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This mock test of CAT Mock Test - 6 for CAT helps you for every CAT entrance exam.
This contains 100 Multiple Choice Questions for CAT CAT Mock Test - 6 (mcq) to study with solutions a complete question bank.
The solved questions answers in this CAT Mock Test - 6 quiz give you a good mix of easy questions and tough questions. CAT
students definitely take this CAT Mock Test - 6 exercise for a better result in the exam. You can find other CAT Mock Test - 6 extra questions,
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QUESTION: 1

Group Question

Answer the following question based on the information given below.

Between 2004 and 2008, Indian Railways has not been able to perform to its potential. Normally, Railway's revenue grows by two percentage points higher than the growth of Indian economy. According to Railway's own statistics, its revenues growth rate was two percentage points lower than the growth rate of Indian GDP in each of these four years. The main problem is a severe capacity constraint that does not allow the Railways to carry more freight even when there is demand. Freight traffic has grown by an average of over 9 percent in the last four years but in order to grow further the railways have to concentrate on infrastructure development. The central government recently set up the National Transport Development Policy Committee to suggest measures to promote greater commercial orientation of transport services in the country.

The committee is chaired by Dr. Rakesh Mohan, former deputy governor, Reserve Bank of India, who earlier headed the expert group on Railways that recommended corporatisation of the railway administration in 2002. This might be the right time for the government to consider taking a second look at railway reforms. A senior officer concerned with transport infrastructure planning in the country said that the committee was likely to recommend a few measures in the direction of railway reforms and that there would soon be consultations in this regard with policy-makers and experts.

This would not be a moment too soon. Railways desperately needs to grow its revenues because its expenses have shot up. Its ordinary working expenses grew by 7.3 percent in the years between 2004-05 and 2007-08, but jumped by 32 percent in the next year on account of the pay commission. A newspaper report pointed out that the railway surplus too has dwindled to Rs. 1 crore from over Rs 4,400 crore the last fiscal.

“The Indian Railways is at a crossroad where business as usual is not sustainable in the long run. If Railways has to be protected as the country’s growth wagon, transformation of the governance structure and augmentation of the accountability levels for delivery and performance is a must,” says infrastructure expert Akhileshwar Sahay who has studied railway reforms across the world. So what can Railways do? Experts on railway restructuring around the world say that a mix of reforms done in Japan and Argentina could solve key problems. There are a couple of problem areas that need attention right away . Some of these can be solved through Japanese style reforms (for administration) while the others will need the Argentinean method (exit non-core businesses).

*Q. Which of the following is true according to the passage?
A. The Indian Railways can learn from Japanese railway reforms.
B. Between 2004 and 2008, the overall growth rate of the railway revenues was two percentage points lower than the growth rate of Indian GDP.*

Solution:

Statement A is validated in the last paragraph “Some of these can be solved through Japanese style reforms (for administration) while...” Statement B misses a crucial detail - the railway revenue growth reduces two percentage points each year as compared to the growth rate of Indian GDR Thus, only statement A is correct.

Hence, the correct answer is option 1.

QUESTION: 2

Between 2004 and 2008, Indian Railways has not been able to perform to its potential. Normally, Railway's revenue grows by two percentage points higher than the growth of Indian economy. According to Railway's own statistics, its revenues growth rate was two percentage points lower than the growth rate of Indian GDP in each of these four years. The main problem is a severe capacity constraint that does not allow the Railways to carry more freight even when there is demand. Freight traffic has grown by an average of over 9 percent in the last four years but in order to grow further the railways have to concentrate on infrastructure development. The central government recently set up the National Transport Development Policy Committee to suggest measures to promote greater commercial orientation of transport services in the country.

The committee is chaired by Dr. Rakesh Mohan, former deputy governor, Reserve Bank of India, who earlier headed the expert group on Railways that recommended corporatisation of the railway administration in 2002. This might be the right time for the government to consider taking a second look at railway reforms. A senior officer concerned with transport infrastructure planning in the country said that the committee was likely to recommend a few measures in the direction of railway reforms and that there would soon be consultations in this regard with policy-makers and experts.

This would not be a moment too soon. Railways desperately needs to grow its revenues because its expenses have shot up. Its ordinary working expenses grew by 7.3 percent in the years between 2004-05 and 2007-08, but jumped by 32 percent in the next year on account of the pay commission. A newspaper report pointed out that the railway surplus too has dwindled to Rs. 1 crore from over Rs 4,400 crore the last fiscal.

“The Indian Railways is at a crossroad where business as usual is not sustainable in the long run. If Railways has to be protected as the country’s growth wagon, transformation of the governance structure and augmentation of the accountability levels for delivery and performance is a must,” says infrastructure expert Akhileshwar Sahay who has studied railway reforms across the world. So what can Railways do? Experts on railway restructuring around the world say that a mix of reforms done in Japan and Argentina could solve key problems. There are a couple of problem areas that need attention right away . Some of these can be solved through Japanese style reforms (for administration) while the others will need the Argentinean method (exit non-core businesses).

*Q. The National Transport Development Policy Committee was set up to:*

Solution:

Option 1 is eliminated since the word “malpractices” has not been mentioned in the passage.

Option 2 is eliminated as the issue of the ticket prices has not been brought up in the passage.

In option 3, “complete corporatization” cannot be inferred from the passage.

The passage mentions -“The central government recently set up the National Transport Development Policy Committee to suggest measures to promote greater commercial orientation of transport services in the country”. This validates option 4.

Hence, the correct answer is option 4.

QUESTION: 3

Between 2004 and 2008, Indian Railways has not been able to perform to its potential. Normally, Railway's revenue grows by two percentage points higher than the growth of Indian economy. According to Railway's own statistics, its revenues growth rate was two percentage points lower than the growth rate of Indian GDP in each of these four years. The main problem is a severe capacity constraint that does not allow the Railways to carry more freight even when there is demand. Freight traffic has grown by an average of over 9 percent in the last four years but in order to grow further the railways have to concentrate on infrastructure development. The central government recently set up the National Transport Development Policy Committee to suggest measures to promote greater commercial orientation of transport services in the country.

The committee is chaired by Dr. Rakesh Mohan, former deputy governor, Reserve Bank of India, who earlier headed the expert group on Railways that recommended corporatisation of the railway administration in 2002. This might be the right time for the government to consider taking a second look at railway reforms. A senior officer concerned with transport infrastructure planning in the country said that the committee was likely to recommend a few measures in the direction of railway reforms and that there would soon be consultations in this regard with policy-makers and experts.

This would not be a moment too soon. Railways desperately needs to grow its revenues because its expenses have shot up. Its ordinary working expenses grew by 7.3 percent in the years between 2004-05 and 2007-08, but jumped by 32 percent in the next year on account of the pay commission. A newspaper report pointed out that the railway surplus too has dwindled to Rs. 1 crore from over Rs 4,400 crore the last fiscal.

“The Indian Railways is at a crossroad where business as usual is not sustainable in the long run. If Railways has to be protected as the country’s growth wagon, transformation of the governance structure and augmentation of the accountability levels for delivery and performance is a must,” says infrastructure expert Akhileshwar Sahay who has studied railway reforms across the world. So what can Railways do? Experts on railway restructuring around the world say that a mix of reforms done in Japan and Argentina could solve key problems. There are a couple of problem areas that need attention right away . Some of these can be solved through Japanese style reforms (for administration) while the others will need the Argentinean method (exit non-core businesses).

**Q. “The Indian Railways is at a crossroad where business as usual js not sustainable in the long run.” implies:**

Solution:

Option 1 does not mention the crossroads and can be ruled out.

Option 3 is too extreme. Option 4 talks about reconsidering resource utilization but does not stress on the future consequences. The word “crossroad” in the quoted text meaning ‘a point at which a crucial decision must be made which will have far- reaching consequences’ is crucial here. Option 2 talks about the necessity for reforms and the consequences if the Railways fails to implement them.

Hence, the correct answer is option 2.

QUESTION: 4

Between 2004 and 2008, Indian Railways has not been able to perform to its potential. Normally, Railway's revenue grows by two percentage points higher than the growth of Indian economy. According to Railway's own statistics, its revenues growth rate was two percentage points lower than the growth rate of Indian GDP in each of these four years. The main problem is a severe capacity constraint that does not allow the Railways to carry more freight even when there is demand. Freight traffic has grown by an average of over 9 percent in the last four years but in order to grow further the railways have to concentrate on infrastructure development. The central government recently set up the National Transport Development Policy Committee to suggest measures to promote greater commercial orientation of transport services in the country.

The committee is chaired by Dr. Rakesh Mohan, former deputy governor, Reserve Bank of India, who earlier headed the expert group on Railways that recommended corporatisation of the railway administration in 2002. This might be the right time for the government to consider taking a second look at railway reforms. A senior officer concerned with transport infrastructure planning in the country said that the committee was likely to recommend a few measures in the direction of railway reforms and that there would soon be consultations in this regard with policy-makers and experts.

This would not be a moment too soon. Railways desperately needs to grow its revenues because its expenses have shot up. Its ordinary working expenses grew by 7.3 percent in the years between 2004-05 and 2007-08, but jumped by 32 percent in the next year on account of the pay commission. A newspaper report pointed out that the railway surplus too has dwindled to Rs. 1 crore from over Rs 4,400 crore the last fiscal.

“The Indian Railways is at a crossroad where business as usual is not sustainable in the long run. If Railways has to be protected as the country’s growth wagon, transformation of the governance structure and augmentation of the accountability levels for delivery and performance is a must,” says infrastructure expert Akhileshwar Sahay who has studied railway reforms across the world. So what can Railways do? Experts on railway restructuring around the world say that a mix of reforms done in Japan and Argentina could solve key problems. There are a couple of problem areas that need attention right away . Some of these can be solved through Japanese style reforms (for administration) while the others will need the Argentinean method (exit non-core businesses).

**Q. What is the main problem of the Railways according to the passage?**

Solution:

The passage mentions “The main problem ....the railways have to concentrate on infrastructure development.” Option 1 is ruled out as commuters are not mentioned in this context. Consequently, option 4 is eliminated.

Option 3 cannot be inferred from the passage.

Option 2 is validated from the above text.

Hence, the correct answer is option 2.

QUESTION: 5

The committee is chaired by Dr. Rakesh Mohan, former deputy governor, Reserve Bank of India, who earlier headed the expert group on Railways that recommended corporatisation of the railway administration in 2002. This might be the right time for the government to consider taking a second look at railway reforms. A senior officer concerned with transport infrastructure planning in the country said that the committee was likely to recommend a few measures in the direction of railway reforms and that there would soon be consultations in this regard with policy-makers and experts.

This would not be a moment too soon. Railways desperately needs to grow its revenues because its expenses have shot up. Its ordinary working expenses grew by 7.3 percent in the years between 2004-05 and 2007-08, but jumped by 32 percent in the next year on account of the pay commission. A newspaper report pointed out that the railway surplus too has dwindled to Rs. 1 crore from over Rs 4,400 crore the last fiscal.

“The Indian Railways is at a crossroad where business as usual is not sustainable in the long run. If Railways has to be protected as the country’s growth wagon, transformation of the governance structure and augmentation of the accountability levels for delivery and performance is a must,” says infrastructure expert Akhileshwar Sahay who has studied railway reforms across the world. So what can Railways do? Experts on railway restructuring around the world say that a mix of reforms done in Japan and Argentina could solve key problems. There are a couple of problem areas that need attention right away . Some of these can be solved through Japanese style reforms (for administration) while the others will need the Argentinean method (exit non-core businesses).

**Q. A suitable title for this passage would be:**

Solution:

The passage throughout talks about how the Indian Railways requires reforms inorder to be sustainable. It talks about looking at commercialization of the railways and increasing revenues. Option 1 is too generic with respect to the theme of the passage.

Option 2 does not capture the essence of the passage and focuses on the history of the Indian Railways.

Option 4 is not apt, as the passage does not talk about the commuting experience.

Option 3 with “revival” is an appropriate title.

Hence, the correct answer is option 3.

QUESTION: 6

The committee is chaired by Dr. Rakesh Mohan, former deputy governor, Reserve Bank of India, who earlier headed the expert group on Railways that recommended corporatisation of the railway administration in 2002. This might be the right time for the government to consider taking a second look at railway reforms. A senior officer concerned with transport infrastructure planning in the country said that the committee was likely to recommend a few measures in the direction of railway reforms and that there would soon be consultations in this regard with policy-makers and experts.

This would not be a moment too soon. Railways desperately needs to grow its revenues because its expenses have shot up. Its ordinary working expenses grew by 7.3 percent in the years between 2004-05 and 2007-08, but jumped by 32 percent in the next year on account of the pay commission. A newspaper report pointed out that the railway surplus too has dwindled to Rs. 1 crore from over Rs 4,400 crore the last fiscal.

“The Indian Railways is at a crossroad where business as usual is not sustainable in the long run. If Railways has to be protected as the country’s growth wagon, transformation of the governance structure and augmentation of the accountability levels for delivery and performance is a must,” says infrastructure expert Akhileshwar Sahay who has studied railway reforms across the world. So what can Railways do? Experts on railway restructuring around the world say that a mix of reforms done in Japan and Argentina could solve key problems. There are a couple of problem areas that need attention right away . Some of these can be solved through Japanese style reforms (for administration) while the others will need the Argentinean method (exit non-core businesses).

*Q. Which of the following would weaken the statement - “Between 2004 and 2008, Indian Railways has not been able to perform to its potential.”?*

Solution:

Options 1, 2 and 4 talk about time periods which differ from the one in the main statement.

If the Indian railways were to be recognized globally for infrastructure in 2006, then it would not have performed abysmally in 2004-2008. Thus, option 3 weakens the given statement.

Hence, the correct answer is option 3.

QUESTION: 7

Group Question

The passage given below is followed by a set of questions. Choose the most appropriate answer to each question.

Much of the tragical lore of the infant mortality, the malnutrition, and the five-in-a-room morality of the city's poor is written in statistics, and the statistical path to the heart is more figurative than literal. Gertie Slayback was statistically down as a woman wage-earner; a sorry case among the thousands of the Borough of Manhattan; and her twice-a-day share in the Subway fares collected in the present year. She was a very atomic one of the city's four millions. But after all, what are the kings and peasants, poets and draymen, but great, greater, or greatest, less, lesser, or least atoms of us? If not of the least, Gertie Slayback was of the very lesser. When she unlocked the front door to her rooming-house of evenings, there was no one to expect her, except on Tuesdays, which evening it so happened her week was up. And when she left of mornings with her breakfast crumblessly cleared up and the box of biscuit and condensed-milk can tucked unsuspectedly behind her camisole in the top drawer there was no one to regret her. There are some who call this freedom. Again there are those for whom one spark of home fire burning would light the world.

Gertie Slayback was one of those. Half a life-time of opening her door upon this or that desert-aisle of hall bedroom had not taught her heart how not to sink or the feel of daily rising in one such room to seem less like a damp bathing-suit, donned at dawn. The only picture which adorned Miss Slayback's dun-colored walls was a passe-partout snowscape, night closing in, and pink cottage windows peering out from under eaves. She could visualize that interior as if she had only to turn the frame for the smell of wood fire and the snap of pine logs and for the scene of two high-back chairs and the wooden crib between. What a fragile, gracile thing is the mind that can leap thus from nine bargain basement hours of hairpins and darning-balls to the downy business of lining a crib in Never-Never Land and warming No Man's slippers before the fire of imagination. There was that picture so acidly etched into Miss Slayback's brain that she had only to close her eyes in the slit-like sanctity of her room and in the brief moment of courting sleep feel the pink penumbra of her vision begin to glow.

**Q. Among the following options, the author of the passage is likely to disagree with which of the following?**

Solution:

Option 1 can be deduced from “Much of the tragical lore of the infant mortality, the malnutrition, and the five-in-a-room morality of the city's poor is written in statistics, and the statistical path to the heart is more figurative than literal.”. This implies how statistics makes the situation of Manhattan's poor seem much more poignant than what may really have been the case. Eliminate option 1.

According to the passage, “Again there are those for whom one spark of home fire burning would light the world. Gertie Slayback was one of those.”. This indicates that Slayback was not content with her lifestyle and did not think highly of the freedom she had. This vindicates option 2 as correct.

Option 3 is supported by “She was a very atomic one of the city's four millions. But after all, what are the kings and peasants, poets and draymen, but great, greater, or greatest, less, lesser, or least atoms of us?”. This implies that most human beings are “atomic” or “diminutive” when compared to landspaces.

Eliminate option 3.

The passage mentions “Half a life-time of opening her door upon this or that desert-aisle of hall bedroom had not taught her heart how not to sink...”. This implies that Gertie Slayback was affected by the monotony of her life despite her lifestyle having stayed the same for a long time. Eliminate option 4.

Hence, the correct answer is option 2.

