

∵ BE is parallel to QD,
In triangle ACD, AE/ED = AP/PQ

∴ PQ = 3 units.

QUESTION: 51

In a triangle ABC, with AB = 24 cm, BC = 36 cm and AC = 50 cm, a semicircle is drawn inside the triangle such that its diameter lies on AC and is tangent to AB and BC. If O is the centre of the semi-circle, find the measure of line AO.

Solution:


 

MB = BN (B is an external point and BM and Bn are tangents to the circle).
Angles BMO and BNO = 90 degrees and OB is common to both. Hence, triangles OBM and OBN are congruent triangles. 
So, OB bisects angle B and hence;


⇒ 3AO = 2(50 - AO)
⇒ 5AO = 100.
∴ AO = 20

QUESTION: 52

Find the area of the square inscribed inside a circle, which is in turn is inscribed inside an equilateral triangle of side 3√3 cm.

Solution:


Given, the side length of the triangle = 3√3 cm.


So, the circle inside the triangle has a radius of length 3/2 cm.
The diameter of the circle is the diagonal of the square = 3 cm.
∴ Side length of the square becomes 3/√2 cm.
∴ Area of the square = (3/√2)2 = 9/2 sq. cms. 

*Answer can only contain numeric values
QUESTION: 53

A right angled triangle has an inradius of length 3 cm and a circumradius of length 12.5 cm. What is the area of the triangle in square cms?


Solution:

We know that circumradius, R = half of hypotenuse.
∴ Hypotenuse H = 25 cm.
Also, inradius  where a and b are the perpendicular sides of the right angled triangle.


⇒ a + b = 31. ....(1)

Also, a+ b2 = H2  
⇒ a2 + b2 = 625 .....(2)
Squaring (1) and subtracting (2) from it, we get:
a2 + b2 + 2ab - a- b2 = 961 - 625
⇒ 2ab = 336
ab = 168
Area of a right angled triangle = ab/2 = 168/2 = 84 sq. cms

QUESTION: 54

How many integers satisfy the following inequality?
(x - 1) (x + 2) (x - 3) ≥ (x + 1) (x - 2) (x + 3)

Solution:

(x - 1) (x + 2) (x - 3) ≥ (x + 1) (x - 2) (x + 3)
Upon expandning we get,
x3 - 2x2 - 5x + 6 ≥ x3 + 2x2 - 5x - 6
Cancelling the common terms we get 
-2x2 + 6 ≥ 2x2 - 6
12 ≤ 4x2
x2 ≤ 3
-1 , 0 1 and  are 3 such integers which statisfy this

QUESTION: 55

Find the range of values of x satisfying the following inequation:

Solution:

|x| + 5 is always greater than zero.
Hence the denominator should be greater than zero for the inequality to hold true.
∣x∣2 + ∣x∣ − 6 > 0
Let |x| be t.
t+ t - 6 > 0
(t + 3) (t - 2) > 0
Hence, t > 2 or t < -3
Since, t = |x|, it cannot be less than -3.
Hence, |x| > 2,
x < -2, x > 2

*Answer can only contain numeric values
QUESTION: 56

A test has 100 questions. 3 marks are awarded for correct answers and -1 for incorrect attempts. No marks are allotted for the questions which are not attempted. The score of a student in the test is 155 and the number of questions he didn't attempt was the lowest possible.  How many questions did he get wrong?


Solution:

Let a, b, c be the numbers of correct , incorrect and not attempted question in the test
As per the question 3a - b = 155 ...(I) 
and a + b + c = 100...(II)
We have to maximimse the number of attempted question, thus minimise the vale of c (I) + (II)
4a + c = 155  or c  = 255 - 4a
The maximum possible value of a can be 63. At which the value of c will be 3.
Value of b = 100-(63+3) = 100-66 = 34 

*Answer can only contain numeric values
QUESTION: 57

Find the value of [log2 100]+[log3 99]+[log4 98]+[log5 97]+....+[log100 2] where [X] equals the largest integer less than or equal to X.


Solution:

[log2 100] = 6 since 26 = 64
Similarly,
[log3 99] = 4
[log4 98] = 3
From [log5 97] to [log9 93], we get 2 each.
From [log10 92] to [log51 51], we get 1. For the rest we get 0.
Hence, sum = 6 + 4 + 3 + 5 x 2 + 42 x 1 = 65

*Answer can only contain numeric values
QUESTION: 58

Solve for x: log10 [log10 (2+log2 (x+2))] = 0 


Solution:

log10 [log10 (2+log2 (x+2))] = 0 
∵ RHS = 0, [log(2 + log2 (x+2))] = 1, which means:
2 + log2 (x + 2) = 10
⇒ log2 (x + 2) = 8
⇒ (x + 2) = 28
∴ x = 256 - 2 = 254

QUESTION: 59

In a biased dice with numbers from 1 to 6, each prime number has an equal chance of showing up and each non-prime number has an equal chance of showing up on a roll of the dice. If the probability that an odd number is rolled is 4/9, what is the probability that 6 is rolled in ane throw of the dice?

