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CAT Mock Test- 9 (November 11) - CAT MCQ


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30 Questions MCQ Test - CAT Mock Test- 9 (November 11)

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CAT Mock Test- 9 (November 11) - Question 1

Read the passage carefully and answer the following questions:

The brave new economy being rebuilt in the wake of the financial meltdown is being built on low-wage service work, as manufacturing’s decline has accelerated and construction ground to a halt. At the beginning of the Great Recession, economist Heather Boushey noted at Slate, manufacturing and construction made up fully half the jobs lost, along with financial services and other business fields, and writers declared the “Mancession” or “He-cession” or even, as Hanna Rosin’s popular book has it, The End of Men. But as others have pointed out, as the recession drags on, it’s women who’ve faced the largest losses, not only in direct attacks on public sector jobs that are dominated by women, but in increased competition from the men pushed out of their previous professions. Some 60 percent of the jobs lost in the public sector were held by women, according to the Institute for Women’s Policy Research. And women have regained only 12 percent of the jobs lost during the recession, while men have regained 63 percent of the jobs they lost.

Women may be overrepresented in the growing sectors of the economy, but those sectors pay poverty wages. The public sector job cuts that have been largely responsible for unemployment remaining at or near 8 percent have fallen disproportionately on women (and women of color are hit the hardest). Those good union jobs disappear, and are replaced with a minimum-wage gig at Walmart—and even in retail, women make only 90 percent of what men make.

“All work is gendered. And the economy that we have assigns different levels of value based off of that,” says Ai-Jen Poo, executive director of the National Domestic Workers Alliance. Poo came to labor organizing through feminism. As a volunteer in a domestic violence shelter for Asian immigrant women, she explains, she realized that it was women who had economic opportunities who were able to break the cycle of violence. She brings a sharp gender analysis to the struggle for respect and better treatment for the workers, mostly women, who “make all other work possible.”

“Society has devalued that work over time,” she notes of the cleaning, caring, cooking, and other work domestic workers perform, largely hidden from public view, “and we think that that has a lot to do with who’s done the work.”

This argument was at the root of the fight for access to employment outside of the “pink-collar” fields. To be trapped in women’s jobs was to be forever trapped in a certain vision of femininity. Breaking out of “women’s work” was a form of breaking through the “feminine mystique” that Betty Friedan decried. But that work still needs to be done, and, Poo notes, the conditions that have long defined domestic work and service work—instability, lack of training, lack of career pathways, low pay—are now increasingly the reality for all American workers, not just women. When we focus on equal access at the top, we miss out the real story, which historian Bethany Moreton points out, “is not ‘Oh wow, women get to be lawyers,’ but that men get to be casualized clerks.”

Q. "Breaking out of women’s work was a form of breaking through the feminine mystique". Which of the following statements best captures the sense of this statement?

Detailed Solution for CAT Mock Test- 9 (November 11) - Question 1

In the passage, the author states that "To be trapped in women’s jobs was to be forever trapped in a certain vision of femininity." So, to escape this trap, women had to engage in tasks that fell outside the ambit of acceptable work for women. 
Option A surmises this point correctly.
Options B and D are out of scope, as they discuss achieving parity with men and performing the same jobs as them. It is not necessary for women to be employed in the same jobs as men. Performing tasks that were outside the ambit of acceptable work was sufficient. 
Option C misses out on the larger picture- breaking through the vision of femininity. 
Option A is the answer.

CAT Mock Test- 9 (November 11) - Question 2

Read the passage carefully and answer the following questions:

It’s been two decades since the Human Genome Project first unveiled a rough draft of our genetic instruction book. The promise of that medical moon shot was that doctors would soon be able to look at an individual’s DNA and prescribe the right medicines for that person’s illness or even prevent certain diseases. That promise, known as precision medicine, has yet to be fulfilled in any widespread way. True, researchers are getting clues about some genetic variants linked to certain conditions and some that affect how drugs work in the body. But many of those advances have benefited just one group: people whose ancestral roots stem from Europe. In other words, white people.

Instead of a truly human genome that represents everyone, “what we have is essentially a European genome,” says Constance Hilliard, an evolutionary historian at the University of North Texas in Denton. “That data doesn’t work for anybody apart from people of European ancestry.” She’s talking about more than the Human Genome Project’s reference genome. That database is just one of many that researchers are using to develop precision medicine strategies. Often those genetic databases draw on data mainly from white participants. But race isn’t the issue. The problem is that collectively, those data add up to a catalog of genetic variants that don’t represent the full range of human genetic diversity.

One solution is to make customized reference genomes for populations whose members die from cancer or heart disease at higher rates than other groups, for example, or who face other worse health outcomes, Hilliard suggests. Hilliard’s hypothesis is that precision medicine, which tailors treatments based on a person’s genetic data, lifestyle, environment and physiology, is more likely to succeed when researchers consider the histories of groups that have worse health outcomes.

And the more specific the better. For instance, African Americans who descended from enslaved people have geographic and ecological origins as well as evolutionary and social histories distinct from those of recent African immigrants to the United States. Those histories have left stamps in the DNA that can make a difference in people’s health today. The same goes for Indigenous people from various parts of the world and Latino people from Mexico versus the Caribbean or Central or South America.