QUESTION: 8

Much of the tragical lore of the infant mortality, the malnutrition, and the five-in-a-room morality of the city's poor is written in statistics, and the statistical path to the heart is more figurative than literal. Gertie Slayback was statistically down as a woman wage-earner; a sorry case among the thousands of the Borough of Manhattan; and her twice-a-day share in the Subway fares collected in the present year. She was a very atomic one of the city's four millions. But after all, what are the kings and peasants, poets and draymen, but great, greater, or greatest, less, lesser, or least atoms of us? If not of the least, Gertie Slayback was of the very lesser. When she unlocked the front door to her rooming-house of evenings, there was no one to expect her, except on Tuesdays, which evening it so happened her week was up. And when she left of mornings with her breakfast crumblessly cleared up and the box of biscuit and condensed-milk can tucked unsuspectedly behind her camisole in the top drawer there was no one to regret her. There are some who call this freedom. Again there are those for whom one spark of home fire burning would light the world.

Gertie Slayback was one of those. Half a life-time of opening her door upon this or that desert-aisle of hall bedroom had not taught her heart how not to sink or the feel of daily rising in one such room to seem less like a damp bathing-suit, donned at dawn. The only picture which adorned Miss Slayback's dun-colored walls was a passe-partout snowscape, night closing in, and pink cottage windows peering out from under eaves. She could visualize that interior as if she had only to turn the frame for the smell of wood fire and the snap of pine logs and for the scene of two high-back chairs and the wooden crib between. What a fragile, gracile thing is the mind that can leap thus from nine bargain basement hours of hairpins and darning-balls to the downy business of lining a crib in Never-Never Land and warming No Man's slippers before the fire of imagination. There was that picture so acidly etched into Miss Slayback's brain that she had only to close her eyes in the slit-like sanctity of her room and in the brief moment of courting sleep feel the pink penumbra of her vision begin to glow.

**Q. Which of the following is untrue with regard to Gertie Slayback's perception of the picture on her wall?**

Solution:

The passage mentions how Gertie Slayback was moved by the picture and she could vividly visualize the life it seemed to depict. This helped fire up her imagination and represented her aspirations. Eliminate option 1.

Option 2 can be inferred from “... there are those for whom one spark of home fire burning would light the world. Gertie Slayback was one of those.” and “There was that picture so acidly etched into Miss Slayback's brain that she had only to close her eyes ... in the brief moment of courting sleep feel the pink penumbra of her vision begin to glow.”.

According to the passage, “What a fragile, gracile thing is the mind that can leap thus from nine bargain basement hours of hairpins and darning-balls to the downy business of lining a crib in Never-Never Land and warming No Man's slippers before the fire of imagination.”. This eliminates option 3.

Though the passage mentions how the snowscape comforted Slayback, it does not hint at Slayback being optimistic about her future. Thus, we cannot infer option 4 to be true.

Hence, the correct answer is option 4.

QUESTION: 9

Much of the tragical lore of the infant mortality, the malnutrition, and the five-in-a-room morality of the city's poor is written in statistics, and the statistical path to the heart is more figurative than literal. Gertie Slayback was statistically down as a woman wage-earner; a sorry case among the thousands of the Borough of Manhattan; and her twice-a-day share in the Subway fares collected in the present year. She was a very atomic one of the city's four millions. But after all, what are the kings and peasants, poets and draymen, but great, greater, or greatest, less, lesser, or least atoms of us? If not of the least, Gertie Slayback was of the very lesser. When she unlocked the front door to her rooming-house of evenings, there was no one to expect her, except on Tuesdays, which evening it so happened her week was up. And when she left of mornings with her breakfast crumblessly cleared up and the box of biscuit and condensed-milk can tucked unsuspectedly behind her camisole in the top drawer there was no one to regret her. There are some who call this freedom. Again there are those for whom one spark of home fire burning would light the world.

Gertie Slayback was one of those. Half a life-time of opening her door upon this or that desert-aisle of hall bedroom had not taught her heart how not to sink or the feel of daily rising in one such room to seem less like a damp bathing-suit, donned at dawn. The only picture which adorned Miss Slayback's dun-colored walls was a passe-partout snowscape, night closing in, and pink cottage windows peering out from under eaves. She could visualize that interior as if she had only to turn the frame for the smell of wood fire and the snap of pine logs and for the scene of two high-back chairs and the wooden crib between. What a fragile, gracile thing is the mind that can leap thus from nine bargain basement hours of hairpins and darning-balls to the downy business of lining a crib in Never-Never Land and warming No Man's slippers before the fire of imagination. There was that picture so acidly etched into Miss Slayback's brain that she had only to close her eyes in the slit-like sanctity of her room and in the brief moment of courting sleep feel the pink penumbra of her vision begin to glow.

*Q. If you were to interview the author, what would be your follow up question to this passage?*

Solution:

The passage centers on Gertie Slayback's feelings towards her life and the role that imagination played in helping her cope with the monotony of her routine. The passage describes her unhappiness but mentions how Gertie Slayback would follow her routine disregarding the same. This is indicated in “When she unlocked the front door to her rooming-house of evenings, there was no one to expect her, except on Tuesdays, which evening it so happened her week was up.”. However, the paragraph does not tell us if Gertie Slayback took any steps to change the status quo of her life. This vindicates option 4.

The question put forth by option 1 is answered in “Half a life-time of opening her door upon this ... had not taught her heart how not to sink or the feel of daily rising in one such room to seem less like a damp bathing-suit, donned at dawn.”.

The passage mentions that Gertie Slayback's perception was not affected by the nature of her work in “... the mind that can leap thus from nine bargain basement hours of hairpins and darning- balls to the downy business of lining a crib in Never-Never Land and warming No Man's slippers before the fire of imagination.”. Eliminate option 2.

According to the passage, “There was that picture so acidly etched into Miss Slayback's brain that she had only to close her eyes in the slit-like sanctity of her room and in the brief moment of courting sleep feel the pink penumbra of her vision begin to glow.”. This tells us how imagination helped Gertie Slayback cope with her routine. Eliminate option 3.

Hence, the correct answer is option 4.

QUESTION: 10

Group Question

Read the passage given below and answer the questions that follow.

“When you’re dead, you’re dead,” I’d always told myself. “You’re childless, so what difference does it make who gets the money, if there’s any left, or the sentimental treasures?” By which I mean my mother’s “sterling” silver, which turned out to be plate, and my flea market discoveries.

But my 10-year-old standard poodle was another story. Unmentioned in the existing document, Henry would be left alone after I died: unfed, unwalked, unloved. Would he die, too, only to be discovered by a neighbor when he started to stink up the joint? I owed him better.

My elder care lawyer raised a skeptical eyebrow when I explained that the inspiration to update everything was my dog. I might as well review all the paperwork, I told him: the power of attorney, the health care proxy, the living will, a codicil here and there, the list of friends’ children who had always been my beneficiaries. But a full year went by while I looked guiltily at the file folder on my desk marked “new will.” That took me by surprise, as I’m not a procrastinator. Remember the hated kid in high school who always had her papers done way in advance and went to the movies while everyone else was pulling an all-nighter? That was me.

But my lawyer, Gregg M. Weiss, was used to people starting the process and then disappearing. “That’s the No. 1 bane of my existence,” he said when I finally resurfaced, all papers ready to be signed.

“Whatever is on anyone’s to-do pile, this typically goes to the bottom. It’s avoidance, not facing the reality of death. The 80-year- olds we see are different. They don’t dillydally.” My mother had needed no admonitions about such things and had her affairs in order before she was out of her 50s, most likely because my father’s sudden death had left her with a mess to clean up when one least needs to be cleaning up messes. My new will splits the difference between being smart and being stubborn. Friends’ children remain the main beneficiaries, along with charities. My health care proxy remains a sensible, loving and brave friend who says that she has no problem pulling the plug under the right circumstances. Another friend replaces the former No. 2 for reasons of geography: A health care proxy who lives 3,000 miles away is not very likely to be available when you need her. My brother is grateful, as he always has been, to be spared that task. He wants me to have the kind of death I choose, but not to be in charge of it. Custody of Henry, my dog, goes to his walker, who loves him so much (and vice versa) that she has refused money to cover his care.

*Q. Which of the following is true about the author?*

Solution:

The author is giving away her wealth to charities and friends’ children, hence, option 1 is validated. Option 2 is ruled out as the passage states that the author was “childless”. Option 3 is ruled out as the passage states - "Remember the hated kid in high school who always had her papers done way in advance and went to the movies while everyone else was pulling an all-nighter? That was me." Option 4 is ruled out as there is no mention of the dog being “sick/ailing”.

Hence, the correct answer is option 1.

QUESTION: 11

Gertie Slayback was one of those. Half a life-time of opening her door upon this or that desert-aisle of hall bedroom had not taught her heart how not to sink or the feel of daily rising in one such room to seem less like a damp bathing-suit, donned at dawn. The only picture which adorned Miss Slayback's dun-colored walls was a passe-partout snowscape, night closing in, and pink cottage windows peering out from under eaves. She could visualize that interior as if she had only to turn the frame for the smell of wood fire and the snap of pine logs and for the scene of two high-back chairs and the wooden crib between. What a fragile, gracile thing is the mind that can leap thus from nine bargain basement hours of hairpins and darning-balls to the downy business of lining a crib in Never-Never Land and warming No Man's slippers before the fire of imagination. There was that picture so acidly etched into Miss Slayback's brain that she had only to close her eyes in the slit-like sanctity of her room and in the brief moment of courting sleep feel the pink penumbra of her vision begin to glow.

*Q. “He (author’s brother) wants me to have the kind of death I choose, but not to be in charge of it.” implies:
A. He is indifferent
B. He supports euthanasia
C. He respects the author’s choices*

Solution:

The author’s brother respects the author’s choice of kind of death. He just does not want to be part of it. This does not make him indifferent. Statement A is ruled out. Statement B cannot be implied as the author’s brother does not want to be in charge of the author’s death particularly but accepts her choice of death (euthanasia is intentionally ending a life to relieve pain). Statement C can be implied as the author’s brother supports her in having a death by choice even though he may not want to be directly involved in it.

Hence, the correct answer is option 4.

QUESTION: 12

Gertie Slayback was one of those. Half a life-time of opening her door upon this or that desert-aisle of hall bedroom had not taught her heart how not to sink or the feel of daily rising in one such room to seem less like a damp bathing-suit, donned at dawn. The only picture which adorned Miss Slayback's dun-colored walls was a passe-partout snowscape, night closing in, and pink cottage windows peering out from under eaves. She could visualize that interior as if she had only to turn the frame for the smell of wood fire and the snap of pine logs and for the scene of two high-back chairs and the wooden crib between. What a fragile, gracile thing is the mind that can leap thus from nine bargain basement hours of hairpins and darning-balls to the downy business of lining a crib in Never-Never Land and warming No Man's slippers before the fire of imagination. There was that picture so acidly etched into Miss Slayback's brain that she had only to close her eyes in the slit-like sanctity of her room and in the brief moment of courting sleep feel the pink penumbra of her vision begin to glow.

*Q. Which of the following would weaken the character sketch of the author’s mother presented in the passage?*

Solution:

The passage states “My mother had needed no admonitions about such things and had her affairs in order before she was out of her 50s,... cleaning up messes.” This validates options 1, 3 and 4. She did not lead a comfortable life as suggested by the latter part of the sentence.

Hence, the correct answer is option 2.

QUESTION: 13

Gertie Slayback was one of those. Half a life-time of opening her door upon this or that desert-aisle of hall bedroom had not taught her heart how not to sink or the feel of daily rising in one such room to seem less like a damp bathing-suit, donned at dawn. The only picture which adorned Miss Slayback's dun-colored walls was a passe-partout snowscape, night closing in, and pink cottage windows peering out from under eaves. She could visualize that interior as if she had only to turn the frame for the smell of wood fire and the snap of pine logs and for the scene of two high-back chairs and the wooden crib between. What a fragile, gracile thing is the mind that can leap thus from nine bargain basement hours of hairpins and darning-balls to the downy business of lining a crib in Never-Never Land and warming No Man's slippers before the fire of imagination. There was that picture so acidly etched into Miss Slayback's brain that she had only to close her eyes in the slit-like sanctity of her room and in the brief moment of courting sleep feel the pink penumbra of her vision begin to glow.

*Q. Why did the author give Henry’s custody to his brother’s walker?*

Solution:

The passage mentions “Custody of Henry, my dog, goes to his walker, who loves him so much (and vice versa) that she has refused money to cover his care.” Option 1 cannot be corroborated from the passage. Considering the author is wealthy, the walker not charging a fee would not be a motivating factor to give her dog to her. Option 3 cannot be corroborated from the passage. The walker loved Henry, and more importantly Henry loved the walker. This would have convinced the author to give custody of Henry to the walker.

Hence, the correct answer is option 4.

QUESTION: 14

Gertie Slayback was one of those. Half a life-time of opening her door upon this or that desert-aisle of hall bedroom had not taught her heart how not to sink or the feel of daily rising in one such room to seem less like a damp bathing-suit, donned at dawn. The only picture which adorned Miss Slayback's dun-colored walls was a passe-partout snowscape, night closing in, and pink cottage windows peering out from under eaves. She could visualize that interior as if she had only to turn the frame for the smell of wood fire and the snap of pine logs and for the scene of two high-back chairs and the wooden crib between. What a fragile, gracile thing is the mind that can leap thus from nine bargain basement hours of hairpins and darning-balls to the downy business of lining a crib in Never-Never Land and warming No Man's slippers before the fire of imagination. There was that picture so acidly etched into Miss Slayback's brain that she had only to close her eyes in the slit-like sanctity of her room and in the brief moment of courting sleep feel the pink penumbra of her vision begin to glow.

**Q. What does the autho's lawyer refer to as 'the No. 1 bane of his existence'?**

Solution:

The passage states “But my lawyer, Gregg M. Weiss, was used to people starting the process and then disappearing. “That’s the No. 1 bane of my existence,” he said when I finally resurfaced, all papers ready to be signed.” This validates option 2. The remaining options are not substantiated by the passage.

Hence, the correct answer is option 2.

QUESTION: 15

Gertie Slayback was one of those. Half a life-time of opening her door upon this or that desert-aisle of hall bedroom had not taught her heart how not to sink or the feel of daily rising in one such room to seem less like a damp bathing-suit, donned at dawn. The only picture which adorned Miss Slayback's dun-colored walls was a passe-partout snowscape, night closing in, and pink cottage windows peering out from under eaves. She could visualize that interior as if she had only to turn the frame for the smell of wood fire and the snap of pine logs and for the scene of two high-back chairs and the wooden crib between. What a fragile, gracile thing is the mind that can leap thus from nine bargain basement hours of hairpins and darning-balls to the downy business of lining a crib in Never-Never Land and warming No Man's slippers before the fire of imagination. There was that picture so acidly etched into Miss Slayback's brain that she had only to close her eyes in the slit-like sanctity of her room and in the brief moment of courting sleep feel the pink penumbra of her vision begin to glow.

*Q. “My health care proxy remains a sensible, loving and brave friend who says that she has no problem pulling the plug under the right circumstances.” The above sentence is based on the assumption that:
A. A health care proxy must be a friend.
B. A health care proxy must be level-headed.*

Solution:

The role of a health care proxy is to take a calm and sensible decision (for someone else) with regards to that person’s death. This role assumes that such a proxy is level-headed and balanced. Every friend may not be levelheaded. Hence, statement A is not a valid assumption. Statement B is an apt assumption.

Hence, the correct answer is option 2.

QUESTION: 16

**Group Question **

Read the passage below and answer the questions that follow.

It was almost 15 years ago that I first met Baba Amte in Hemalkasa. I was reporting from the Nagpur legislature session and decided to travel to the place where Amte’s son Dr Prakash provides medical treatment for free to tribals from Gadchiroli and neighbouring districts from Andhra Pradesh. There was a long weekend and we decided to put it to good use by visiting the Amtes and seeing their work first hand. Dr Prakash told us to be ready at 7 am sharp and join Baba for a morning walk. Well, it was not at all a walk. We were literally jogging to keep pace with the 85 year young Baba as he sprinted with the spirit of a deer. Huffing and puffing, we asked him so many questions - personal included (he was an atheist and his wife Sadhana who joined us in the walk was an ardent devotee of Lord Shiva) - and Baba was more than happy to answer us. It was an amazing love story and it really takes something to stay married to a man who was crazy enough to inject himself with leprosy-causing bacteria to test the efficacy of the vaccine. While Baba was fired up by the cause, Sadhanatai believed in him and loved him in an absolute selfless manner.

Coming back to Baba, we asked him what future did he see for India when the communal fire seemed to be engulfing it. And he laughed. "Oh, this keeps happening all the time. We have seen this during Bapu’s time, then we saw during Khalistan and we have seen that again during the 90s. We have done well, haven’t we? I believe in youth and I know they will always shun violence," Baba said. We were amazed by the positivity he showed and we asked him if he was ever depressed in his life. "When you see people shunned by the society just because they were afflicted by a disease and when you see the life they go through, you know your life is far better. I have two eyes, two ears, all my limbs are absolutely fine. What more do you want to stay positive?" By the time we returned to the government rest house after the invigorating 'walk', we were fully mesmerized by the man. From Baba, who took up the Gandhian cause and followed it in true spirit, his wife Sadhana who simply followed him no questions asked, his sons Dr Prakash and Dr Vikas or his grandson who was not lured by any of the urban pleasures of life, each person was worthy of great respect.