Solution:

Let P(2) = P(3) = P(5) = x
and let P(1) = P(4) = P(6) = y
Now, we know the probability of an odd number is 4/9.
2x + y = 4/9 or 18x + 9y = 4
Also, total probability is 1.
Hence, 3x+3y = 1
x + y = 1/3
Solving the 2 equations, we get x = 1/9 and y = 2/9.
Hence, probability of getting a six = 2/9

QUESTION: 60

Ram gives out loans to people via 2 schemes. Scheme I charges an interest of 5% compounded annually. Scheme II is charged on simple interest p%. If it is known that both the scheme will have same return in 3 years. what is value of p?

Solution:

Let the amount loaned be L.
Return received after 3 years from scheme I = (1.05)3 L = 1.157625L
For the scheme II: 
Interest received at the end of 3-years

Total amount recieved

Equating the both = L(1+0.03P) = 1.156725L
Thus 0.03P = 0.156725
P% = 5.254%

QUESTION: 61

Ram buys rice from a whole sale dealer at Rs. 100 per Kg and sells it to his customers. While purchasing the rice, he noticed that the wholesaler was cheating him and was using a scale that showed 10% more weight than it was weighing. Instead of fighting with the wholesaler, he decided to markup his selling price in such a way that he earns a profit of 10%. What should the selling price (per Kg) be if Ram uses an accurate scale while selling to his customers?

Solution:

If he puts 1 kg of rice, the scale will show 1.1kg. Thus Ram has to pay Rs 110/kg
Now he intends to make a profit of 10% by selling this. 
Total amount he should get back = Rs 1.1 × 110 = Rs121121.
Thus by selling 1 kg rice he is getting Rs 121
The rate at which he sells = Rs121/kg

QUESTION: 62

A milk seller buys milk at Rs 50/L and then mixes some water into it, after which he marks up the price of the solution by 20% and gives a discount of 20% on the marked price. If he earns a profit of 20% in the entire transaction, what is the amount of water(in mL) mixed for every 2L of pure milk? Assume that the cost of water is negligible.

Solution:

The SP of 1 L of milk-water solution = 50 x 1.2 x 0.8 = 48
Now, he is earning a profit of 20%.
Hence,
1.2CP = 48
CP = 40
So, the CP of 1L solution is Rs 40.
Since the cost of water is 0, the entire Rs 40 constitutes milk only
Rs 50 is the CP of 1000mL of milk.
Hence, Rs 40 is the CP of 800mL of milk.
Hence, in every 800mL of pure milk, 200mL of water is mixed.
Hence in every 4mL of pure milk, 1 mL of water is mixed.
Hence, in 2L, 500mL of water is mixed.

QUESTION: 63

Jack has three more cards than Bill. Together they have 47 cards. If x represents the number of cards Bill has, then an equation that can be used to determine the number of cards each one has is


Solution:

Bill has x cards.
Jack has 3 more cards than Bill. So, Jack has x+3 cards.
So, together Bill and Jack have x+x+3=2x+3 cards.
The question states that they have 47 cards between them.
50, 2x + 3 = 47

QUESTION: 64

How many terms are common in the following series?
S1 = 9, 18, 27, 36, 45, ....... (up to 1000 terms)
S2 = 16, 27, 38, 49, 60, 71, ....... (up to 1000 terms)

Solution:

The m th term of Series 1 can be written as 9m.
The n th term of series 2 can be written as 5 + 11n.
The first term of both series is 27.
The common difference = LCM(9,11) = 99
The last term of the first series = 9000, which is less than the last term of the second series.
Hence,
27 + (t-1)99 <= 9000
3 + (t-1)11 <= 1000
t - 1 <= 90.xx
t - 1 = 90
t = 91.

*Answer can only contain numeric values
QUESTION: 65

If three numbers a, b, c are in AP with a common difference of 5, and three numbers p, b, q are in GP with a common ratio of 5, also (q - p) is 14.4 times (c - a), find the value of b. Enter -1 if it cannot be determined.


Solution:

a = b - 5
c = b + 5
p = b/5
q = 5b
q - p = 14.4 (c - a)
5b - b/5 = 14.4 (b + 5 - b + 5)
5b - 0.2b = 14.4 x 10
4.8b = 144
b = 30.

QUESTION: 66

Out of a certain number of students in the college, square root of one-third the total students were selected to represent in a sports tournament. 4 more students were selected as extras for the squad. The remaining 26/27 of the total students failed to be selected for the tournament. How many students did the college have in total?

Solution:

Let the total number of students be x. Students selected = √x/3.
Extras selected = 4.
And the remaining students formed 26/27 of the total students.
So, the students selected including the extras for the tournament 


When x = 27, total students selected

∵ 7/27 ≠ 1/27, we reject this solution.
When x = 432, total students selected 

∵ 16/432 = 1/27, this is our answer.

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