Results of a survey conducted by Science News revealed that one big drawback to Hilliard’s proposal may be social rather than scientific. Many respondents expressed concern that even well-intentioned scientists might do research that ultimately increases bias and discrimination toward certain groups. As one respondent put it, “The idea of diversity is being stretched into an arena where racial differences will be emphasized and commonalities minimized. The fear is that any differences that are found would be exploited by those who want to denigrate others. This is truly the entry to a racist philosophy.” Indeed, the Chinese government has come under fire for using DNA to identify members of the Uighur Muslim ethnic group, singling them out for surveillance and sending some to “reeducation camps.”

Hilliard says that the argument that minorities become more vulnerable when they open themselves to genetic research is valid. “Genomics, like nuclear fusion, can be weaponized and dangerous,” she says in response to respondents' concerns. “Minorities can choose to be left out of the genomic revolution or they can make full use of it,” by adding their genetic data to the mix.

Q. Which of the following statements is Constance Hilliard least likely to agree with?

Detailed Solution for CAT Mock Test- 9 (November 11) - Question 2

In African American example, Hilliard says, "African Americans who descended from enslaved people have geographic and ecological origins as well as evolutionary and social histories distinct from those of recent African immigrants to the United States. Those histories have left stamps in the DNA that can make a difference in people’s health today." So, according to her, geographical ancestry affects DNA profile and hence would agree with the statement in option A.
Option C , too, follows from the inference drawn based on the African-American example elucidated above. Hilliard believes that other factors like ecological and geographical origins also play a crucial role in determining the genetic makeup.
"That data doesn’t work for anybody apart from people of European ancestry". Hilliards makes this remark on the efficacy of the existing database. Hence, she would agree with the statement in option D.
This leaves us with option B. The author does not discuss Hilliard's views on the health outcomes of minorities in the passage. And moreover, genetic data obtained from few members could potentially benefit the entire group at large. Hence, Hilliard is least likely to agree with the statement in option B.
Option B is the answer.

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CAT Mock Test- 9 (November 11) - Question 3

Read the passage carefully and answer the following questions:

It’s been two decades since the Human Genome Project first unveiled a rough draft of our genetic instruction book. The promise of that medical moon shot was that doctors would soon be able to look at an individual’s DNA and prescribe the right medicines for that person’s illness or even prevent certain diseases. That promise, known as precision medicine, has yet to be fulfilled in any widespread way. True, researchers are getting clues about some genetic variants linked to certain conditions and some that affect how drugs work in the body. But many of those advances have benefited just one group: people whose ancestral roots stem from Europe. In other words, white people.

Instead of a truly human genome that represents everyone, “what we have is essentially a European genome,” says Constance Hilliard, an evolutionary historian at the University of North Texas in Denton. “That data doesn’t work for anybody apart from people of European ancestry.” She’s talking about more than the Human Genome Project’s reference genome. That database is just one of many that researchers are using to develop precision medicine strategies. Often those genetic databases draw on data mainly from white participants. But race isn’t the issue. The problem is that collectively, those data add up to a catalog of genetic variants that don’t represent the full range of human genetic diversity.

One solution is to make customized reference genomes for populations whose members die from cancer or heart disease at higher rates than other groups, for example, or who face other worse health outcomes, Hilliard suggests. Hilliard’s hypothesis is that precision medicine, which tailors treatments based on a person’s genetic data, lifestyle, environment and physiology, is more likely to succeed when researchers consider the histories of groups that have worse health outcomes.

And the more specific the better. For instance, African Americans who descended from enslaved people have geographic and ecological origins as well as evolutionary and social histories distinct from those of recent African immigrants to the United States. Those histories have left stamps in the DNA that can make a difference in people’s health today. The same goes for Indigenous people from various parts of the world and Latino people from Mexico versus the Caribbean or Central or South America.

Results of a survey conducted by Science News revealed that one big drawback to Hilliard’s proposal may be social rather than scientific. Many respondents expressed concern that even well-intentioned scientists might do research that ultimately increases bias and discrimination toward certain groups. As one respondent put it, “The idea of diversity is being stretched into an arena where racial differences will be emphasized and commonalities minimized. The fear is that any differences that are found would be exploited by those who want to denigrate others. This is truly the entry to a racist philosophy.” Indeed, the Chinese government has come under fire for using DNA to identify members of the Uighur Muslim ethnic group, singling them out for surveillance and sending some to “reeducation camps.”

Hilliard says that the argument that minorities become more vulnerable when they open themselves to genetic research is valid. “Genomics, like nuclear fusion, can be weaponized and dangerous,” she says in response to respondents' concerns. “Minorities can choose to be left out of the genomic revolution or they can make full use of it,” by adding their genetic data to the mix.

Q. The central point in the fifth paragraph is that

Detailed Solution for CAT Mock Test- 9 (November 11) - Question 3

{As one respondent put it, “The idea of diversity is being stretched into an arena where racial differences will be emphasized, and commonalities minimized. The fear is that any differences that are found would be exploited by those who want to denigrate others. This is truly the entry to a racist philosophy.” Indeed, the Chinese government has come under fire for using DNA to identify members of the Uighur Muslim ethnic group, singling them out for surveillance and sending some to “reeducation camps.”}
In the fifth paragraph, the author discusses one of the consequences of genetic research that many are worried about- the results being used to amplify racial differences and target certain racial/ethnic groups. Option A aptly captures this inference.
Option B is a distortion. The author does not assert that Hilliard's proposal is devoid of scientific flaws.
Options C and D are tangential to the discussion. The author does not present any information regarding discriminatory policies or diverse opinions in the passage. 