**Q. “It was almost 15 years ago that I first met Baba Amte in Hemalkasa.” Which of the following is a valid inference drawn from the above text?
A. The author was a youth when he first met Baba Amte.
B. The author was a believer in Baba Amte's principles.
C. Baba Amte has lived in Hemalkasa.**

Solution:

Statement A cannot be inferred as the author’s current age is not specified to corroborate his age 15 years ago. Statement B cannot be inferred as a believer would be familiar with or up to date with the activities of Baba Amte. The author and Baba Amte may just have happened to meet at Hemalkasa, it cannot be inferred that Baba Amte lived there. Therefore, statement C is not validated. Hence, none of the statements is a valid inference.

Hence, the correct answer is option 4.

QUESTION: 17

It was almost 15 years ago that I first met Baba Amte in Hemalkasa. I was reporting from the Nagpur legislature session and decided to travel to the place where Amte’s son Dr Prakash provides medical treatment for free to tribals from Gadchiroli and neighbouring districts from Andhra Pradesh. There was a long weekend and we decided to put it to good use by visiting the Amtes and seeing their work first hand. Dr Prakash told us to be ready at 7 am sharp and join Baba for a morning walk. Well, it was not at all a walk. We were literally jogging to keep pace with the 85 year young Baba as he sprinted with the spirit of a deer. Huffing and puffing, we asked him so many questions - personal included (he was an atheist and his wife Sadhana who joined us in the walk was an ardent devotee of Lord Shiva) - and Baba was more than happy to answer us. It was an amazing love story and it really takes something to stay married to a man who was crazy enough to inject himself with leprosy-causing bacteria to test the efficacy of the vaccine. While Baba was fired up by the cause, Sadhanatai believed in him and loved him in an absolute selfless manner.

Coming back to Baba, we asked him what future did he see for India when the communal fire seemed to be engulfing it. And he laughed. "Oh, this keeps happening all the time. We have seen this during Bapu’s time, then we saw during Khalistan and we have seen that again during the 90s. We have done well, haven’t we? I believe in youth and I know they will always shun violence," Baba said. We were amazed by the positivity he showed and we asked him if he was ever depressed in his life. "When you see people shunned by the society just because they were afflicted by a disease and when you see the life they go through, you know your life is far better. I have two eyes, two ears, all my limbs are absolutely fine. What more do you want to stay positive?" By the time we returned to the government rest house after the invigorating 'walk', we were fully mesmerized by the man. From Baba, who took up the Gandhian cause and followed it in true spirit, his wife Sadhana who simply followed him no questions asked, his sons Dr Prakash and Dr Vikas or his grandson who was not lured by any of the urban pleasures of life, each person was worthy of great respect.

*Q. “.....the 85 year young Baba as he sprinted with the spirit of a deer” implies that:*

Solution:

The line talks about Baba Amte going for his walks with great energy. This implies his state of fitness. Option 1 can be ruled out as it talks about his personality/nature and not his fitness and activity. Option 2 talks about “sport” and not fitness, while option 4 is vague with “career”. Both options 2 and 4 cannot be inferred from the current statement and can be ruled out. Option 3 is clearly implied.

Hence, the correct answer is option 3.

QUESTION: 18

It was almost 15 years ago that I first met Baba Amte in Hemalkasa. I was reporting from the Nagpur legislature session and decided to travel to the place where Amte’s son Dr Prakash provides medical treatment for free to tribals from Gadchiroli and neighbouring districts from Andhra Pradesh. There was a long weekend and we decided to put it to good use by visiting the Amtes and seeing their work first hand. Dr Prakash told us to be ready at 7 am sharp and join Baba for a morning walk. Well, it was not at all a walk. We were literally jogging to keep pace with the 85 year young Baba as he sprinted with the spirit of a deer. Huffing and puffing, we asked him so many questions - personal included (he was an atheist and his wife Sadhana who joined us in the walk was an ardent devotee of Lord Shiva) - and Baba was more than happy to answer us. It was an amazing love story and it really takes something to stay married to a man who was crazy enough to inject himself with leprosy-causing bacteria to test the efficacy of the vaccine. While Baba was fired up by the cause, Sadhanatai believed in him and loved him in an absolute selfless manner.

Coming back to Baba, we asked him what future did he see for India when the communal fire seemed to be engulfing it. And he laughed. "Oh, this keeps happening all the time. We have seen this during Bapu’s time, then we saw during Khalistan and we have seen that again during the 90s. We have done well, haven’t we? I believe in youth and I know they will always shun violence," Baba said. We were amazed by the positivity he showed and we asked him if he was ever depressed in his life. "When you see people shunned by the society just because they were afflicted by a disease and when you see the life they go through, you know your life is far better. I have two eyes, two ears, all my limbs are absolutely fine. What more do you want to stay positive?" By the time we returned to the government rest house after the invigorating 'walk', we were fully mesmerized by the man. From Baba, who took up the Gandhian cause and followed it in true spirit, his wife Sadhana who simply followed him no questions asked, his sons Dr Prakash and Dr Vikas or his grandson who was not lured by any of the urban pleasures of life, each person was worthy of great respect.

**Q. According to the passage, what future did Baba Amte see for India?**

Solution:

The passage states - “...I believe in youth and I know they will always shun violence," Baba said. We were amazed by the positivity he showed and we asked him if he was ever depressed in his life.” Option 1 resonates with this. Option 2 contradicts this by stating that Baba Amte was confident about communal rights happening in India. Option 3 can be ruled out as the passage does not talk about India becoming “industrious”. Option 4 too can be ruled out as the passage is not about “youth engagement in the Indian government”.

Hence, the correct answer is option 1.

QUESTION: 19

It was almost 15 years ago that I first met Baba Amte in Hemalkasa. I was reporting from the Nagpur legislature session and decided to travel to the place where Amte’s son Dr Prakash provides medical treatment for free to tribals from Gadchiroli and neighbouring districts from Andhra Pradesh. There was a long weekend and we decided to put it to good use by visiting the Amtes and seeing their work first hand. Dr Prakash told us to be ready at 7 am sharp and join Baba for a morning walk. Well, it was not at all a walk. We were literally jogging to keep pace with the 85 year young Baba as he sprinted with the spirit of a deer. Huffing and puffing, we asked him so many questions - personal included (he was an atheist and his wife Sadhana who joined us in the walk was an ardent devotee of Lord Shiva) - and Baba was more than happy to answer us. It was an amazing love story and it really takes something to stay married to a man who was crazy enough to inject himself with leprosy-causing bacteria to test the efficacy of the vaccine. While Baba was fired up by the cause, Sadhanatai believed in him and loved him in an absolute selfless manner.

Coming back to Baba, we asked him what future did he see for India when the communal fire seemed to be engulfing it. And he laughed. "Oh, this keeps happening all the time. We have seen this during Bapu’s time, then we saw during Khalistan and we have seen that again during the 90s. We have done well, haven’t we? I believe in youth and I know they will always shun violence," Baba said. We were amazed by the positivity he showed and we asked him if he was ever depressed in his life. "When you see people shunned by the society just because they were afflicted by a disease and when you see the life they go through, you know your life is far better. I have two eyes, two ears, all my limbs are absolutely fine. What more do you want to stay positive?" By the time we returned to the government rest house after the invigorating 'walk', we were fully mesmerized by the man. From Baba, who took up the Gandhian cause and followed it in true spirit, his wife Sadhana who simply followed him no questions asked, his sons Dr Prakash and Dr Vikas or his grandson who was not lured by any of the urban pleasures of life, each person was worthy of great respect.

*Q. Which of these statements weakens what is said about Baba Amte’s wife in the passage?*

Solution:

The passage states how Baba Amte’s wife stood by him no questions asked. She loved him, believed in him and was selfless in her marriage. She even stood by him when he injected himself with leprosy-causing bacteria to test the efficacy of the vaccine. This validates options 1, 3 and 4. The passage shows her as a caring wife, supportive spouse and a sacrificing partner. Option 2 would weaken this as it would mean she placed her needs before her family’s. Hence, the correct answer is option 2.

QUESTION: 20

Coming back to Baba, we asked him what future did he see for India when the communal fire seemed to be engulfing it. And he laughed. "Oh, this keeps happening all the time. We have seen this during Bapu’s time, then we saw during Khalistan and we have seen that again during the 90s. We have done well, haven’t we? I believe in youth and I know they will always shun violence," Baba said. We were amazed by the positivity he showed and we asked him if he was ever depressed in his life. "When you see people shunned by the society just because they were afflicted by a disease and when you see the life they go through, you know your life is far better. I have two eyes, two ears, all my limbs are absolutely fine. What more do you want to stay positive?" By the time we returned to the government rest house after the invigorating 'walk', we were fully mesmerized by the man. From Baba, who took up the Gandhian cause and followed it in true spirit, his wife Sadhana who simply followed him no questions asked, his sons Dr Prakash and Dr Vikas or his grandson who was not lured by any of the urban pleasures of life, each person was worthy of great respect.

*Q. “Dr Prakash provides medical treatment for free to tribals from Gadchiroli and neighbouring districts from Andhra Pradesh.” From the text, we can infer that:*

Solution:

Options 1 and 4 cannot be corroborated from the text. It says that Prakash is a doctor who provides free service/treatment. He could specialize in any medical field. Also, he may be providing free services as part of social service, passion or to continue his father’s legacy. This does not give evidence that he is an “established” doctor. Option 2 may be a fact but cannot be inferred from the quoted text as nothing about family relations has been mentioned in the text. Also, “like” in option 2 is vague. In the presence of option 3, all options fall short. Option 3 is apt.

Dr Prakash is providing medical services pro bono in Gadchiroli. It is very likely that tribals there will respect him. Hence, the correct answer is option 3.

QUESTION: 21

Coming back to Baba, we asked him what future did he see for India when the communal fire seemed to be engulfing it. And he laughed. "Oh, this keeps happening all the time. We have seen this during Bapu’s time, then we saw during Khalistan and we have seen that again during the 90s. We have done well, haven’t we? I believe in youth and I know they will always shun violence," Baba said. We were amazed by the positivity he showed and we asked him if he was ever depressed in his life. "When you see people shunned by the society just because they were afflicted by a disease and when you see the life they go through, you know your life is far better. I have two eyes, two ears, all my limbs are absolutely fine. What more do you want to stay positive?" By the time we returned to the government rest house after the invigorating 'walk', we were fully mesmerized by the man. From Baba, who took up the Gandhian cause and followed it in true spirit, his wife Sadhana who simply followed him no questions asked, his sons Dr Prakash and Dr Vikas or his grandson who was not lured by any of the urban pleasures of life, each person was worthy of great respect.

*Q. Which word best describes Baba Amte?*

Solution:

“Somber” meaning ‘serious’ is contrary to how Baba Amte has been described in the passage. Baba Amte is described as an "atheist", it is not the same as "anti- religious". “Supercilious” refers to ‘scornful’ or ‘arrogant’ which is not how Baba Amte was. He was simple and lived with and for the common man. Option 3 “principled” is apt as Baba Amte was disciplined in his lifestyle, followed the Gandhian philosophy in that manner and lived for the people in the purest way.

Hence, the correct answer is option 3.

QUESTION: 22

Group Question

A passage is followed by questions pertaining to the passage. Read the passage and answer the questions. Choose the most appropriate answer.

Judgments of aesthetic value rely on our ability to discriminate at a sensory level. Aesthetics examines our affective domain response to an object or phenomenon. Immanuel Kant, writing in 1790, observes of a man "If he says that canary wine is agreeable he is quite content if someone else corrects his terms and reminds him to say instead: It is agreeable to me," because "Everyone has his own (sense of) taste". The case of "beauty" is different from mere "agreeableness" because, "If he proclaims something to be beautiful, then he requires the same liking from others; he then judges not just for himself but for everyone, and speaks of beauty as if it were a property of things."

Aesthetic judgments may be culturally conditioned to some extent. Victorians in Britain often saw African sculpture as ugly, but just a few decades later, Edwardian audiences saw the same sculptures as being beautiful. The Abuse of Beauty, Evaluations of beauty may well be linked to desirability, perhaps even to sexual desirability. Thus, judgments of aesthetic value can become linked to judgments of economic, political, or moral value. We might judge a Lamborghini to be beautiful partly because it is desirable as a status symbol, or we might judge it to be repulsive partly because it signifies for us over-consumption and offends our political or moral values.

Anthropology, especially the savanna hypothesis proposed by Gordon Orians and others, predicts that some of the positive aesthetics that people have are based on innate knowledge of productive human habitats. It had been shown that people prefer and feel happier looking at trees with spreading forms much more than looking at trees with other forms, or non-tree objects; also Bright green colors, linked with healthy plants with good nutrient qualities, were more calming than other tree colors, including less bright greens and oranges.

*Q. According to the author the contextual aspect of beauty, as mentioned in paragraph 2, is reflected by:*

Solution:

Option 3 is the correct answer as is evident in the passage- “...judgments of aesthetic value can become linked to judgments of economic, political, or moral value.” Option 1 is not the correct response as beauty cannot be objective (thereby universal) and contextual at the same time.

Option 2 also refers to commonalities (mankind’s inner 19/95 qualities) which, like option 1, are antithetical to the contextual (specific) aspect of beauty.

Option 4 is merely based on an example and loses out to the completeness provided by option 3. Hence, the correct answer is option 3.

QUESTION: 23

Judgments of aesthetic value rely on our ability to discriminate at a sensory level. Aesthetics examines our affective domain response to an object or phenomenon. Immanuel Kant, writing in 1790, observes of a man "If he says that canary wine is agreeable he is quite content if someone else corrects his terms and reminds him to say instead: It is agreeable to me," because "Everyone has his own (sense of) taste". The case of "beauty" is different from mere "agreeableness" because, "If he proclaims something to be beautiful, then he requires the same liking from others; he then judges not just for himself but for everyone, and speaks of beauty as if it were a property of things."

Aesthetic judgments may be culturally conditioned to some extent. Victorians in Britain often saw African sculpture as ugly, but just a few decades later, Edwardian audiences saw the same sculptures as being beautiful. The Abuse of Beauty, Evaluations of beauty may well be linked to desirability, perhaps even to sexual desirability. Thus, judgments of aesthetic value can become linked to judgments of economic, political, or moral value. We might judge a Lamborghini to be beautiful partly because it is desirable as a status symbol, or we might judge it to be repulsive partly because it signifies for us over-consumption and offends our political or moral values.

Anthropology, especially the savanna hypothesis proposed by Gordon Orians and others, predicts that some of the positive aesthetics that people have are based on innate knowledge of productive human habitats. It had been shown that people prefer and feel happier looking at trees with spreading forms much more than looking at trees with other forms, or non-tree objects; also Bright green colors, linked with healthy plants with good nutrient qualities, were more calming than other tree colors, including less bright greens and oranges.

**Q. Aesthetics, from an anthropological perspective, tends to reflect:**

Solution:

Option 2 is the correct answer as is evident from the phrase- “...innate knowledge of productive human habitats”. ‘Productive human habitats’ indicate a utilitarian perspective.

Options 1 and 3 are aspects of option 2 as is evident from the passage. Option 2 encapsulates what has been mentioned in options 1 and 3.

Option 4 is beyond the scope of the passage.

Hence, the correct answer is option 2.

QUESTION: 24

Judgments of aesthetic value rely on our ability to discriminate at a sensory level. Aesthetics examines our affective domain response to an object or phenomenon. Immanuel Kant, writing in 1790, observes of a man "If he says that canary wine is agreeable he is quite content if someone else corrects his terms and reminds him to say instead: It is agreeable to me," because "Everyone has his own (sense of) taste". The case of "beauty" is different from mere "agreeableness" because, "If he proclaims something to be beautiful, then he requires the same liking from others; he then judges not just for himself but for everyone, and speaks of beauty as if it were a property of things."

Aesthetic judgments may be culturally conditioned to some extent. Victorians in Britain often saw African sculpture as ugly, but just a few decades later, Edwardian audiences saw the same sculptures as being beautiful. The Abuse of Beauty, Evaluations of beauty may well be linked to desirability, perhaps even to sexual desirability. Thus, judgments of aesthetic value can become linked to judgments of economic, political, or moral value. We might judge a Lamborghini to be beautiful partly because it is desirable as a status symbol, or we might judge it to be repulsive partly because it signifies for us over-consumption and offends our political or moral values.

Anthropology, especially the savanna hypothesis proposed by Gordon Orians and others, predicts that some of the positive aesthetics that people have are based on innate knowledge of productive human habitats. It had been shown that people prefer and feel happier looking at trees with spreading forms much more than looking at trees with other forms, or non-tree objects; also Bright green colors, linked with healthy plants with good nutrient qualities, were more calming than other tree colors, including less bright greens and oranges.

*Q. Beauty as a ‘property of things’ implies:*

Solution:

Option 1 is contrary to the objective nature of beauty as a shared conception thereby making it an incorrect response. Options 2 and 4 are not relevant to the question asked. Option 3 is the correct answer as is evident from the phrase- “If he proclaims something to be beautiful, then he requires the same liking from others...” in the first paragraph, implying a shared conception (commonality) of beauty which further implies objectivity.

Hence, the correct answer is option 3.

QUESTION: 25

Arrange statements 1-4 given below in a logical sequence in order to form a coherent paragraph. Your answer will be the order of statement numbers that forms this logical sequence e.g. 2314.

1. Some of the drugs most often associated with this term include alcohol, amphetamines, barbiturates, benzodiazepines, cocaine, methaqualone, and opium alkaloids.