CAT Mock Test- 9 (November 11) - Question 4

Read the passage carefully and answer the following questions:

Cryptocurrencies have long been heralded as the future of finance, but it wasn’t until 2020 that it finally caught on to an old idea: making money with money. In the crypto world, decentralized finance (or DeFi) encompasses a wide array of blockchain-based applications intended to enhance cryptocurrency holders’ returns without relying on intermediaries — to earn the kind of passive returns an investor might get from a savings account, a Treasury bill, or an Apple Inc. bond.

The idea seems to be catching fire: Deposits in DeFi applications grew from about $1 billion in June to just under $40 billion by late January 2021, suggesting that DeFi could be a major element of crypto from here on out. In the tradition of disruptive innovations — as Clayton Christensen envisioned them — DeFi can be the evolution of blockchain technology that might launch it into mainstream.

The premise of DeFi is simple: Fix the longstanding inefficiency in crypto finance of capital being kept idle at a nonzero opportunity cost. Now, most investors buy crypto with the hope that the value of the currency itself will rise, as Bitcoin has. In general, that strategy has worked just fine. The value of cryptocurrencies has appreciated so rapidly that there just wasn’t much incentive to worry about gains of a few percent here and there.

But the recent rise of stablecoins, which are designed keep their value constant, has changed that calculation. The combined market cap of stablecoins such as Terra and USDC has more than quadrupled in 2020. Now, vast passive income opportunities are being awakened by DeFi.

The appeal of a lower-risk approach to crypto is obvious and has the potential to expand the pool of investors. For the first time, it’s possible to be compensated for owning cryptos (even in the absence of price appreciation), which brings real, tangible utilities to digital currencies and changes the narrative of an asset class whose sole purpose used to be about being sold at a higher price. Therefore, many of the DeFi protocols today might have the potential to become big and bold enough to rival their centralized counterparts, while staying true to their decentralized roots. Furthermore, with volatility out of the picture and the promise of more stable returns, institutional investors are now considering crypto as part of their investments in alternatives.

The search for passive returns on crypto assets, called “yield farming,” is already taking shape on a number of new lending platforms. Compound Labs has launched one of the biggest DeFi lending platforms, where users can now borrow and lend any cryptocurrency on a short-term basis at algorithmically determined rates. A prototypical yield farmer moves assets around pools on Compound, constantly chasing the pool offering the highest annual percentage yield (APY). Practically, it echoes a strategy in traditional finance — a foreign currency carry trade — where a trader seeks to borrow the currency charging a lower interest rate and lend the one offering a higher return.

Crypto yield farming, however, offers more incentives. For instance, by depositing stablecoins into a digital account, investors would be rewarded in at least two ways. First, they receive the APY on their deposits. Second, and more importantly, certain protocols offer an additional subsidy, in the form of a new token, on top of the yield that it charges the borrower and pays to the lender.

Q. Which of the following statements cannot be inferred from the passage?
I. DeFi is a form of finance that does not rely on financial intermediaries.
II. Capital invested in crypto finance would have zero opportunity cost with increased deposits in DeFi applications.
III. Deposits in DeFi applications would make cryptocurrency investments free from volatility.
IV. People follow traditional financial strategies on DeFi lending platforms.

Detailed Solution for CAT Mock Test- 9 (November 11) - Question 4

"Decentralized finance (or DeFi) encompasses a wide array of blockchain-based applications intended to enhance cryptocurrency holders’ returns without relying on intermediaries". Statement I can be inferred from this line.
"The premise of DeFi is simple: Fix the longstanding inefficiency in crypto finance of capital being kept idle at a nonzero opportunity cost." However, it is not possible to conclude from this line that the opportunity cost would come down to zero. Statement II cannot be inferred.
Statement III cannot be inferred either. The passage only talks about reduced volatility, in the case of DeFi lending platforms and stablecoins. 
The passage only discusses a one-off example, i.e., about 'yield farming', in the case of Compound, and how investors follow a traditional financial strategy. However, this one example cannot be the basis to conclude that people, in general,  follow traditional financial strategies on DeFi lending platforms.
Hence, statements II, III and IV cannot be inferred. Option C is the answer. 

CAT Mock Test- 9 (November 11) - Question 5

Read the passage carefully and answer the following questions:

Cryptocurrencies have long been heralded as the future of finance, but it wasn’t until 2020 that it finally caught on to an old idea: making money with money. In the crypto world, decentralized finance (or DeFi) encompasses a wide array of blockchain-based applications intended to enhance cryptocurrency holders’ returns without relying on intermediaries — to earn the kind of passive returns an investor might get from a savings account, a Treasury bill, or an Apple Inc. bond.

The idea seems to be catching fire: Deposits in DeFi applications grew from about $1 billion in June to just under $40 billion by late January 2021, suggesting that DeFi could be a major element of crypto from here on out. In the tradition of disruptive innovations — as Clayton Christensen envisioned them — DeFi can be the evolution of blockchain technology that might launch it into mainstream.

The premise of DeFi is simple: Fix the longstanding inefficiency in crypto finance of capital being kept idle at a nonzero opportunity cost. Now, most investors buy crypto with the hope that the value of the currency itself will rise, as Bitcoin has. In general, that strategy has worked just fine. The value of cryptocurrencies has appreciated so rapidly that there just wasn’t much incentive to worry about gains of a few percent here and there.

But the recent rise of stablecoins, which are designed keep their value constant, has changed that calculation. The combined market cap of stablecoins such as Terra and USDC has more than quadrupled in 2020. Now, vast passive income opportunities are being awakened by DeFi.

The appeal of a lower-risk approach to crypto is obvious and has the potential to expand the pool of investors. For the first time, it’s possible to be compensated for owning cryptos (even in the absence of price appreciation), which brings real, tangible utilities to digital currencies and changes the narrative of an asset class whose sole purpose used to be about being sold at a higher price. Therefore, many of the DeFi protocols today might have the potential to become big and bold enough to rival their centralized counterparts, while staying true to their decentralized roots. Furthermore, with volatility out of the picture and the promise of more stable returns, institutional investors are now considering crypto as part of their investments in alternatives.

The search for passive returns on crypto assets, called “yield farming,” is already taking shape on a number of new lending platforms. Compound Labs has launched one of the biggest DeFi lending platforms, where users can now borrow and lend any cryptocurrency on a short-term basis at algorithmically determined rates. A prototypical yield farmer moves assets around pools on Compound, constantly chasing the pool offering the highest annual percentage yield (APY). Practically, it echoes a strategy in traditional finance — a foreign currency carry trade — where a trader seeks to borrow the currency charging a lower interest rate and lend the one offering a higher return.

Crypto yield farming, however, offers more incentives. For instance, by depositing stablecoins into a digital account, investors would be rewarded in at least two ways. First, they receive the APY on their deposits. Second, and more importantly, certain protocols offer an additional subsidy, in the form of a new token, on top of the yield that it charges the borrower and pays to the lender.

Q. Which of the following would the author cite as a reason for activity in DeFi applications being nascent until recently?

Detailed Solution for CAT Mock Test- 9 (November 11) - Question 5

"The value of cryptocurrencies has appreciated so rapidly that there just wasn’t much incentive to worry about gains of a few percent here and there". Option B can be inferred from this line.
Options A,C and D have not been mentioned in the passage and can be eliminated. Option B is the answer.

CAT Mock Test- 9 (November 11) - Question 6

Read the passage carefully and answer the following questions:

Cryptocurrencies have long been heralded as the future of finance, but it wasn’t until 2020 that it finally caught on to an old idea: making money with money. In the crypto world, decentralized finance (or DeFi) encompasses a wide array of blockchain-based applications intended to enhance cryptocurrency holders’ returns without relying on intermediaries — to earn the kind of passive returns an investor might get from a savings account, a Treasury bill, or an Apple Inc. bond.

The idea seems to be catching fire: Deposits in DeFi applications grew from about $1 billion in June to just under $40 billion by late January 2021, suggesting that DeFi could be a major element of crypto from here on out. In the tradition of disruptive innovations — as Clayton Christensen envisioned them — DeFi can be the evolution of blockchain technology that might launch it into mainstream.

The premise of DeFi is simple: Fix the longstanding inefficiency in crypto finance of capital being kept idle at a nonzero opportunity cost. Now, most investors buy crypto with the hope that the value of the currency itself will rise, as Bitcoin has. In general, that strategy has worked just fine. The value of cryptocurrencies has appreciated so rapidly that there just wasn’t much incentive to worry about gains of a few percent here and there.

But the recent rise of stablecoins, which are designed keep their value constant, has changed that calculation. The combined market cap of stablecoins such as Terra and USDC has more than quadrupled in 2020. Now, vast passive income opportunities are being awakened by DeFi.

The appeal of a lower-risk approach to crypto is obvious and has the potential to expand the pool of investors. For the first time, it’s possible to be compensated for owning cryptos (even in the absence of price appreciation), which brings real, tangible utilities to digital currencies and changes the narrative of an asset class whose sole purpose used to be about being sold at a higher price. Therefore, many of the DeFi protocols today might have the potential to become big and bold enough to rival their centralized counterparts, while staying true to their decentralized roots. Furthermore, with volatility out of the picture and the promise of more stable returns, institutional investors are now considering crypto as part of their investments in alternatives.

The search for passive returns on crypto assets, called “yield farming,” is already taking shape on a number of new lending platforms. Compound Labs has launched one of the biggest DeFi lending platforms, where users can now borrow and lend any cryptocurrency on a short-term basis at algorithmically determined rates. A prototypical yield farmer moves assets around pools on Compound, constantly chasing the pool offering the highest annual percentage yield (APY). Practically, it echoes a strategy in traditional finance — a foreign currency carry trade — where a trader seeks to borrow the currency charging a lower interest rate and lend the one offering a higher return.

Crypto yield farming, however, offers more incentives. For instance, by depositing stablecoins into a digital account, investors would be rewarded in at least two ways. First, they receive the APY on their deposits. Second, and more importantly, certain protocols offer an additional subsidy, in the form of a new token, on top of the yield that it charges the borrower and pays to the lender.