2. Use of these drugs may lead to criminal penalty in addition to possible physical, social, and psychological harm, both strongly depending on local jurisdiction.

3. Drug abuse has a huge range of definitions related to taking a psychoactive drug or performance enhancing drug for a non-therapeutic or non-medical effect.

4. All of these definitions imply a negative judgement of the drug use in question (compare with the term responsible drug use for alternative views).

Solution:

Statement 3 gives an opening to the paragraph by enlarging upon the term “drug abuse”.

Statement 4 follows statement 3 logically, by maintaining the continuity of the definitions mentioned in 3 and elaborating upon what they imply.

Statement 1 follows, since it talks about the drugs associated with the term “drug abuse” being discussed.

The words “use of these drugs” in statement 2 talks about all the drugs mentioned in statement 1 and so, 2 follows 1.

Hence, the correct answer is 3412.

QUESTION: 26

Arrange statements 1-5 given below in a logical sequence in order to form a coherent paragraph. Your answer will be the order of statement numbers that forms this logical sequence e.g. 23514.

1. The creation of the Black Tigers is based on the LTTE's studies of Asymmetric warfare thus using suicide cadres to balance the government's greater resources.

2. The Black Tigers are believed to be the most effective unit of its kind in the world, as with the rest of the LTTE, it is also secular, not driven by religious fanaticism.

3. The LTTE are keeping the Black Tiger unit active, as witnessed by their commemoration ceremonies. 4. They will then be called up if needed, and if so will have a last meal with the LTTE leader Velupillai Prabhakaran. 5. The Tiger unit get extensive training but are then believed to return to their previous unit, without revealing their new assignment.

Solution:

There is a link between statements 3 and 2, as 3 talks about the LTTE keeping the Black Tigers active while 2 mentions the Black Tigers' effectiveness and its secularism 'as with the rest of LTTE'.

Statements 1 and 5 are also linked as 1 mentions Asymmetric warfare and 5 describes it.

There is a strong 5-4 link as 5 talks about the Tiger unit returning to their previous unit and statement 4 speaks about the members “then” being called up if needed.

The 3-2 link should precede the 1-5-4 link, as statements 3 and 2 are more introductory in nature while 1, 5, and 4 go into the specifics of their training.

Hence, the correct answer is 32154.

QUESTION: 27

Arrange statements 1-5 given below in a logical sequence in order to form a coherent paragraph. Your answer will be the order of statement numbers that forms this logical sequence e.g. 23514.

1. This increased capacity per unit area can be used to decrease cost and/or increase functionality.

2. But, since the speed and power consumption gains are apparent to the end user, there is fierce competition among the manufacturers to use finer geometries. |

3. In general, as the feature size shrinks, almost everything, including functionality improves - the cost per unit and the switching power consumption go down, and the speed goes up.

4. ICs have consistently migrated to smaller feature sizes over the years, allowing more circuitry to be packed on each chip. 5. ICs with nanometer-scale devices are not without their problems, principal among which is leakage current.

Solution:

One of the prominent links is between 4 and 1; it starts off with “this increased capacity” in 1. This is picked up from 4 which talks about increase in capacity.

The increase in functionality mentioned in 1 is spoken about in 3 which details the improvement in functionality with a shrink in size. This is then contrasted by 5, which warns that despite the advantages mentioned in 3, shrinking sizes do cause certain problems. 5 should then be followed by 2, which starts with "But" and tells us why manufacturers still opt for fine geometries inspite of the disadvantage mentioned in 5.

Hence, the correct answer is 41352.

QUESTION: 28

The following question consists of a certain number of sentences. Some sentences are grammatically incorrect or inappropriate. Identify the number of sentences that are grammatically __correct and appropriate__.

1. Having finished supper, they banqueted afresh on conversation, Homer narrating his wanderings and telling of the cities he had visited.

2. At length they retired to rest; but the following morning Glaucus resolved to go to his master and acquaint him with his meeting with Homer.

3. Having left the goats in the charge of a fellow-servant, he left Homer at home, promising to return quickly.

4. Glaucus told the whole story to his friend.

Solution:

Sentence 2 is correct in balance, tense and construction (telling and narrating etc.).

Sentences 1,3 and 4 are grammatically correct as well.

Hence, the correct answer is 4.

QUESTION: 29

The following question consists of a certain number of sentences. Some sentences are grammatically __incorrect or inappropriate__. Identify the number of sentences that are grammatically incorrect.

1. Most of the military disasters have been caused by the home government.

2. Napoleon undoubtedly owed much of his extraordinary success to his goodwill.

3. Hence the saying: If you know the enemy and know you, you need not fear the result of a hundred battles.

4. If you know yourself but not the enemy, for every victory gained one will also suffer a defeat.

Solution:

Statement 3 should have the pronoun “you” (second one) in the emphatic case. Simply put, the word should be ‘yourself as it reflects on the person ‘you’.

In statement 4, for pronoun consistency, the word “one” should be replaced by the pronoun ‘you’.

Statements 1 and 2 are grammatically correct.

Hence, the correct answer is 2.

QUESTION: 30

The following question consists of a certain number of sentences. Some sentences are grammatically incorrect or inappropriate. Identify the number of sentences that are grammatically __incorrect__.

1. I stood to silence where I was, for I did not know what to do.

2. Of bell or knocker there was no sign.

3. Though these frowning walls and dark window openings it was not likely that my voice could penetrate.

4. The time I waited seemed endless, and I felt doubts and fears crowding upon me.

5. What sort of place had I come to, and among what kind of people? What sort of grim adventure was it on which I had embarked? Was this a customary incident in the life of a solicitor's clerk sent out to explain the purchase of a London estate to a foreigner?

Solution:

In statement 1, the preposition “to” with “silence” is used incorrectly. We may say the following: To silence the class, she raised her voice. But in the current context, we say that one stands in silence.

If you are a fast reader, you may not have noticed the “though” in statement 3. It should be ‘through’.

The other statements are correct.

Hence, the correct answer is 2.

QUESTION: 31

Answer the question based on the passage given below. Type in the correct option number as your answer.

Contemporary management theory tends to distinguish between leadership and management, and places greater emphasis on leaders. Managers are described as those who merely embrace processes and seek stability, while leaders tolerate risk and create change. Organizations need both, but leaders are more important.

*Which of the following best strengthens the above argument?*

Solution:

“Organizations need both (leaders and managers), but leaders are more important,” needs to be strengthened.

Option 1 establishes leaders as important as creators of the systems that are well designed and maintained. It does strengthen the argument but only if it is assumed that leaders manage the systems through good managers, hence not the best option.

Option 2 accommodates the leader as well as the manager. Hence establishes that good leaders engage managers to maintain the stability in which area the leaders may be inadequate and strengthens the argument.

Option 3 is eliminated because of the word ‘must’. It does not mention managers, but states that leaders themselves should have managerial skills.

Option 4 talks about a different kind of managerial skills found in leaders and is irrelevant to the argument.

Hence, the correct answer is option 2.

QUESTION: 32

Answer the question based on the passage given below. Type in the correct option number as your answer.

Why do good, ordinary people sometimes become perpetrators of evil? The most extreme transformation of this kind is, of course, the story of God’s favorite angel, Lucifer - a story that has set the context for my psychological investigations into lesser human transformations in response to the corrosive influence of powerful situational forces. Such forces exist in many common behavioral contexts, distorting our usual good nature by pushing us to engage in deviant, destructive, or evil behavior. When embedded in new and unfamiliar settings, our habitual ways of thinking, feeling, and acting no longer function to sustain the moral compass that has guided us reliably in the past.

*Which of the following is the most likely inference from the passage? *

Solution:

Option 1 is contrary to the passage. The individual’s inner nature, dispositions, and personality traits are not the primary factors; one needs to take account of situational forces.

Option 3 is partially true, but is eliminated because of the word ‘easy’. It is presumptuous in the light of the paragraph to say that ‘it is easy to ... be seduced ...' etc.

Option 4 is eliminated because it states ‘individuals ... can turn permanently evil’, which is not supported by the passage. Option 2 supports every aspect of the paragraph and follows directly from what is stated in the paragraph.

Hence, the correct answer is option 2.

QUESTION: 33

The statement(s) below are the summary of a paragraph.Choose the option that best represents the paragraph that was summarised.

The monarchy enjoys a special, quasi-religious, role in Thai society; and the king is widely and deeply revered. Mostly, the foreign media have censored themselves and, fully aware of the sensitivities, avoided all but the most fawningly positive reports. But in our view, this has become unsustainable, for two reasons. First, King Bhumibol Adulyadej turned 81 in December, and has been frail. His heir-apparent, the crown prince, does not enjoy the same standing. The looming succession is an important political issue and cannot simply be ignored. Second, last year saw Thailand descend into something close to mob rule. Protesters against the elected government took over airports, dealing a terrible blow to the important tourist industry in the process. They did so in the name of the king, and the royal family never repudiated them.

Solution:

The gist of the paragraph is: Since the King is revered in Thailand, the foreign press had not said anything against him.

This is not sustainable now for two reasons. The crown prince is not as good as the earlier monarch and the monarchy had not condemned the protests against the democratic government. This gist is best captured in option 4.

Option 1 does not mention the extremely positive reports of the foreign media towards the Thai King. Secondly, the phrase, ‘anything favourable’ is too strong an expression and something which cannot be justified by the paragraph.

Option 2 does not mention the reputation of the crown prince and the impending succession, which is an important part of the paragraph.

Option 3 does not mention the monarchy condoning mob rule.Secondly, it mentions the Thai King by name which is not necessary. (Note: A summary should, as far as possible only contain the essence of the paragraph. Names, dates and numbers are to be avoided unless absolutely necessary).

Hence, the correct answer option is 4.

QUESTION: 34

The statement(s) below are the summary of a paragraph. Choose the option that best represents the paragraph that was summarised.

Post Traumatic Stress Disorder, or PTSD, is the persistence of debilitating psychological symptoms. It can include flashbacks and nightmares, increased arousal in the form of insomnia, anger and an inability to concentrate, and impaired personal relationships. Although lasting psychological damage from horrific experiences has been recognised since time immemorial, it is only since 1980, when veterans were still experiencing stress from the Vietnam war, that PTSD has been a formal psychiatric diagnosis.

Solution:

The main points of the paragraph are: Post Traumatic Stress Disorder is the persistence of debilitating psychological symptoms. Though it was experienced from time immemorial it got recognised as an illness only in 1980. Option 3 captures this essence well.

An abbreviation in a precis without explaining it is incorrect. Hence among other reasons options 1 and 2 can be eliminated. Option 4 somehow attributes the recognition directly to the Vietnam War- this is not the intent of the paragraph.

Hence, the correct answer is option 3.

QUESTION: 35

Group Question

Answer the following question based on the information given below.

The annual Korus Masters chess tournament features the world's eight best chess players, pitted against each other in a double round-robin format. In this format, each player plays one match against every other player. This match consists of two games, with black pieces for one player and white for the other in one game, and vice versa in the second game. Each player plays exactly one match every day.

If a game results in a win, the winner gets one point and the loser gets none. In case of a draw, both players get half a point each.

Given below is a table with each day's matches, and the total points of each player at the end of every day.

Day 5 was a nightmare for Romonevich as he lost both the games scheduled. At the end of Day 7, Tupolev was second in the overall rankings and had more points than Adams.

Given below are a few details about the wins, losses, and draws that occured in the matches:

1. The only players who won both their games against a particular player were Anand (vs Romonevich) and Carlson (vs Leiko).

2. In the match between Kremnik and Levonian, both games were won by the player playing with black pieces.

3. The only other instance of a player winning with black pieces was when Kremnik beat Romonevich after drawing the first game.

4. Leiko won 6 games with white pieces.

5. Adams won with white pieces against Anand and Levonian.

6. There were eight occasions in all when both games between two players ended in a draw.

The following abbreviations are used wherever necessary:

An - Anand

Ad - Adams

C - Carlson

K - Kremnik

Leiko - Leiko

Levo - Levonian

R - Romonevich

T - Tupolev

*Q. On how many days was Anand leading in terms of points?*

Solution:

In the given table, we have each day's matches and the points of some players. Now, for example, if we know Anand's points at the end of the first day (1.5), and that Anand played Tupolev that day, we can find out Tupolev's points (0.5), since in every match, a total of two points are at stake from two games.

Also it is given that on Day 5 Anand won both of his match against Romonevich, so his score will be 6, and on Day 6 his score was 7, which means Carlson earned 1 point against him. Lastly it is given that Tupolev finished second, which means he must have ended with 8 points. (8.5 + T + 7.5 + 7 + Ad + 6.5 + 6 + 5.5) must equal to 56.

T + Ad = 15

T > Ad

T = 8

Thus, we can complete the entire points table for every day as shown above. Looking at the table, we can say that Anand was in the solo lead on the last day and joint lead after the first, third, fifth and sixth days. Hence, option 2.

QUESTION: 36

The annual Korus Masters chess tournament features the world's eight best chess players, pitted against each other in a double round-robin format. In this format, each player plays one match against every other player. This match consists of two games, with black pieces for one player and white for the other in one game, and vice versa in the second game. Each player plays exactly one match every day.

If a game results in a win, the winner gets one point and the loser gets none. In case of a draw, both players get half a point each.

Given below is a table with each day's matches, and the total points of each player at the end of every day.

Day 5 was a nightmare for Romonevich as he lost both the games scheduled. At the end of Day 7, Tupolev was second in the overall rankings and had more points than Adams.

Given below are a few details about the wins, losses, and draws that occured in the matches:

1. The only players who won both their games against a particular player were Anand (vs Romonevich) and Carlson (vs Leiko).

2. In the match between Kremnik and Levonian, both games were won by the player playing with black pieces.

3. The only other instance of a player winning with black pieces was when Kremnik beat Romonevich after drawing the first game.

4. Leiko won 6 games with white pieces.

5. Adams won with white pieces against Anand and Levonian.

6. There were eight occasions in all when both games between two players ended in a draw.

The following abbreviations are used wherever necessary:

An - Anand

Ad - Adams

C - Carlson

K - Kremnik

Leiko - Leiko

Levo - Levonian

R - Romonevich

T - Tupolev

*Q. Which player increased his points by the same amount every day?*

Solution:

Looking at the table, we can say that Adams increased his points by 1 every day. Hence, option 3.

QUESTION: 37

The annual Korus Masters chess tournament features the world's eight best chess players, pitted against each other in a double round-robin format. In this format, each player plays one match against every other player. This match consists of two games, with black pieces for one player and white for the other in one game, and vice versa in the second game. Each player plays exactly one match every day.

If a game results in a win, the winner gets one point and the loser gets none. In case of a draw, both players get half a point each.

Given below is a table with each day's matches, and the total points of each player at the end of every day.

Day 5 was a nightmare for Romonevich as he lost both the games scheduled. At the end of Day 7, Tupolev was second in the overall rankings and had more points than Adams.

Given below are a few details about the wins, losses, and draws that occured in the matches:

1. The only players who won both their games against a particular player were Anand (vs Romonevich) and Carlson (vs Leiko).

2. In the match between Kremnik and Levonian, both games were won by the player playing with black pieces.

3. The only other instance of a player winning with black pieces was when Kremnik beat Romonevich after drawing the first game.

4. Leiko won 6 games with white pieces.

5. Adams won with white pieces against Anand and Levonian.

6. There were eight occasions in all when both games between two players ended in a draw.

The following abbreviations are used wherever necessary:

An - Anand

Ad - Adams

C - Carlson

K - Kremnik

Leiko - Leiko

Levo - Levonian

R - Romonevich

T - Tupolev

*Q. In how many matches between two players did one game end in a win and one in a draw?*

Solution:

If in a match, one game ended in a win and one in a draw, the winning player would get 1.5 points that day, and the losing player would get 0.5 points. We can look at the table and count how many times this happens, i.e 11.

Hence, option 4.

QUESTION: 38

If a game results in a win, the winner gets one point and the loser gets none. In case of a draw, both players get half a point each.

Day 5 was a nightmare for Romonevich as he lost both the games scheduled. At the end of Day 7, Tupolev was second in the overall rankings and had more points than Adams.

Given below are a few details about the wins, losses, and draws that occured in the matches:

2. In the match between Kremnik and Levonian, both games were won by the player playing with black pieces.

3. The only other instance of a player winning with black pieces was when Kremnik beat Romonevich after drawing the first game.

4. Leiko won 6 games with white pieces.

5. Adams won with white pieces against Anand and Levonian.

6. There were eight occasions in all when both games between two players ended in a draw.

An - Anand

Ad - Adams

C - Carlson

K - Kremnik

Leiko - Leiko

Levo - Levonian

R - Romonevich

T - Tupolev

**Q. Who was leading at the end of the second day's matches?**

Solution:

From the points table, we can see that Romonevich was leading with 3 points at the end of the second day.

Hence, option 4.

QUESTION: 39

Group Question

Answer the following question based on the information given below.

Naina and Sachin have invited their friends Emily and Walter for a card game at their house. They are playing with a standard deck of 52 playing cards, which consists of four suits (called Clubs, Diamonds, Hearts and Spades) of 13 cards each. Each of the 13 cards in a suit has a different face value, from 1 to 13. The cards with face values from 2 to 10 have the respective number printed on them, and the cards with face values 1, 11, 12 and 13 have A, J, Q and K respectively printed on them. Each of the four players has 13 cards. The suit-wise distribution of cards with each player is given in the following table. However, the cards from one of the four suits are not known for each player.