Q. The primary purpose of the passage is to

Detailed Solution for CAT Mock Test- 9 (November 11) - Question 6

Option A talks about a 'crisis', which is out of scope. Option A can be eliminated.
Option B can be eliminated. The author does not talk about the shortcomings of blockchain technology in the passage. Also, rather than highlighting anything unconventional about cryptocurrencies, the author attempts to bring about a development in the area that mirrors conventional investment logic. 
Option D is close but goes beyond the scope of the passage. The focus is only on DeFi and not other income opportunities. Also, earning income through interests is not a novel concept.
Option C is the answer. The passage talks about a longstanding inefficiency  in crypto finance of capital being kept idle at a nonzero opportunity cost and how DeFi could help overcome this issue. The passage further highlights the future potential of DeFi. 

CAT Mock Test- 9 (November 11) - Question 7

Read the passage carefully and answer the following questions:

When investigating witchcraft, one needs to differentiate between real and imaginary magic in the early modern period. If we want to understand the connection between the imaginary magic of the witches and economic behaviour, we need to deal with the connection between the economy and the real magic practised by ‘common’ people. In pre-industrial Europe, magic was a part of everyday life, very much like religion. People didn’t just believe in the efficacy of magic, they actively tried to use magic themselves. Simple forms of divination and healing magic were common, as was magic related to agriculture. The peasant household used divination to find out if the time was right for certain agricultural activities. Charms were supposed to keep the livestock in good health. Urban artisans and merchants also used economic magic to increase their wealth.

Of all the forms of magic, magical treasure-hunting had the greatest economic significance. Treasure hunters drew on a vast magical arsenal. They had spell books of any description, divining rods available in any kind of wood, amulets to protect them against evil spirits, and lead tablets etched with magical signs.  To the utter horror of the ecclesiastical authorities, they invoked angels and saints. Treasure hunters talked to ghosts. Some of them even tried to conjure up demons. However,  common people simply didn’t see treasure magic as witchcraft, and most of the judges agreed. 

Separate from these real forms of magic, there was the imaginary magic of the witches. Nobody was ever (or could ever be) guilty of witchcraft in the full sense of the word, which was defined by the late Middle Ages as a crime that consisted of five elements: a pact with the devil; sexual intercourse with demons; the magical flight (on a broomstick or a similar device); the witches’ dance (often referred to by the antisemitic term ‘witches’ sabbath’); and malevolent magic. Early modern Europe and Britain treated witchcraft as a capital crime.

At first glance, the relation between the economy and the imaginary magic of the witches seems to be entirely negative. Witches were often accused of attacking livestock. They magically made frost, storm and hail, and thereby caused crop failure. Indeed, their weather magic was said to endanger the economy of entire regions. Still, at least in the majority of the witch trials on the European continent, the witches didn’t profit from their magic. Weather magic especially looked like a strange form of auto-aggression because the hailstorms the witches supposedly conjured up damaged their own fields as well. As a rule, the pact with the devil as it appears in trial records was not a contract like that of Goethe’s Faust, which was mostly about the wishes of the magician. Rather, it stated simply that the witch submitted to the will of the demon. She did what a demon told her and became the instrument of the demon’s abyssal hatred of all creation. Witchcraft was mostly about destruction for destruction’s sake, not about the personal interests and wishes of the witches, let alone their economic advantage.

Q. In pre-industrial Europe, magic was practised for all of the following purposes, EXCEPT:

Detailed Solution for CAT Mock Test- 9 (November 11) - Question 7

"Urban artisans and merchants also used economic magic to increase their wealth." Option A can be inferred from this line.
"Charms were supposed to keep the livestock in good health". Option B can be inferred from this line.
Peasant households used divination to ascertain the right time for certain agricultural practices. The passage makes no mention of remedies to improve crop health. Option C cannot be inferred.
Simple divination was practised. Divination refers to the practice of seeking knowledge of the future by supernatural means; in this case, magic.

*Answer can only contain numeric values
CAT Mock Test- 9 (November 11) - Question 8

The four sentences (labelled 1, 2, 3, 4) below, when properly sequenced would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer:

  1. Some infections are noisy.
  2. Other microbes are silent houseguests, so unobtrusive that we don’t even notice them.
  3. They come with signs and symptoms of illness, either because the pathogen is causing a ruckus or because the body has grown cantankerous in its effort to evict an unwelcome tenant.
  4. Coronavirus infections seem capable of running the gamut.

Detailed Solution for CAT Mock Test- 9 (November 11) - Question 8

1 will immediately precede 3 because "they" in 3 refers to "some infections" in 1, and the word "ruckus" in 3 is also related to "some infections" being "noisy" in 1. 2 will come immediately after 3 because 1 and 3 talk about some infections. And 2 talks about the "other microbes". 4 will clearly be the concluding sentences stating the coronavirus has both the features discussed in the previous lines. Hence, the order will be 1324.

CAT Mock Test- 9 (November 11) - Question 9

Modern history abounds with violence fueled by apocalyptic myths, not always explicitly religious in nature. The aim of the Jacobin terror in revolutionary France was the creation of a modern state. If the violent suppression of the peasant revolt in the Vendée is included, the casualties ran into the hundreds of thousands. The myths that possessed these anarchists in their campaigns of assassination were secular myths of social transformation. Lenin avowedly followed the Jacobin example when he used the Cheka to create a modern state in Russia. One of the factors that distinguished Nazism and fascism from conventional tyrannies was the belief that a new society could be fashioned by the systematic use of terror. Violent jihadism has more in common with these modern totalitarian movements than is commonly supposed.

Detailed Solution for CAT Mock Test- 9 (November 11) - Question 9

Option A: Violent jihadism is justified on the secular myth of social transformation, rather than idea of religious apocalypse.

The paragraph we have argues that violent jihadism has a lot in common with the totalitarian movements in history which were powered by the promise of social transformation. But the paragraph does not say that violent jihadism is not based on the idea of religious apocalypse. Also, this option does not sum up the paragraph we have. So this is definitely ruled out.

Option B: The myth of social transformation has underpinned many totalitarian movements in modern history, and violent jihadism too exploits this.

This, clearly, is the main idea of the paragraph. Many totalitarian movements in modern history have been fueled by the myth of social transformation. Violent jihadism also draws on this idea. Option B summarizes the paragraph well.

Option C: Although it is believed that violence is fueled by religion, the reality is that it is unleashed on the premise of the creation of a modern state.

This option categorially rules out the idea that violence is fueled by religion. It claims that it is only unleashed on the premise of the creation of a modern state. This is not what the paragraph given states. It states that violence is fueled by apocalyptic myths which are "not always"? explicitly religious. So we rule this option out.

Option D: Modern history illustrates that it is a myth that societies can be transformed by the systematic use of terror.

This option says that societies cannot be transformed by the systematic use of terror and that modern history confirms this. Clearly, this is not what the paragraph conveys and so this is not the right option to sum up the paragraph.

Hence, the answer is B

CAT Mock Test- 9 (November 11) - Question 10

Nineteenth-century liberals recognized that democracy comes in various forms, and dreaded the version advocated by Rousseau, in which an inspired lawgiver interprets and implements the will of the people. Nowadays such fears are dismissed as elitist. But the old-fashioned liberals grasped a vital truth: popular government has no necessary connection with the freedom of individuals or minorities. Of course, liberals today will say this can be remedied by installing the rule of constitutional rights. Such systems are fragile, however, and count for nothing when large sections of society are indifferent or actively hostile to liberal values. Where this is the case, democracy means not much more than the tyranny of the majority.

Detailed Solution for CAT Mock Test- 9 (November 11) - Question 10

Option A. Inspired lawgivers in liberal democracies are better equipped to interpret and implement the will of the people than in illiberal democracies.

We can rule this option out straight away, as this is not what the paragraph says. The paragraph does not talk about lawgivers in liberal democracies as better equipped to interpret the will of the people as compared to those in illiberal democracies.

Option B. Nineteenth-century liberals believed that democracy means not much more than the tyranny of the majority.

Again, this is not what the paragraph states. Nineteenth-century liberals only dreaded the version of democracy where the lawgiver declares himself to be the interpreter and implementer of the will of the people. They did not equate democracy to the tyranny of the majority.

Option C. Constitutional rights are fragile and ineffective in ensuring protection of the freedom of individuals in any democracy.

The paragraph does declare that constitutional rights are fragile and not effective in protecting freedom of individuals and minorities. But this is in the specific context where “when large sections of society are indifferent or actively hostile to liberal values?. That is, in illiberal democracies constitutional rights provide little by way of support to minorities. However, option C generalizes this to say that constitutional rights are fragile and infective in any democracy. This is not what the paragraph says.

Option D. Popular governments in illiberal democracies use the power of the majority to clamp down on the freedom of minorities.

This option sums up the main idea of the paragraph best. In illiberal democracies, where the majority is indifferent or actively hostile to liberal values, popular governments use the power of majority to clamp down on the freedom of minorities.

Hence, the answer is D

*Answer can only contain numeric values
CAT Mock Test- 9 (November 11) - Question 11

Sheldon Cooper and Barry Kripke are 2 rival scientists at a world-renowned university. They both require highly expensive laser equipment for their research project but the university could afford only one. Not wanting to take sides of either of the scientists, Dr Siebert proposed them to use their logical brains to compete in a game and the winner would be allowed to use the equipment first. The game had following rules

  1. An electric dog will be placed on the building which has ground floor as Level 0, 1st floor as Level 1 and so on. The dog will be placed on level N where N is an integer.
  2. Each of the scientists will take a turn alternatively in deciding whether the dog jumps down 1 or 3 or 4 levels
  3. Whichever scientist is able to make the dog land on level 0 will win
  4. If the dog is at level 2, the only move possible is to bring down the dog by 1 level

Both the scientist play with the intention of winning and can not skip their turn

Q. What is the lowest 3-digit level at which the dog should be placed given that Kripke starts the game and wins?


Detailed Solution for CAT Mock Test- 9 (November 11) - Question 11

Let us work from the bottom of the building to understand the winning scenarios:
If the dog is at level 1, the command of 1 level down has to be given and thus dog will reach level 0 which will result in a win. Thus level 1 is always a winning position
If the dog is at level 2, the person will have no other option but to bring down the dog by level 1. His opponent will start at level 1 and win the game. Thus level 2 is a losing position

W = Win
L = Lose
If the dog is at Level 3 or Level 4, the dog can be given command of jumping down 3 or 4 levels and thus dog will reach level 0 and the person giving the command will be the winner.