*Q. In this game, a ‘pure run’ is when a player has four cards of the same suit with their face values consecutive. How many ‘pure runs’ in all do the four players have?*

Solution:

For each of the four players, the missing cards of a particular suit can be determined by seeing the cards of the other players for that suit. Using this logic, the completed table is given below.

We can see that the only two ‘pure runs’ are the 10, J, Q, K of Clubs with Naina, and the 8, 9, 10, J of Spades with Walter.

Hence, option 2.

QUESTION: 40

Naina and Sachin have invited their friends Emily and Walter for a card game at their house. They are playing with a standard deck of 52 playing cards, which consists of four suits (called Clubs, Diamonds, Hearts and Spades) of 13 cards each. Each of the 13 cards in a suit has a different face value, from 1 to 13. The cards with face values from 2 to 10 have the respective number printed on them, and the cards with face values 1, 11, 12 and 13 have A, J, Q and K respectively printed on them. Each of the four players has 13 cards. The suit-wise distribution of cards with each player is given in the following table. However, the cards from one of the four suits are not known for each player.

*Q. A ‘short run’ is when a player has three cards of the same suit with their face values consecutive. How many ‘short runs’ in all do the four players have? (Three of the four cards in a ‘pure run’ cannot be counted as a ‘short run’).*

Solution:

From the table, we can see that there are two ‘short runs’: 10, J, Q of Hearts with Naina and 6, 7, 8 of Hearts with Emily.

Hence, option 2.

QUESTION: 41

Naina and Sachin have invited their friends Emily and Walter for a card game at their house. They are playing with a standard deck of 52 playing cards, which consists of four suits (called Clubs, Diamonds, Hearts and Spades) of 13 cards each. Each of the 13 cards in a suit has a different face value, from 1 to 13. The cards with face values from 2 to 10 have the respective number printed on them, and the cards with face values 1, 11, 12 and 13 have A, J, Q and K respectively printed on them. Each of the four players has 13 cards. The suit-wise distribution of cards with each player is given in the following table. However, the cards from one of the four suits are not known for each player.

Q. A ‘group’ is when a player has three cards of the same face value. How many ‘groups’ in all do the four players have, if the cards that are a part of a ‘short run’ or a ‘pure run’ are excluded?

Solution:

From the table, we can see that there are two ‘groups’: three J’s with Naina and three A’s with Walter. However, two of the J's that Naina has are a part of a ‘run’, so they should be excluded.

Hence, option 2.

QUESTION: 42

Naina and Sachin have invited their friends Emily and Walter for a card game at their house. They are playing with a standard deck of 52 playing cards, which consists of four suits (called Clubs, Diamonds, Hearts and Spades) of 13 cards each. Each of the 13 cards in a suit has a different face value, from 1 to 13. The cards with face values from 2 to 10 have the respective number printed on them, and the cards with face values 1, 11, 12 and 13 have A, J, Q and K respectively printed on them. Each of the four players has 13 cards. The suit-wise distribution of cards with each player is given in the following table. However, the cards from one of the four suits are not known for each player.

*Q. The ‘pure runs’, ‘short runs’ and ‘groups’ with each player are excluded, and the face values of the remaining cards are added up to calculate the ‘penalty points’ for each player. Which of the following is not equal to the ‘penalty points’ for any of the players?*

Solution:

After excluding the two ‘pure runs’, the two ‘short runs’ and one ‘group’ as seen in questions 1 to 3, the cards with each player are as follows: Naina: 3, 4, J of Diamonds and 2, 5, K of Spades.

Hence, the total ‘penalty points’ are 3 + 4 + 11 + 2 + 5 + 13 = 38 Emily: 3, 5, 6, 8 of Clubs, 2, 5, 7, 9 of Diamonds and A, Q of Spades.

Hence, the total ‘penalty points’ are3 + 5 + 6 + 8 + 2 + 5 + 7 + 9 + 1 +12 = 58 Walter: 2, 7 of Clubs, 10, K of Spades, and 4, 9 of Hearts.

Hence, the total ‘penalty points’ are 2 + 7 + 10 + 13 + 4 + 9 = 45 Sachin: All his cards, which have a total face value of 4 + 9 + 6 + 8 + 12 + 2 + 3 + 5 + 13 + 3 + 4 + 6 + 7 = 82, which are his ‘penalty points’.

Hence, option 4.

QUESTION: 43

Group Question

Answer the following question based on the information given below.

In Rosemary school, which had 200 students in Class X, the results in the recent examinations, which had three papers in the area of Mathematics, Science and English were as follows:

I. The number of students who passed in English was 20 less than those who did not pass in English.

II. The number of students who passed in more than one subject was 90.

III. Of the students who had passed in English, 35 did not pass in Science.

IV. 45 students had passed in both Mathematics and Science.

V. Of the students who had passed in Science, 60 students had passed in exactly one other paper as well.

VI. The number of students who had passed only in Science was twice that of the number who had passed only in Mathematics.

VII. Further, the number of students who had passed in all the three subjects was half of the number of students who did not pass in any of the three subjects.

*Q. How many students did not pass in any subject?*

Solution:

Let the number of students who passed in English be x and those who did not pass in English be y, then we have, y - x = 20, and y + x = 200

Solving the above two equations for x and y, we have x = 90 and y = 110 The given information can be represented in pictorial form is as shown:

Where,

f = number of students who passed only in English

e = number of students who passed only in Mathematics From (VI), the number of students who passed only in Science will be 2e

d = number of students who passed in both Mathematics and English but not in Science

b = number of students who passed in both English and Science but not in Mathematics

c = number of students who passed in both Mathematics and Science but not in English

a = number of students who passed in all the three subjects From (VII), 2a = number of students who did not pass in any of the subjects Now from (II), we have, a + b + c + d = 90 ... (i)

From (III), d+ f = 35 . . . ( ii )

From (IV), a + c = 45 ... (iii)

From (V), c + b = 60 ... (iv)

Also, from equations (iv) and (i), a + d = 30 . . . ( v ) Also, a + b + d + f = 90 ... (vi)

From (v) and (vi), b + f =60 ... (vii)

From (iv) and (vii), c = f ... (viii)

From (iii) and (v), c - d = 15 ... (ix)

From (ii) and (ix), f + c = 50 ... (x)

From (viii) and (x), c = 25 ... (xi)

From (iv), b = 35 ... (xii)

From (iii), a = 20 ... (xiii)

From (viii), f = 25 ... (xiv)

From (ix), d = 10 ... (xv)

Now,

3a + b + c + d + f = 155 from (xi to xv)

We have, 3e = 45, implying that e = 15 ... (xvi) Now, the distribution would look as shown below:

From the above diagram we get that the number of students who did not pass in any subject is 40. Answer: 40

QUESTION: 44

In Rosemary school, which had 200 students in Class X, the results in the recent examinations, which had three papers in the area of Mathematics, Science and English were as follows:

I. The number of students who passed in English was 20 less than those who did not pass in English.

II. The number of students who passed in more than one subject was 90.

III. Of the students who had passed in English, 35 did not pass in Science.

IV. 45 students had passed in both Mathematics and Science.

V. Of the students who had passed in Science, 60 students had passed in exactly one other paper as well.

VI. The number of students who had passed only in Science was twice that of the number who had passed only in Mathematics.

VII. Further, the number of students who had passed in all the three subjects was half of the number of students who did not pass in any of the three subjects.

*Q. How many students passed in Science but did not pass in Mathematics or English?*

Solution:

From the solution to the first question of the set, we find that 30 students passed only in Science.

Answer: 30

QUESTION: 45

In Rosemary school, which had 200 students in Class X, the results in the recent examinations, which had three papers in the area of Mathematics, Science and English were as follows:

I. The number of students who passed in English was 20 less than those who did not pass in English.

II. The number of students who passed in more than one subject was 90.

III. Of the students who had passed in English, 35 did not pass in Science.

IV. 45 students had passed in both Mathematics and Science.

V. Of the students who had passed in Science, 60 students had passed in exactly one other paper as well.

VI. The number of students who had passed only in Science was twice that of the number who had passed only in Mathematics.

VII. Further, the number of students who had passed in all the three subjects was half of the number of students who did not pass in any of the three subjects.

*Q. The percentage point difference between the number of students who have passed in exacfly one subject and those who have passed in exactly three subjects is:*

Solution:

Percentage of students passing in exactly one subject = (25 + 15 + 30)/200 = 35% Percentage of students passing in all three subjects = 20/200 = 10% The percentage point difference between the two is 25.

Answer: 25

QUESTION: 46

I. The number of students who passed in English was 20 less than those who did not pass in English.

II. The number of students who passed in more than one subject was 90.

III. Of the students who had passed in English, 35 did not pass in Science.

IV. 45 students had passed in both Mathematics and Science.

V. Of the students who had passed in Science, 60 students had passed in exactly one other paper as well.

VI. The number of students who had passed only in Science was twice that of the number who had passed only in Mathematics.

VII. Further, the number of students who had passed in all the three subjects was half of the number of students who did not pass in any of the three subjects.

*Q. How many students have passed in both Mathematics and English but not in Science?*

Solution:

From the diagram shown in the solution of the first question of the set, we find that 10 students passed in both Mathematics and English but not in Science.

Answer: 10

QUESTION: 47

Group Question

Answer the following question based on the information given below.

A survey was carried out to assess the acceptability of private insurance players. A group of 100 respondents was identified and they were to be queried on the following parameters : Reliability, Claim Settlements and Ethical Sales. The insurance companies to be surveyed were camouflaged as C_{1}, C_{2}, C_{3} and C_{4}. The query was based on two factors: Acceptable and Non-acceptable. The chart below gives the details of the respondents who answered the queries as acceptable for the said parameters.

In the above chart, 1 does not necessarily represent C_{1}. Similarly 2 may or may not represent C_{2}. Also, the three parameters of 1 may not necessarily stand for the same company. For. eg: Reliability of 1 could be of company C_{1} while Claim Settlement of 1 could be of Company C_{2}.

It was further observed that a single respondent had answered only one query on any one parameter i.e. no respondent had answered to two parameters that were asked for in the survey.

Further

1. The total number of respondents who had accepted the companies C_{2} and C_{4} on all the parameters was 29 and 26 respectively.

2. C_{3} had equal number of respondents accepting it on at least two of the parameters and further the total number of respondents that C_{3} had on all the parameters was greater than the total number of respondents who had accepted C_{1} on all parameters put together.

3. C_{1} had witnessed different number of respondents for each of the three parameters.

4. C_{2} did not have 10 or 5 respondents giving a positive reply for any of the parameters.

Further to have a more comprehensive analysis of the survey a point system was adopted wherein the company for whom the number of respondents for any particular parameter was highest was awarded 5 points. Similarly, the company which witnessed second highest number of respondents for that same parameter was awarded 3 points, third highest was awarded a single point and the company which had the least number of respondents accepting it on that particular parameter was supposed to get zero points.

*Q. What could be the total points scored by C _{4} on all parameters put together?*

Solution:

C_{2} cannot have 2 or 6 respondents in Reliability as no possible combination of the number of respondents in Ethical Sales and Claim Settlement will give a total of 29 respondents. And further C_{2} also did not have 5 or 10 number of respondents on any of the parameters, thereby implying that the number of respondents on Reliability for C_{2} was 7. This further implies that the number of respondents for Claim Settlement and Ethical Sales was 8 and 14 respectively.

C_{4} cannot have had 5 respondents on Reliability as the total number of respondents with any other combination will never yield a total of 26.

Based on above the following four combinations of distribution of the number of respondents is possible as shown below.

Case 1:

Case 2:

Case 3:

Case 4:

Thus, the total points obtained by C4 can be either 7 or 8. Hence, option 4.

QUESTION: 48

A survey was carried out to assess the acceptability of private insurance players. A group of 100 respondents was identified and they were to be queried on the following parameters : Reliability, Claim Settlements and Ethical Sales. The insurance companies to be surveyed were camouflaged as C_{1}, C_{2}, C_{3} and C_{4}. The query was based on two factors: Acceptable and Non-acceptable. The chart below gives the details of the respondents who answered the queries as acceptable for the said parameters.

In the above chart, 1 does not necessarily represent C_{1}. Similarly 2 may or may not represent C_{2}. Also, the three parameters of 1 may not necessarily stand for the same company. For. eg: Reliability of 1 could be of company C_{1} while Claim Settlement of 1 could be of Company C_{2}.

It was further observed that a single respondent had answered only one query on any one parameter i.e. no respondent had answered to two parameters that were asked for in the survey.

Further

1. The total number of respondents who had accepted the companies C_{2} and C_{4} on all the parameters was 29 and 26 respectively.

2. C_{3} had equal number of respondents accepting it on at least two of the parameters and further the total number of respondents that C_{3} had on all the parameters was greater than the total number of respondents who had accepted C_{1} on all parameters put together.

3. C_{1} had witnessed different number of respondents for each of the three parameters.

4. C_{2} did not have 10 or 5 respondents giving a positive reply for any of the parameters.

Further to have a more comprehensive analysis of the survey a point system was adopted wherein the company for whom the number of respondents for any particular parameter was highest was awarded 5 points. Similarly, the company which witnessed second highest number of respondents for that same parameter was awarded 3 points, third highest was awarded a single point and the company which had the least number of respondents accepting it on that particular parameter was supposed to get zero points.

*Q. If C _{3} had 5 respondents for Reliability, what could be the ratio of the number of respondents who had accepted C_{3} on ‘Claim Settlement’ to that of the number of respondents who had accepted C_{1} on Ethical Sales?*

Solution:

Consider the solution to the first question.

C_{3} having 5 respondents for Reliability is possible in cases 1 and 4.

On Claim Settlement, in case 1, there were 12 respondents in case of C_{3}, whereas the number of respondents for C_{1} on Ethical Sales was 8.

The ratio would then be 12 : 8, i.e. 3 : 2.

Similarly in case 4, there were 10 respondents in case of C_{3} for Claim settlement, whereas the number of respondents for C_{1} on Ethical sales was 12.

Hence the required ratio would be 10 : 12, i.e. 5 : 6. Hence, option 4.

QUESTION: 49

A survey was carried out to assess the acceptability of private insurance players. A group of 100 respondents was identified and they were to be queried on the following parameters : Reliability, Claim Settlements and Ethical Sales. The insurance companies to be surveyed were camouflaged as C_{1}, C_{2}, C_{3} and C_{4}. The query was based on two factors: Acceptable and Non-acceptable. The chart below gives the details of the respondents who answered the queries as acceptable for the said parameters.

In the above chart, 1 does not necessarily represent C_{1}. Similarly 2 may or may not represent C_{2}. Also, the three parameters of 1 may not necessarily stand for the same company. For. eg: Reliability of 1 could be of company C_{1} while Claim Settlement of 1 could be of Company C_{2}.

It was further observed that a single respondent had answered only one query on any one parameter i.e. no respondent had answered to two parameters that were asked for in the survey.

Further

1. The total number of respondents who had accepted the companies C_{2} and C_{4} on all the parameters was 29 and 26 respectively.

2. C_{3} had equal number of respondents accepting it on at least two of the parameters and further the total number of respondents that C_{3} had on all the parameters was greater than the total number of respondents who had accepted C_{1} on all parameters put together.

3. C_{1} had witnessed different number of respondents for each of the three parameters.

4. C_{2} did not have 10 or 5 respondents giving a positive reply for any of the parameters.

Further to have a more comprehensive analysis of the survey a point system was adopted wherein the company for whom the number of respondents for any particular parameter was highest was awarded 5 points. Similarly, the company which witnessed second highest number of respondents for that same parameter was awarded 3 points, third highest was awarded a single point and the company which had the least number of respondents accepting it on that particular parameter was supposed to get zero points.

*Q. If the total number of respondents for each of the four companies, on all three parameters combined, is different; what would be the difference between the number of respondents who had accepted C _{4} on Claim Settlement and C_{1} in Ethical Sales?*

Solution:

Consider the solution to the first question.

The total number of respondents being different for each company gets satisfied in condition 4.

In such a case, the difference between the number of respondents who had accepted C_{4} on Claim Settlement and C _{1} on Ethical Sales would be 12 - 12 = 0 Hence, option 1.

QUESTION: 50

A survey was carried out to assess the acceptability of private insurance players. A group of 100 respondents was identified and they were to be queried on the following parameters : Reliability, Claim Settlements and Ethical Sales. The insurance companies to be surveyed were camouflaged as C_{1}, C_{2}, C_{3} and C_{4}. The query was based on two factors: Acceptable and Non-acceptable. The chart below gives the details of the respondents who answered the queries as acceptable for the said parameters.

_{1}. Similarly 2 may or may not represent C_{2}. Also, the three parameters of 1 may not necessarily stand for the same company. For. eg: Reliability of 1 could be of company C_{1} while Claim Settlement of 1 could be of Company C_{2}.

It was further observed that a single respondent had answered only one query on any one parameter i.e. no respondent had answered to two parameters that were asked for in the survey.

Further

_{2} and C_{4} on all the parameters was 29 and 26 respectively.