W = Win
L = Lose
If the dog is at Level 5, it can be given the command to go down either 1 or 3 or 4 levels and will land on Level 4 or Level 2 or Level 1. The person would want the dog to land in such a way that the opponent gets the dog in losing position thus at this stage dog has to jump down 3 levels and land at level 2. Thus level 5 is a winning position
If the dog is at Level 6, it can be given the command to go down either 1 or 3 or 4 levels and will land on Level 5 or Level 3 or Level 2.The person would want the dog to land in such a way that the opponent gets the dog in losing position thus at this stage dog has to jump down 4 levels and land at level 2. Thus level 6 is a winning position.
If the dog is at Level 7, it can be given the command to go down either 1 or 3 or 4 levels and will land on Level 6 or Level 4 or Level 3. All of which is a winning position for the opponent. Therefore, whoever gets Level 7 is sure to lose

W = Win
L = Lose
If the dog is in level 8, then he can be given the command to jump down 1 level leaving the opponent at Level 7 which is a losing position. Thus level 8 is winning position.
If the dog is at Level 9, it can be given the command to go down either 1 or 3 or 4 levels and will land on Level 8 or Level 6 or Level 5.All of which are a winning position and hence level 9 is a losing position
If the dog is at Level 10, it can be given the command to go down either 1 or 3 or 4 levels and will land on Level 9 or Level 7 or Level 6.The person would want the dog to land in such a way that the opponent gets the dog in losing position thus at this stage dog has to jump down 3 levels and land at level 7. Thus level 10 is a winning position.

W = Win
L = Lose
We see that a similar condition has been discussed earlier also, and hence a pattern is emerging.
If the player receives the dog on the level which is of form 7k or 7k+2 then the person is sure to lose the game.
The lowest 3-digit number is 100 but it is of the form 7k+2 hence a losing position. Hence 101 is the lowest 3-digit number which is a winning position.

CAT Mock Test- 9 (November 11) - Question 12

5 friends Akbar, Birbal, Chandan, Dhanush and Eeshwar, are standing in a line, not necessarily in the same order. Each of them is wearing is a shirt of unique colour among Red, Green, Blue, Yellow and Black not necessarily in the same order. Each of them also was wearing a pant which is unique among Red, Green, Blue, Yellow and Black not necessarily in the same order. They each own a device among iPhone, iPad, Apple Watch, iPod and Airpods.

The following things about the arrangements are known:

  1. Nobody wear shirt and pant of the matching colours
  2. Friend wearing Black pants is at the one of the extremes of the line and owns iPhone
  3. The friend who owns Airpods and is wearing Blue pants is standing just behind the iPod owner but is ahead of the friend wearing green pants.
  4. The guy wearing the Black shirt is standing at the end of the line and he owns iPad
  5. Birbal who is wearing a Red shirt, is standing ahead of the friend with Blue pants
  6. Eeshwar owns Apple Watch
  7. The friend with Black pants is one of the neighbours of the friend who is wearing Yellow pants
  8. Dhanush who is in the middle of the line is wearing a Blue Shirt and is standing ahead of the person who owns Airpods

Q. Which of the following is the correct combination of colour of pant and colour of shirt in the same order

Detailed Solution for CAT Mock Test- 9 (November 11) - Question 12

Let us start with the position we know
>The guy wearing the Black shirt is standing at the end of the line owns iPad
> Dhanush who is in the middle of the line is wearing a Blue Shirt and is standing ahead of the person who owns Airpods

We are given that Dhanus is standing ahead of the person owning Airpods, thus Airpods owner has to be at fourth place
> Friend wearing Black pants is at one of the extremes of the line and owns an iPhone. Thus this person has to be in first position

> The friend who owns Airpods and is wearing Blue pants is standing just behind the iPod owner but is ahead of the friend wearing green pants.
Here we know the location of iPod owner. Thus only remaining device (Apple watch) is also known and can be represented as follows:
Using the following information we can further fill the table
> Eeshwar owns Apple Watch
> The friend with Black pants is one of the neighbours of the friend who is wearing Yellow pants

From the above table, we can conclude that the Red coloured pant has to be worn by Dhanush.
Also, we are given that Birbal wears a red shirt and is standing ahead of the friend with Blue pants. It is possible only when Birbal is in first position

We are given that no one wears a shirt and pant of matching colours. Thus we can say that Yellow Shirt was worn by the friend at fourth place and the green shirt was worn by Eeshwar.

Further information is not given
We can see that out of the option on Green Pant and Black Shirt combination is correct

CAT Mock Test- 9 (November 11) - Question 13

5 friends Akbar, Birbal, Chandan, Dhanush and Eeshwar, are standing in a line, not necessarily in the same order. Each of them is wearing is a shirt of unique colour among Red, Green, Blue, Yellow and Black not necessarily in the same order. Each of them also was wearing a pant which is unique among Red, Green, Blue, Yellow and Black not necessarily in the same order. They each own a device among iPhone, iPad, Apple Watch, iPod and Airpods.