2. C_{3} had equal number of respondents accepting it on at least two of the parameters and further the total number of respondents that C_{3} had on all the parameters was greater than the total number of respondents who had accepted C_{1} on all parameters put together.

3. C_{1} had witnessed different number of respondents for each of the three parameters.

4. C_{2} did not have 10 or 5 respondents giving a positive reply for any of the parameters.

Further to have a more comprehensive analysis of the survey a point system was adopted wherein the company for whom the number of respondents for any particular parameter was highest was awarded 5 points. Similarly, the company which witnessed second highest number of respondents for that same parameter was awarded 3 points, third highest was awarded a single point and the company which had the least number of respondents accepting it on that particular parameter was supposed to get zero points.

*Q. Which of the following combinations of statements can be true?
1. The ratio of number of respondents that had accepted C _{2} and C_{4} on Ethical Sales is 7 : 5.
2. The ratio of number of respondents that had accepted C_{2} and C_{4} on Ethical Sales is 7 : 8.
3. The ratio of number of respondents that had accepted C_{3} and C_{4} on Claim Settlement is 2 : 1.
4. The ratio of number of respondents who had accepted C_{3} and C_{1} on R eliability is 2 : 5 or 5 : 2.*

Solution:

Consider statements 1 and 2: The ratio of number of respondents that had accepted C_{2} and C_{4} on Ethical Sales is 14 : 10, i.e. 7 : 5 in case 1 and case 3.

In case 2 it is 14 : 12, i.e. 7 : 6.

In case 4 it is 14 : 8, i.e. 7 : 4.

Hence, statement can be true for cases 1 and 3, but statement 2 is not true. Consider statement 3: The ratio of number of respondents that had accepted C_{3} and C_{4} on Claim Settlement is 12 : 10, i.e. 6 : 5 in cases 1 and 3. It is 10 : 12 i.e. 5 : 6 in cases 2 and 4.

Hence, statement 3 is definitely false.

Hence, option 2 is eliminated.

Consider statement 4: The ratio of number of respondents who had accepted C_{3} and C_{1} on Reliability in case 1 and case 4 is 5 : 2. In case 2, it is 6 : 5. In case 3, it is 2 : 5.

Hence, statement 4 is true for case 1, case 3 and case 4. Hence, option 1.

QUESTION: 51

Group Question

Answer the following question based on the information given below.

Sophia, a music maniac on Sunday recently purchased a set of 10 audio CD’s of her favorite English bands labeled from CD1 to CD10. Back home however to her surprise she found that CD1 had exactly one of her favorite bands, whereas CD2 had exactly two, CD3 had exactly 3 and so on till CD10 which had 10 of her favorite bands. Starting from Monday right up to Saturday she listened to exactly four CD’s everyday. During this period however she could not listen to two of her purchased CD’s but she could listen to each of remaining eight CD’s for exactly three days. The number of her favorite bands that she could listen to on each day starting from Monday to Saturday in that order was 18,12, 23, 19, 32 and 25.

*Q. Which CD of the following was the one which Sophia could not listen to?*

Solution:

If Sophia would have listened to each of the CD’s on exactly three days of the week, then she would have listened to a total of 55 * 3 = 165 of her favorite bands.

However the number of favorite bands she could listen to in the given week was: 18+ 12 + 23 + 19 + 32 + 25 = 129

Hence it implies that the number of her favorite bands that she did not listen to from two CD’s was (165-129) / 3 = 36 / 3 = 12

So the two CD’s that Sophia did not listen to could be (CD2 and CD10) OR (CD3 and CD9) OR (CD4 and CD8) OR (CD5 and CD7) On Tuesday, the number of favorite bands that she could listen to was 12.

This could have been possible in either of the two following cases:

Case 1: She listened to CD1, CD2, CD3 and CD6.

Case 2: She listened to CD1, CD2, CD4 and CD5.

Hence it can be concluded that Sophia had definitely listened to CD1 and CD2.

On Friday, the number of favorite bands that Sophia had listened to was 32.

Now this could have been possible in two cases:

Case 3: She listened to CD5, CD8, CD9 and CD10.

Case 4: She listened to CD6, CD7, CD9 and CD10. Again it can be concluded that she would have definitely listened to CD9 and CD10. Coming back to combinations which we have previously arrived at, i.e. (CD2 and CD10) OR (CD3 and CD9) OR (CD4 and CD8) OR (CD5 and CD7), it now becomes evident that combinations (CD2 and CD10) and (CD3 and CD9) are ruled out. The only possible combinations that she could have not listened to would be (CD4 and CD8) OR (CD5 and CD7).

Further between CD5 and CD7 she would have definitely listened to one of them. So the only combination that she could not have listened to would be (CD4 and CD8).

Hence, option 4.

QUESTION: 52

Sophia, a music maniac on Sunday recently purchased a set of 10 audio CD’s of her favorite English bands labeled from CD1 to CD10. Back home however to her surprise she found that CD1 had exactly one of her favorite bands, whereas CD2 had exactly two, CD3 had exactly 3 and so on till CD10 which had 10 of her favorite bands. Starting from Monday right up to Saturday she listened to exactly four CD’s everyday. During this period however she could not listen to two of her purchased CD’s but she could listen to each of remaining eight CD’s for exactly three days. The number of her favorite bands that she could listen to on each day starting from Monday to Saturday in that order was 18,12, 23, 19, 32 and 25.

*Q. Which of the following CD did Sophia not listen to on Friday?*

Solution:

On Friday, two possible cases: (i) : CD5, CD8, CD9 and CD10. (ii) : CD6, CD7, CD9 and CD10.

So, Sophia did not listen to CD3.

Hence, option 1.

QUESTION: 53

Sophia, a music maniac on Sunday recently purchased a set of 10 audio CD’s of her favorite English bands labeled from CD1 to CD10. Back home however to her surprise she found that CD1 had exactly one of her favorite bands, whereas CD2 had exactly two, CD3 had exactly 3 and so on till CD10 which had 10 of her favorite bands. Starting from Monday right up to Saturday she listened to exactly four CD’s everyday. During this period however she could not listen to two of her purchased CD’s but she could listen to each of remaining eight CD’s for exactly three days. The number of her favorite bands that she could listen to on each day starting from Monday to Saturday in that order was 18,12, 23, 19, 32 and 25.

*Q. Which of the following CD did Sophia not listen to on two consecutive days of the said week?
Note: On Saturday, Sophia did not listen to CD10 but had listened to CD3.*

Solution:

From the solution to the first question of the set, Tuesday: CD1, CD2, CD3 and CD6 Friday: CD6, CD7, CD9 and CD10 Given that Sophia did not listen to CD10 on Saturday, the only way in which she could have listened to 25 of her favorite bands would be the combination of CD3, CD6, CD7 and CD9.

Hence this implies that she could have listened to CD5 on the remaining days, i.e. on Monday, Wednesday and Thursday The table below gives the possible combination of various days of the week.

Thus, she did not listen to CD3 on two consecutive days. Hence, option 3.

QUESTION: 54

Sophia, a music maniac on Sunday recently purchased a set of 10 audio CD’s of her favorite English bands labeled from CD1 to CD10. Back home however to her surprise she found that CD1 had exactly one of her favorite bands, whereas CD2 had exactly two, CD3 had exactly 3 and so on till CD10 which had 10 of her favorite bands. Starting from Monday right up to Saturday she listened to exactly four CD’s everyday. During this period however she could not listen to two of her purchased CD’s but she could listen to each of remaining eight CD’s for exactly three days. The number of her favorite bands that she could listen to on each day starting from Monday to Saturday in that order was 18,12, 23, 19, 32 and 25.

*Q. Which of the following CD did Sophia not listen to for three consecutive days of the said week?
Note: On Saturday, Sophia did not listen to CD10 but had listened to CD3.*

Solution:

Sophia listens either CD1 or CD2 on three consecutive days. Hence, option 4.

QUESTION: 55

Group Question

Answer the following question based on the information given below.

Each of the five friends: Annie, Brenda, Cindy, Dane and Emily had written exactly one of the tests from GMAT, CAT, XAT, SNAP and JMET, not necessarily in that order. The percentage scores obtained by them in the tests were 50, 45, 40, 35 and 30, not necessarily in that order.

Further, it is known that:

1. Cindy did not write SNAP.

2. Brenda did not write JMET.

3. The percentage score in SNAP was more by 5 points than the test which Emily had written.

4. The percentage score that Annie obtained was more by 10 points when compared to the score in CAT. 5. The percentage score in GMAT was more than the percentage score in the test written by Cindy by 5 points.

6. The percentage score in the test written by Dane was more than the percentage score obtained in XAT by 10 points.

*Q. If Annie had written GMAT, then what was the percentage score obtained in JMET?*

Solution:

Tabulating the given information we have:

From (3), SNAP - Emily = 5

From (4), Annie - CAT = 10

From (5), GMAT - Cindy = 5

From (6), Dane - XAT = 10

Now, we consider that Annie had written GMAT.

By 4, we know that percentage obtained by Annie in the test that she wrote is 10% points more compared to that obtained in CAT.

So, her score could be any of 50%, 45% or 40%.

Case 1: Annie scored 50% in GMAT Then, the percentage obtained in CAT will be 40%. Also, the percentage obtained by Cindy will be 45%.

Now, by 6, the marks scored by Dane is more than that in XAT by 10% points. So, the marks in XAT could be 30%, 35% or 40%. But marks scored in CAT is already 40%, so that in XAT could be either 30% or 35%. If marks scored in XAT is 35%, then marks scored by Dane would be 45%, which is ruled out since Cindy had scored 45% marks. So, the score in XAT would be 30% and that scored by Dane, would thus be 40%. Marks scored in SNAP could be one of 35% or 45%.

Cindy scored 45% and she did not write SNAP. So, marks scored in SNAP cannot be 45%.

So, the marks scored in SNAP will be 35%, and hence that in JMET will be 45%.

Case 2: Annie scored 45% in GMAT Then Cindy would have scored 40% marks and the marks scored in CAT would be 35%.

Marks scored in XAT could be one of 30% or 40%. If the marks scored in XAT is 30%, then Dane would have scored 40% marks.

But, this is ruled out since Cindy has scored 40% marks.

So, the marks scored in XAT has to be 40%. Then, Dane would have scored 50%. Now, Emily could have scored one of 35% or 30%. If Emily scores 35% marks, then marks scored in SNAP has to be 40%, which is ruled out since marks scored in XAT is 40%.

If Emily scores 30% marks, then marks scored in SNAP has to be 35%, which is again ruled out since marks scored in CAT is 35%.

So, it can be concluded that if Annie had written GMAT, then her score could not have been 45%.

Case 3: Annie scored 40% marks in GMAT Then Cindy would have scored 35% marks and the marks scored in CAT would have been 30%.

Marks scored in XAT would have to be 35%. Then, Dane would have scored 45% marks.

Now, Emily could have scored either 50% or 30%.

If Emily scores 50% marks, then score in SNAP has to be 55% which is ruled out.

If Emily scores 30% marks, then score in SNAP has to be 35%, which is again ruled out since score in XAT is 35%.

So, it can be concluded that if Annie had written GMAT, then her score could not have been 40%.

Thus, Annie could have scored only 50% marks in GMAT. The corresponding score in JMET is 45%.

Answer: 45

QUESTION: 56

Each of the five friends: Annie, Brenda, Cindy, Dane and Emily had written exactly one of the tests from GMAT, CAT, XAT, SNAP and JMET, not necessarily in that order. The percentage scores obtained by them in the tests were 50, 45, 40, 35 and 30, not necessarily in that order.

Further, it is known that:

1. Cindy did not write SNAP.

2. Brenda did not write JMET.

3. The percentage score in SNAP was more by 5 points than the test which Emily had written.

4. The percentage score that Annie obtained was more by 10 points when compared to the score in CAT. 5. The percentage score in GMAT was more than the percentage score in the test written by Cindy by 5 points.

6. The percentage score in the test written by Dane was more than the percentage score obtained in XAT by 10 points.

*Q. What was the score (in percentage) of Emily? (Assume the data from the previous question.)*

Solution:

As seen eariler, there is only one acceptable case, which can be summarized as follows: Annie - GMAT - 50 Brenda - SNAP - 35 Cindi - JMET - 45 Dane - CAT - 40 Emily - XAT - 30 Thus, Emily wrote XAT and she scored 30%.

Answer: 30

QUESTION: 57

Each of the five friends: Annie, Brenda, Cindy, Dane and Emily had written exactly one of the tests from GMAT, CAT, XAT, SNAP and JMET, not necessarily in that order. The percentage scores obtained by them in the tests were 50, 45, 40, 35 and 30, not necessarily in that order.

Further, it is known that:

1. Cindy did not write SNAP.

2. Brenda did not write JMET.

3. The percentage score in SNAP was more by 5 points than the test which Emily had written.

4. The percentage score that Annie obtained was more by 10 points when compared to the score in CAT. 5. The percentage score in GMAT was more than the percentage score in the test written by Cindy by 5 points.

6. The percentage score in the test written by Dane was more than the percentage score obtained in XAT by 10 points.

*Q. What percentage of marks did Brenda score in the test she had written? (Assume data from the previous question.)*

Solution:

As seen earlier, Brenda scored 35% in SNAP. Answer: 35

QUESTION: 58

Each of the five friends: Annie, Brenda, Cindy, Dane and Emily had written exactly one of the tests from GMAT, CAT, XAT, SNAP and JMET, not necessarily in that order. The percentage scores obtained by them in the tests were 50, 45, 40, 35 and 30, not necessarily in that order.

Further, it is known that:

2. Brenda did not write JMET.

3. The percentage score in SNAP was more by 5 points than the test which Emily had written.

4. The percentage score that Annie obtained was more by 10 points when compared to the score in CAT. 5. The percentage score in GMAT was more than the percentage score in the test written by Cindy by 5 points.

6. The percentage score in the test written by Dane was more than the percentage score obtained in XAT by 10 points.

*Q. At most how many of the following statements can be true?
1. Annie had written SNAP and had scored 50% marks.
2. Annie had written SNAP and had scored 45% marks.
3. If Annie had written SNAP, then Dane had written CAT.
4. If Annie had written SNAP, then Brenda had scored 30% marks in the test she had written.
5. If Annie had written SNAP, then Cindy had written JMET.*

Solution:

If Annie had written SNAP, then her score would be one among from 50, 45, and 40.

Case 1: If Annie had scored 50%.

Then score of Emily would have been 45%.

And Dane would have scored 40%. So, score in XAT would be 30%.

If Annie had scored 50%, score in CAT would be 40%

Thus, Annie - SNAP - 50% Dane - CAT - 40% Emily - 45% Now GMAT - Cindy = 5 If Emily had written GMAT, score of Cindy would be 40%, which is not true.

Hence, score in GMAT would be 35% and hence, Cindy would have scored 30% and would have written XAT.

As Brenda did not write JMET, Emily would have written JMET.

Emily - JMET - 45% Brenda - GMAT - 35% Cindy - XAT - 30% Thus, statements 1 and 3 are true.

Case 2: If Annie had scored 45%.

Then score of Emily would have been 40%, score of Dane would be 50%, score in CAT would be 35%.

Again Emily would have scored 40% in XAT.

So, score in GMAT has to be 50%. But then Cindy should have scored 45% which is not possible.

Thus, statement 2 cannot be true.

Case 3: If Annie had scored 40%.

Then score of Emily would have been 35% and score in CAT has to be 30%.

Dane could have obtained one among from 50% or 45%.

If Dane obtains 50%, then score in XAT has to be 40% which has to be ruled out since Annie had obtained 40% in SNAP. This implies that Dane had obtained 45% then score in XAT would be 35%. Then Cindy would have obtained 30%. But then score in GMAT would be 35% which is not true.

Hence it can be concluded that score of Annie could not have been 40%.

Hence for all the possible SNAP and Annie’s scores, only case 1 is possible.

So, at most, two statements are true.

Answer: 2

QUESTION: 59

Group Question

Answer the following question based on the information given below.

12 teams have a photo shoot lined up for the entire next week, which has 6 working days, Sunday being a holiday. On each day, exactly two teams have to be scheduled for the photo shoot. The teams are represented by alternate letters of the English alphabet starting from A such that the 12th team is W. The photographer has found out certain things about these teams and has to prepare a schedule accordingly.

1. The photo of team A has to be taken before team S.

2. Photos of teams O and E have to be clicked on the same day; and this day should be before Wednesday.

3. The only teams available for a photo session on Thursday are C, I and K.

4. The photo of team G has to be clicked exactly 2 days after the photo of team M is clicked, i.e. if the photo of team M is clicked on Monday, then that of team G has to be clicked on Wednesday.

5. Team W always wants their photo to be clicked on Friday.

6. Team Q and U should have their photos clicked on consecutive days.

The order of teams on a particular day is not important.

*Q. If Team M wants to click their photo on Monday, in how many ways can the photo shoot be completed?*

Solution:

If Team M clicks their photo on Monday, Team G would click their photo on Wednesday.

Team O and Team E have to click their photos on Tuesday as they have to do so before Wednesday.

Team W wants their photo to be clicked on Friday.

Now, there are only 3 teams available on Thursday thus they have to be clicked on Thursday.

Now, Tuesday and Thursday are booked because of above reasons thus Q and U have to be clicked on Friday or Saturday which can be done in 2 ways.

Out of C, I and K two teams can be chosen in 3 ways.

If A is clicked on Monday S can be clicked on Wednesday and Saturday thus 2 ways. If A is clicked on Wednesday, then S can be clicked on Saturday which is only 1 way. Thus, total ways = 2 x 3 * ( 2 + 1 )= 1 8 ways.

Hence, option 4.

QUESTION: 60

12 teams have a photo shoot lined up for the entire next week, which has 6 working days, Sunday being a holiday. On each day, exactly two teams have to be scheduled for the photo shoot. The teams are represented by alternate letters of the English alphabet starting from A such that the 12th team is W. The photographer has found out certain things about these teams and has to prepare a schedule accordingly.

1. The photo of team A has to be taken before team S.

2. Photos of teams O and E have to be clicked on the same day; and this day should be before Wednesday.

3. The only teams available for a photo session on Thursday are C, I and K.

4. The photo of team G has to be clicked exactly 2 days after the photo of team M is clicked, i.e. if the photo of team M is clicked on Monday, then that of team G has to be clicked on Wednesday.

5. Team W always wants their photo to be clicked on Friday.

6. Team Q and U should have their photos clicked on consecutive days.

*Q. If team Q is scheduled for Wednesday, then in how many different ways can the schedule for entire week be made?*

Solution:

Q and U have to be scheduled on consecutive days. Thus, if Q is scheduled on a Wednesday, U has to be scheduled on either Tuesday or Thursday.

However, only C, I or K can be scheduled on Thursday.

Therefore, U has to be scheduled on Tuesday.

Since the photo shoot of both O and E has to happen on the same day and before Wednesday, it can now only be held on Monday.

M and G are shot on alternate days, with M being shot earlier. The only combination of alternate days available is Wednesday and Friday.

Therefore, M and G have to be scheduled on Wednesday and Friday respectively.

Now, the only days left for A and S are Tuesday and Saturday. Since A has to be scheduled before S, A and S are scheduled on Tuesday and Saturday respectively.

The only teams left now are C, I and K with the extra slot being available on Saturday. This arrangement can be done in three different ways as given below:

1) Thursday - C, I and Saturday - K

2) Thursday - C, K and Saturday - 1

3) Thursday - 1, K and Saturday - C Thus, if team Q is scheduled for Wednesday, three different schedules can be made for the entire week. Hence, option 3.

QUESTION: 61

12 teams have a photo shoot lined up for the entire next week, which has 6 working days, Sunday being a holiday. On each day, exactly two teams have to be scheduled for the photo shoot. The teams are represented by alternate letters of the English alphabet starting from A such that the 12th team is W. The photographer has found out certain things about these teams and has to prepare a schedule accordingly.

1. The photo of team A has to be taken before team S.

2. Photos of teams O and E have to be clicked on the same day; and this day should be before Wednesday.

3. The only teams available for a photo session on Thursday are C, I and K.

4. The photo of team G has to be clicked exactly 2 days after the photo of team M is clicked, i.e. if the photo of team M is clicked on Monday, then that of team G has to be clicked on Wednesday.

5. Team W always wants their photo to be clicked on Friday.

6. Team Q and U should have their photos clicked on consecutive days.

*Q. Which among the following teams cannot be scheduled for Tuesday?*

Solution:

Teams O and E have to be scheduled on the same day and before Wednesday.

Thus, teams O and E have to be scheduled for either Monday or Tuesday.

C, I and K are the only teams that can be scheduled on a Thursday. If one of these teams is scheduled on some other day, the other two teams automatically get scheduled on Thursday.

Among these three, only C is one of the options.

Therefore, we start by checking if C can be scheduled for Tuesday.

If team C is scheduled for Tuesday, then I and K have to be scheduled for Thursday.

Also, O and E have to be mandatorily scheduled on Monday.

Also, W has to be scheduled on Friday.

Thus, there are no slots available on Monday and Thursday, there is a solitary slot available on Tuesday and Friday each and both slots on Wednesday and Saturday are available at this point.

Since G is scheduled exactly 2 days after M, they have to be on alternate days.

For this to happen, M has to be scheduled for Wednesday and G has to be scheduled for Friday.

Q and U are to be scheduled on consecutive days.

The only pair of slots now available on consecutive days is on Tuesday and Wednesday. Thus, Q and U are scheduled for Tuesday and Wednesday in any order.

Therefore, A and S have to be scheduled on the same day i.e. on Saturday.

However, the photo of team A has to be taken before the photo of team S. Therefore, A and S cannot be scheduled for the same day.

Thus, scheduling C on Tuesday does not lead to a valid schedule.

Thus, C cannot be scheduled for Tuesday.

All the other teams given in the options can be scheduled for Tuesday without violating any conditions. Hence, option 2.

QUESTION: 62

1. The photo of team A has to be taken before team S.

2. Photos of teams O and E have to be clicked on the same day; and this day should be before Wednesday.

3. The only teams available for a photo session on Thursday are C, I and K.

4. The photo of team G has to be clicked exactly 2 days after the photo of team M is clicked, i.e. if the photo of team M is clicked on Monday, then that of team G has to be clicked on Wednesday.

5. Team W always wants their photo to be clicked on Friday.

6. Team Q and U should have their photos clicked on consecutive days.

*Q. If photo of team E is scheduled on Monday, on which day is photo of team G scheduled?*

Solution:

Photos of teams O and E are scheduled on Monday.

Photos of two teams among C, I, K are scheduled on Thursday.

So, from 4, photo of team M has to be clicked on Wednesday and that of team G on Friday. Hence, option 3.

QUESTION: 63

Group Question

Answer the following question based on the information given below.

Ten friends ranked 10 Indian newspapers from 1 to 10. It turned out that all of them gave a different rank to different newspapers and each newspaper was given a different rank by different friends.

Some data has been deliberately kept missing from the table.

*Q. What is the rank that Aarif gave to Hindustan Times?*

Solution:

The missing ranks for TOI are: 3, 6 and 9 The missing ranks for Hindustan Times are: 1 and 8

The missing rank for Indian Express is: 8 The missing rank for New Indian Express is: 10

The missing rank for Deccan Herald is: 10 The missing rank for Deccan Chronicle is: 7

The missing rank by Rahul is: 3

The missing ranks by Aarif are: 1,9 and 10 The missing ranks by Amardeep are: 8 and 10

The missing rank by Mkhaya is: 8

The missing ranks by Viru are: 6 and 7 Thus, we can obtain detailed rank allocation as follows:

Thus, the rank given by Aarif to Hindustan Times is 1. Hence, option 4.

QUESTION: 64

Ten friends ranked 10 Indian newspapers from 1 to 10. It turned out that all of them gave a different rank to different newspapers and each newspaper was given a different rank by different friends.

Some data has been deliberately kept missing from the table.

*Q. What is the dissimilarity magnitude between Taaz and Dale if it is calculated as sum of absolute differences of the ranks allocated by them to different subjects?*

Solution:

The subject wise sum of absolute differences is |1 - 8| + |10 - 1| + |9 - 7| + |8 - 10| + |4 - 3| + |2 - 6| + |3 - 5| + |5 - 4| + |6 - 2| + |7 - 9| = 34

Hence, option 4.

QUESTION: 65

Ten friends ranked 10 Indian newspapers from 1 to 10. It turned out that all of them gave a different rank to different newspapers and each newspaper was given a different rank by different friends.

Some data has been deliberately kept missing from the table.

*Q. What is the dissimilarity magnitude between Aarif and Viru if it is calculated as sum of absolute differences of the ranks allocated by them to different subjects?*

Solution:

The subject wise sum of absolute differences is |6 - 9| + |9 - 6| + |1 - 10| + |2 - 3| + |7 - 2| + |10 - 5| + |4 - 11 + |3 - 7| + |5 - 8| + |8 - 4| = 40

Hence, option 3.

QUESTION: 66

Ten friends ranked 10 Indian newspapers from 1 to 10. It turned out that all of them gave a different rank to different newspapers and each newspaper was given a different rank by different friends.

Some data has been deliberately kept missing from the table.

*Q. What is the sum of all the ranks assigned to all the papers?*

Solution:

Each of the ten friends given ranks 1 to 10 to the newspapers.

Required sum = 10(1 + 2 + 3 + ... + 10) = 10 * 55 = 550. Hence, option 3.

QUESTION: 67

Let 4, 5, 6 and 6 be the lengths of consecutive sides of a quadrilateral. Let x be its area. Which of the following options is correct?

Solution:

Let ABCD be the quadrilateral where the AB = 4, BC = 5, CD = 6 and DA = 6.

2x = Area ΔABC + Area ΔBCD + Area ΔCDA + Area ΔDAB {(4 x 5)/2} + {(5 x 6)/2} + {(6 x 6)/2} + {(4 x 6)/2} Hence x 27.5

Hence, option 4.

QUESTION: 68

f(x) is defined as f(x) = f(x + 1) - x for x > 0 and f(1) = 7 then which of the following must be true?

Solution:

f(x) = f (x + 1) - x

f(x+ 1) = f(x) + x and f(1) = 7

f(2) = f(1) + 1 = 7 + 1 = 8

f(3) = f(2) + 2 = 8 + 2 = 10

f(4) = f(3) + 3 = 10 + 3 = 13

f(5) = f(4) + 4 = 13 + 4 = 17

f(6) = f(5) + 5 = 17 + 5 = 22

f(7) = f(6) + 6 = 22 + 6 = 28

As it can be seen that the corresponding values of function will be even for 2 consecutive values for x greater than 1 and then odd for next 2 consecutive values and this pattern is repeated.

f(1) + f(2) + f(3) + ... + f(n) will always be even for n where n is multiple of 4.

f(1) + f(2) + f(3) + ... + f(8n) will be even for any value of n.

And also as the even and odd parity changes after 2 values of x.

So f( 1) + f(2) + f(3) + ... + f(n) will always be odd for odd values of n.

Hence, option 2 and 3 both are correct.

Hence, option 4.

QUESTION: 69

A hollow sphere of radius 5 cm is placed over the hollow cylinder of radius 5 cm and of height 10 cm. Sphere has a small entering point at the top from which water enters the sphere at rate of 3.64 cm^{3}/sec. Sphere also has a leak at the bottom through which the water enters the cylinder at rate of 0.5 cm^{3}/sec into the cylinder. How much time will be required so that the water level in the cylinder just touches the bottom part of the sphere, after the sphere is filled?( Assume the thickness to be negligible and base of the cylinder is enclosed and the top base is open over which the sphere is kept. Also assume that the water which overflows from the sphere doesn’t enter the cylinder.)

Solution:

So by this time 83.335 cm^{3} leaks into the cylinder.

Also half of the sphere is inside the cylinder so the actual height at which the water level in the cylinder just touches the sphere is 5 cm and not 10 cm.

So the volume of water actually required is 125πcm^{3} = 392.5 cm^{3}

The amount of water required = 392.5 - 83.335 = 309.165 cm^{3}

Hence, option 2.

QUESTION: 70

The cost of Toy A is twice that of Toy B which, in turn, is twice that of Toy C. However 2 of the 3 toys are sold at a profit of x% each and the third is sold at a loss of x%. The net profit/loss is 60% of the cost price of Toy C. Which of the following can be the value of x?

Solution:

Let the CP of Toy C be 100 .

CP of Toy B = 200 and CP of Toy A = 400 Substituting the values present in the options in place of x, the following values of individual profits/losses are obtained.

The required net profit/loss is 60% of C’s CP, Hence, the sum of individual profits/losses of A, B, C must be ±60 (because there can be a net profit or net loss).

When x = 25 or x = 15, it is not possible to get the sum as ±60 as there will be a ‘5’ in the unit’s place. Hence, options 2 and 4 are eliminated.

When x = 20, 80 - 40 + 20 = 60

When x = 30, 120, 60, 30 cannot be expressed in the form (l + m - n) to get ±60 Hence, option 3.

Alternatively, Let the CPs of Toy A, B, C be 400, 200 and 100 respectively.

Similarly, profit (or loss) on toy B and C is 2x and x respectively.

Depending on which product is sold at a loss, the total profit (or loss) can take 3 values: 4x + 2x - x i. e . 5x

4x + x - 2x i.e. 3x

2x + x - 4x i.e. - x (loss of x)

Now, total profit or loss is 60% of the cost price of C i.e. 60. x = 60/5 = 12% or x = 60/3 = 20% or x = 60%

Only 20% is given in the options. Hence, option 3.

QUESTION: 71

In 2000, manufacturing cost of an item was Rs. 428. It increased by 5%, 6%, 4% in the successive years and decreased by 7% in the fourth year. The same item was manufactured in 2004 and sold at Rs. 598. What was the profit (in Rs.) earned? (Assume that “manufacturing cost” is the only cost involved.) (Round off your answer to the nearest integer.)

Solution:

Effective percentage change = 1.05 * 1.06 * 1.04 * 0.93 = 1.076

Manufacturing cost in 2004 = 1.076 * 428 = 461 Profit = 598-461 = 137

Answer: 137

QUESTION: 72

A poll was taken in a class to decide the place for their picnic. Number of votes for Shimla exceeded by 50% than that of for Munnar. On the next day, 10 of the absent students voted for Munnar due to which the majority was for Munnar by 2 votes. How many students were there in the class initially?

Solution:

Let number of votes for Shimla be x and Number of votes for Munnar be y. As number of votes for Shimla exceeded by 50% than that of for Munnar, x = 1.5 y . ..... (i)

Now, y + 10 = x + 2 ...... (ii) From (i) and (ii) y = 16 x = 24

Therefore, total number of students = 16 + 24 = 40

Answer: 40

QUESTION: 73

Consider the arrangement given in the following diagram:

Two mini robots A and B are placed at the two ends of a plank of negligible width such that they can move with a constant speed of 0.8 m/s both towards and away from each other. Initially, both are charged to energy of 3J. Three charging stations are placed at equal distances from each other. On reaching a charging station, the robots gain 1J of energy only if their energy is more than 0.1 J. Also, on movement, they lose 0.5J per metre. In case of collision, robots lose 1J of energy. Cushions are placed at both ends of the plank such that they merely change the direction of movement but robots do not gain or lose any energy.

What is the total distance covered by both the robots together before they came to rest if B started 2.5 seconds after A?

Solution:

Since A started before B, it covered some distance before B started moving towards it.

Distance covered by A before B started = 2.5 * 0.8 = 2 m Now, as both A and B move with equal speed towards each other, both will cover equal distance.

Thus, we know that they meet at a distance of 3m from B.

Energy level of A immediately after collision = 3 - (0.5 * 2) + 1 - (0.5 x 2) + 1 - 0.5 - 1(on collision) = 1.5 J

Energy level of B immediately after collision = 3 - (0.5 x 2) + 1 - 0.5 - 1 = 1.5 J On collision, both start moving in the opposite directions.

We can observe that both A and B come to rest before the second collision.

Distance travelled by A before coming to rest = 5 + 5 + 2 = 12m

Distance travelled by B before coming to rest = 3 + 3 + 2 = 8m Combined distance travelled by both = 12 + 8 = 20 m Hence, option 2.

QUESTION: 74

There are three milk-water solutions - A, B, C - of equal volume. The concentration of milk in A is twice that in B and thrice that in C. Six different mixtures - I, II, III, IV, V and VI - are formed by mixing different combination of volumes of A, B and C. In any mixture, the ratio (by volume) of the three milk-water solutions is 2 : 3 : 4 (in any order). What is the ratio of milk in the mixture with highest concentration of milk to milk in the mixture with lowest concentration of milk?

Solution:

Let the concentration of milk in A, B and C be 6x, 3x and 2x respectively.

Since A, B and C are mixed in the ratio 2 : 3 : 4 (in any order), there are 6 possible combinations for A : B : C.

1) 2 : 3 : 4 => Milk = (2 x 6x) + (3 x 3x) + (4 * 2x) = 29x

Similarly,

2) 3 : 2 : 4 => Milk = 32x

3) 2 : 4 : 3 => Milk = 30x

4) 3 : 4 : 2 => Milk = 34x

5) 4 : 3 : 2 => Milk = 37x

6) 4 : 2 : 3 => Milk = 36x Required ratio = 37 : 29 Hence, option 4.

QUESTION: 75

33 kg of rice costing 24.5 per kg is mixed with 55 kg of rice at 40.5 per kg. Find average cost (in Rs.) per kg of the resultant mixture. (Round off your answer upto one decimal place, if required.)

Solution:

Let x is the average cost of the resultant mixture.

QUESTION: 76

Saw powder has two components M and N. The proportion of M, by weight, must be maintained at 50% to 60% of the mixture. 240 kg of N is available. The density of M is 10 gm/cc and the density of N is 5 gm/cc. The greatest possible weight of M is taken so that the mixture can be used. What is the capacity (in litres) of the container which can store saw powder of the specification mentioned. Assume that the container is filled up to its maximum capacity.

Solution:

The greatest proportion of M is taken to make the mixture usable, i.e., 60%. 40% of the mixture = N = 240 kg

60% of the mixture = M = 360 kg 5 gm of N occupies 1 cc while 10 gm of M occupies 1 cc.

Total volume occupied by M and N = (360000/10) + (240000/5) = 84000 cc = 84 litres

Answer: 84

QUESTION: 77

Speed varies with time taken as well as distance covered. However, whether the variation is direct or inverse is not known. All the three parameters are raised to the same power. In one case, time taken increase by 50% and distance increases by 20%. Which of following statements can be true?

i. Speed increases by 80%

ii. Speed decreases by 20%

iii. Speed neither increases nor decreases

iv. Speed increases by 25%

Solution:

Let original time taken and distance covered be t and d respectively.

New Time = 1.51

New Distance = 1.2d

New speed (S) can vary in the following ways,

Thus, statements i, ii and iv can be true. Hence, option 3.

QUESTION: 78

Ram, a farmer has to distribute up to Rs. 99,820 among his three sons Rajesh, Suresh and Mahesh in such a manner that for every 13 rupees that Rajesh gets, Suresh should get 15 rupees and Mahesh should get 18 rupees. What is the maximum share of Mahesh?

Solution:

Rajesh, Suresh and Mahesh get the amount in the ratio 13 : 15 : 18.

So 46x = 99820 =>x = 2170

Maximum share of Mahesh = 18 * 2170 = Rs. 39,060 Hence, option 3.

QUESTION: 79

Only Amarchand, Bebidevi and Chatursen contested Rampur’s Zilla Parishad elections. Amarchand got 50% more votes than Bebidevi and 9000 more votes than Chatursen. Bebidevi’s margin in beating Chatursen was 5 percentage points of the total votes cast. If only 83.33% of the eligible voters voted in the election, find the number of eligible voters in Rampur. Assume that each voter voted for exactly one of the three candidates.

Solution:

Denote the three people by their initials.

If B got x votes, A and C got 1.5x and (1.5x - 9000) votes respectively. Each voter voted for exactly one candidate.

So Total number of people who voted = x + 1.5x + 1.5x - 9000 = 4x - 9000

B got 5 percentage point votes more than C.

Total number of people who voted = 4x - 9000 = 45000

QUESTION: 80

Ten years ago, the average age of a family of 7 members was 37 years. One member died 6 years ago at the age of 65. Due to a wedding 2 years ago, a new member was added into the family. The average age of the family today is 42 years. Find the present age of the new member.

Solution:

10 Years ago: Total age of 7 members = 37 * 7 = 259

Total age of 6 members = 259 - 61 = 198 (since the member who died was 61 then).

Now: Total age of 6 members = 198 + 10 * 6 = 258

Total age of 7 members = 42 * 7 = 294 (current average age = 42 given in the question).

Current age of new member = 36

Note: Our calculations are simplified since we took 10 years ago as a base, and proceeded directly to the current time. The question provides us the average ages for precisely these times. The new member joining two years ago is not used while solving (it is actually extra information in the question).

QUESTION: 81

A cube of maximum volume is cut out from a cone having height 6 units and circumference of base as units. What percentage of volume of cone is left out?

Solution:

Let ‘a’ be the side of the cube.

Note: ED is the diagonal of the top surface of the cube and BC is the diameter of the cone.

QUESTION: 82

A supply package is to be dropped from a Boeing 747 cargo plane to a relief service camp in Afghanistan. The plane's altitude is fixed at 1000 ft, and its horizontal speed is fixed at 235 ft/s. The present angle of depression to the target is 30°. The plane needs to drop the supplies with a certain horizontal speed, when it is at a horizontal distance of 500 ft from the target. How long should the pilot wait before dropping the supply package?

Solution:

Please refer to the figure. A and D represent the current position of the plane and the service camp respectively.

As shown in figure, the plane will drop the supply package at point E, after covering a horizontal distance of AE = x.

Now the time required to cover this distance of x = AE = CB = 1230 ft with a speed of 235 ft/s will be = 1230/235 * 5.2 sec. Hence, option 2.

QUESTION: 83

Solution:

QUESTION: 84

There are three friends namely A, B and C and they always work in pair. They replace one by another to finish the work. They work out in following three ways.

1. Two days after A and B started working, A was replaced by C.

2. Four days after B and C started working, B was replaced by A.

3. C and A started working and from the second day, C was replaced by B.

They complete the work in exactly five days whichever way they follow. Find the number of days required for A, B and C respectively to complete the work alone.

Solution:

Let the workdone by A, B, C be a, b and c units.

Let the total work is W units.

Way 1: W = (2a + 2b) + (3c + 3b) = 2a + 5b + 3c ... (i)

Way 2: W = (4b + 4c) + (a + c) = a + 4b + 5c ... (ii)

Way 3: W = (a + c) + (4a + 4b) = 5a + 4b + c ... (iii)

From (ii) and (iii), a = c

From (i) and (ii), a + b = 2c

Substituting a = c, we get b = c Thus, a = b = c And W = 10a

Thus, each of the three working alone will require 10 days to complete the work.

Hence, option 3.

QUESTION: 85

Solution:

Assuming (pq + pr+ qr 0), by property of equal ratios,

QUESTION: 86

In a class, the teacher decides to tinker with the seating arrangement. First he asks 8 students to sit per bench, and then the last bench in the arrangement has only 3 students. Then he asks 9 students to sit per bench, and then the last bench in the arrangement has only 4 students. If m is the minimum number of students his class can have then what is the sum of digits of m?

Solution:

There are 3 students on the final bench, when 8 students sit per bench.

m = 8x+ 3 ...(i)

There are 4 students on the final bench, when 9 students sit per bench.

m = 9y + 4 ...(ii)

[9 x (i) - 8 x (ii)] gives,

m = 72(x - y) - 5 a m is an integer of the form 72k - 5.

The minimum number of students is 72 x 1 - 5 = 67

Sum of digits of m is 6 + 7 = 13

Answer: 13

QUESTION: 87

For which values of m is the difference between the roots of x^{2} - mx + m = 0 positive?

Solution:

Let p and q be the roots of x^{2} - mx + m = 0 The roots of the equation are given by

QUESTION: 88

Five students of a class appear for a scholarship test. When the results came out, the following things were observed: The average score of Aman is equal to the average score of Baman, Chaman and Daman. The average score of Baman is equal to the average score of Chaman, Daman and Aman. The average score of Chaman and Daman is 40. Find average score of Aman and Baman.

Solution:

Let the score of each student be denoted by their initials. By the given conditions,

Using equation (iii) in equations (i) and (ii) we get, 3A = B + 80

3B = A + 80

Adding the above 2 equations, we get, 3A + 3B = A + B + 160

2A + 2B = 160

(A + B)/2 = 40

Answer: 40

QUESTION: 89

A trader comes as a guest lecturer for a Mathematics class and gives a certain problem in class which says the difference between the compound interest (with annual compounding) and the simple interest earned in two years on a certain sum at the rate of 18% p.a. is Rs. 972. What will the same sum amount to (in Rs.) after three years at the rate of 18% p.a. when the interest is compounded annually? (Round off your answer upto two decimal places.)

Solution:

The difference between simple and compound interest at the end of 2 years is given by

QUESTION: 90

What is the sum of all positive integers upto 990, which are divisible by 7 and not by 2?

Solution:

The positive integers divisible by 7 are 7, 14, 21,28, ... Among these, 14, 28, 42 ... are also divisible by 2.

The series of integers whose sum we want is: 7, 21, 35, ...

This is an arithmetic progression with the first term = 7 and the common difference = 14.

The last term in this progression is 987, which is 141 x 7. The nth term in an arithmetic progression is given by a_{n} = a_{1} + (n - 1 )d

987 = 7 + (n - 1 )14

994 = 14n

n = 71

= 35.5 x 994 = 35287

Hence, option 3.

Alternatively, The required sum should also be divisible by 7.

Options 2 and 4 are eliminated. 990/7 = 141.43

141 positive integers upto 990 are divisible by 7.

Of these, 71 are odd and 70 are even.

Sum of these 71 odd numbers is asked. This sum should also be odd.

So, option 1 can also be eliminated.

Hence option 3.

QUESTION: 91

f_{1}(n) = n^{3} - 4n

f_{2}(n) = n^{2} + 2n

Let S_{1} be a set of numbers, from 1 to 100, for which f_{1}(n) is divisible by 24, and S_{2} be a set of numbers, from 1 to 100, for which f_{2}(n) is divisible by 24.

How many elements does S_{1} S_{2} contain?

Solution:

f_{1}(n) = (n^{3} - 4n) = n(n^{2} - 4) = n(n - 2)(n + 2) Hence, f_{1}(n) is the product of three consecutive odd numbers or the product of three consecutive even numbers.

If n is odd, then f_{1}(n) is the product of three consecutive odd numbers.

Now, the product of three consecutive odd numbers is never divisible by 24.

If n is even, then f_{1}(n) is the product of three consecutive even numbers.

Now, the product of three consecutive even numbers is always divisible by 24.

Hence for every even n, f_{1}(n) is divisible by 24.

Hence S_{1} contains all the even numbers from 1 to 100.

Now, consider f_{2}(n) = n^{2} + 2n = n(n + 2) If n is odd, then n(n + 2) will be odd.

Hence, n(n + 2) cannot be divisible by 24.

Hence, n must be even.

Let n = 2k ...(where k is some integer) Hence, f_{2}(n) = 2k(2k + 2) = 4k(k + 1) Now, k(k + 1) is divisible by 2 for any value of k.

Hence if either of k or k + 1 is divisible by 3 then 4k(k + 1) will be divisible by 24.

Hence 4k(k + 1) will not be divisible by 24 if and only if k is of the form 3a + 1 Hence, except these numbers f_{2}(x) will be divisible by 24.

NOW, n 100

k 50

From 1 to 50, there are (49 - 1)/3 + 1 = 16 + 1 = 17 numbers of form 3a + 1 ... (49 is largest number of form 3a + 1) Hence, except these even numbers, for all the other even numbers, f_{2}(x) will be divisible by 24.

Hence, for 50 - 17 = 33 even numbers f_{2}(x) will be divisible by 24.

Now S_{1} contains all even numbers from 1 to 100 and S_{2} contains 33 even numbers from 1 to 100.

Hence S_{1 }_{ }S_{2} contains 33 elements.

Answer: 33

QUESTION: 92

There are two tanks, Tank A and Tank B. Tap 1 is used to fill Tank A and tap 2 (attached to Tank A) is used to fill Tank B. Tap 3 attached to Tank B supply the usable water. Tap 1 can fill the tank 1 in 4 hours, when other two taps are close. If tap 2 and tap 3 are open, then tap 1 can fill both tanks in 9 hours without spilling any water from any tank. Tank 2 is sufficient to provide water supply to a user for exactly 6 hours.

How many hours will be needed to fill Tank 1 and Tank 2 if only tap 3 is closed? (Assume that the inlet taps close as soon as the tank is full.)

Solution:

Let the volume of tank A, tank B be a, b respectively.

Let the rate of flow through tap 1, tap 2 and tap 3 in one hour be x, y and z units respectively.

Tap 1 fills tank A in 4 hours (when tap 2 and tap 3 are closed). => a = 4x ... (i)

Tank B is sufficient to provide water supply to a user for exactly 6 hours. => b = 6z ... (ii)

Tap 1 fills both the tanks in 9 hours (when tap 2 and tap 3 are open). => 9 (x - z) = a + b ... (iii)

Substituting value of a, b in (iii), 9x - 9z = 4x + 6z i.e. x = 3z

a = 4x= 12z

Volume of both tanks = a + b = 18z

Time require to fill both tanks (when tap 3 is closed) = (18z)/x = (18z)/3z = 6 hours

Answer: 6

QUESTION: 93

ABCFED is the map of a field such that ABCD and CDEF are two trapeziums with one of the parallel sides CD common between them. Also, DE = EG, EG || FC, AG and BH are perpendicular to CD, DG = 5 cm, BH = 12 cm, BC = 15 cm, EF = 19 cm and m ∠DEG = 60°. What is the length of the perimeter of the map?

Solution:

HC^{2} + BH^{2} = BC^{2}

So HC = 9 cm.

DE = EG = DG = 5 cm ...[since DE = EG and ∠DEG = 60° making ∠DEG equilateral]

FC = EG = 5 cm ...[EF || GC and EG || FC, making EFCG a parallelogram]

EF = GC = 19 cm GH = GC - HC = 19 - 9 = 10 cm

AB = GH = 10 cm ...[ABCD is a rectangle] AD^{2} = AG^{2} + DG^{2} ...[Using Pythagoras Theorem in right angled ΔAGD]

AD = 13 cm

Perimeter o f the map = (AB + BC + CF + FE + ED + DA) = 10 + 15 + 5 + 19 + 5 + 1 3 = 67 cm

Hence, option 1.

QUESTION: 94

An alloy P made up of metals A and B by mixing them in the ratio 3 : 5. Another alloy Q contains metals B and C in the ratio 3 :1 . Now, P and Q are mixed in a certain ratio such that the concentration of B in the mixture is 70%. Find the ratio in which P and Q were mixed.

Solution:

Let the weight of alloy P used in the mixture be 8X units such that it contains 3X units of A and 5X units of B in it. Also let the weight of alloy Q be 4Y units such that it contains 3Y units B and Y units of C .

Total B in the alloy = 5X + 3Y.

From the given conditions; 5X + 3Y = 0 .7 (8X + 4Y )

X: Y = 1 : 3

Now P : Q = 2X : Y = 2 : 3

Hence, option 3.

QUESTION: 95

Priya bought 15 shares of a company at Rs. 30 on Monday. After monitoring their price for the next 4 days, she sold all the shares on the fifth day i.e. on Friday. Whenever the price of a share dips on a particular day, she bought either 3 shares or 5 shares of the same company. There is at least one instance when she bought 3 shares and at least one instance when she bought 5 shares of the company. The maximum difference in the prices of the share on any two consecutive days is Rs. 5.

What can be the maximum profit (in Rs.) earned by Priya?

Solution:

To get maximum profit, Priya should have bought shares at minimum cost. Also, the cost price of 5 shares should be less than the cost price of 3 shares.

The only way this could happen is the price goes down for the first two days and rises for the next two days.

Let x and y be the consecutive decreases in the price.

i.e., 30, (30 - x) and (30 - x - y) are the prices on the first three days, where x, y [1,5].

In order to have maximum profit, the price on the last day should be maximum possible i.e., ( 30 - x - y ) + 5 + 5 = 40 - x - y Amount invested = 15 * 30 + 3 * (30 - x ) + 5 * ( 30 - x - y ) = 690 - 8x - 5y ... (i) Amount earned = (40 - x - y )* 23 = 920 - 23x - 23y ... (ii) Subtracting (i) from (ii), profit = 230 - 15x - 18y

In order to have maximum profit, values of x and y must be minimum possible i.e., 1.

Profit = Rs. 197

Hence, option 4.

QUESTION: 96

Solution A contains vegetable oil, alcohol and water in the ratio of 2 : 5 : 7 and solution B contains the same in the ratio of 3 : 5 : 6. A new solution is made by mixing the two solutions in a certain ratio. Which of the following is an obtainable ratio of vegetable oil, alcohol and water in the new solution?

Solution:

In both the solutions, the proportion of alcohol is the same. Hence, in any solutions made by using these two solutions, the proportion of alcohol should be the same. Out of the options, only option 3 satisfies the above condition.

Hence, option 3.

QUESTION: 97

A train running between Delhi and Agra passes 10 stations en-route. In how many ways can it stop at three of these ten stations such that no two of them are consecutive?

Solution:

If we remove the 3 stations at which the train will stop we will have 7 stations left.

There will be 6 gaps in between the 7 stations and 2 at the end, therefore, 8 places in which the 3 stations at which the trains stop can be arranged.

The three stations at which the train stops can be arranged in these 8 gaps in ^{8}C_{3} = 56 ways.

Answer: 56

QUESTION: 98

x^{2} + (a - 2)x - a + 2 = 0, where a is strictly a real number. The square of difference between the roots of this equation is minimized when a =

Solution:

x^{2} + (a - 2)x - a + 2 = 0

The minimum value of this expression is at a = 0 Hence, option 2.

QUESTION: 99

Solution:

Since, the LHS and RHS of the inequality are non-negative, let us square both the sides of the inequality.

Thus, x can take integer values from 4 to 101, which is a count of 98 values.

Answer: 98

QUESTION: 100

A and B start running in opposite directions from the same point along a circular track of circumference 600 m. They meet at Q for the first time and at P (which is 120 m away from Q) for the second time. B and C start running along the same track in opposite directions and meet at Q’ for the first time and at P’ (which is 150 m away from Q’) for the second time. If A and C run on the same track in opposite directions, find the number of distinct points at which they meet, excluding the starting point.(Speed of A < speed of B < speed of C)

Solution:

Since gap between first and second meeting point of A and B is 120 m; and A is slower than B,

Time in which A runs 120 m is the same as time in which B runs 600 - 120 = 480 m Ratio of speeds of A and B is 1 : 4.

Similarly, time in which B runs 150 m is the same as time in which C runs 600 - 150 = 450 m

Ratio of speeds of B and C is 1 : 3.

Now when A and C run in opposite directions, their speeds are in the ratio 1:12.

When two persons are running in opposite directions along a circular track with their ratio of speeds as 1 : n, they meet at (n + 1) different points along the path including the starting point.

So, A and C meet at 12 + 1 = 13 points along the track (including the starting point). Since the starting point is to be ignored, they meet at 12 distinct points.

Answer: 12

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