The following things about the arrangements are known:

  1. Nobody wear shirt and pant of the matching colours
  2. Friend wearing Black pants is at the one of the extremes of the line and owns iPhone
  3. The friend who owns Airpods and is wearing Blue pants is standing just behind the iPod owner but is ahead of the friend wearing green pants.
  4. The guy wearing the Black shirt is standing at the end of the line and he owns iPad
  5. Birbal who is wearing a Red shirt, is standing ahead of the friend with Blue pants
  6. Eeshwar owns Apple Watch
  7. The friend with Black pants is one of the neighbours of the friend who is wearing Yellow pants
  8. Dhanush who is in the middle of the line is wearing a Blue Shirt and is standing ahead of the person who owns Airpods

Q. Positions of how many friends can be uniquely determined?

Detailed Solution for CAT Mock Test- 9 (November 11) - Question 13

Let us start with the position we know
>The guy wearing the Black shirt is standing at the end of the line owns iPad
> Dhanush who is in the middle of the line is wearing a Blue Shirt and is standing ahead of the person who owns Airpods

We are given that Dhanus is standing ahead of the person owning Airpods, thus Airpods owner has to be at fourth place
> Friend wearing Black pants is at one of the extremes of the line and owns an iPhone. Thus this person has to be in first position

> The friend who owns Airpods and is wearing Blue pants is standing just behind the iPod owner but is ahead of the friend wearing green pants.
Here we know the location of iPod owner. Thus only remaining device (Apple watch) is also known and can be represented as follows:
Using the following information we can further fill the table
> Eeshwar owns Apple Watch
> The friend with Black pants is one of the neighbours of the friend who is wearing Yellow pants

From the above table, we can conclude that the Red coloured pant has to be worn by Dhanush.
Also, we are given that Birbal wears a red shirt and is standing ahead of the friend with Blue pants. It is possible only when Birbal is in first position

We are given that no one wears a shirt and pant of matching colours. Thus we can say that Yellow Shirt was worn by the friend at fourth place and the green shirt was worn by Eeshwar.

Further information is not given
We can determine all the attributes for only three friends

CAT Mock Test- 9 (November 11) - Question 14

Directions (35–39): Read the following passage and answer the questions that follow:
7 people A, B, C, D, E, F & G who are experts of different subjects History, Mathematics, Geography, English, Biology, Chemistry & Physics (not necessarily in same order) have to go to different cities Goa, Punjab, Pune, New Delhi, Lucknow, Dehradun & Mumbai (not necessarily in same order) for seminar. No two persons are experts of the same subjects. No two people have to go to the same city. One person is an expert of one subject & goes to one city only. They have to go on different days of the week starting from Monday.
G has to go after Thursday. Only 1 person has to go between the person who is an expert of Geography & the person who is an expert of English. At least 2 people have to go between G & B. Only 2 people has to go between C & E who is an expert of Physics. 3 persons has to go between G & D who has to go immediately before the person who has to go to Goa. B, who has to go to Pune, goes immediately before the person who is an expert of Chemistry. Only 2 people goes between the person who goes to Mumbai & the person who goes to New Delhi. C goes after E. F who is a mathematics expert goes immediately before the person who has to go to Mumbai. The person who goes to Punjab is an expert of History & goes immediately after the person who is an expert of Biology.
Q. Which of the following statements is definitely true?

Detailed Solution for CAT Mock Test- 9 (November 11) - Question 14

3 persons have to go between G & D who have to go immediately before the person who has to go to Goa.
G has to go after Thursday.

B, who has to go to Pune, goes immediately before the person who is an expert of Chemistry.
At least 2 people has to go between G & B. So case 1 is eliminated.

Only 2 people have to go between C & E who is an expert of Physics.
C goes after E. So Case 3 – b is eliminated.

F, who is a mathematics expert, goes immediately before the person who has to go to Mumbai. 
Only 2 people go between the person who goes to Mumbai & the person who goes to New Delhi.

The person who goes to Punjab is an expert of History & goes immediately after the person who is an expert of Biology.

Only 1 person has to go between the person who is an expert of Geography & the person who is an expert of English. So Case 2 is now rejected.

CAT Mock Test- 9 (November 11) - Question 15

5 friends Anay, Bhola, Chintu, Dinu and Eshwar spend their entire salary on Rent, Groceries and Travel. The following graph shows the amount of money spent by each of the 5 friends on a particular expense as a percentage of the total amount of money spent by all of the 5 friends on a particular expense. For example, if the amount spend by all the friends on Rent is ‘R’ then the amount spent by Anay on rent is 0.26R. The total amount of money spent by exactly 3 friends is equal.

The amount spent on traveling is how much percent more than the amount spent on rent by all the friends combined?

Detailed Solution for CAT Mock Test- 9 (November 11) - Question 15

Let R be the total amount spent by all the friends on Rent, G be the total amount spent by all the friends on Groceries and T be the total amount spent by all the friends on Travelling.
The given information in table form is as shown below:-

The total amount of money spent by exactly 3 friends is equal.
There are 10 possible combinations for this. 
But as can be observed the amount spent by Anay, Bhola and Chintu on each of Rent, Groceries and Travel is greater than the amount spent by Eshwar on each of Rent, Groceries and Travel.
Thus, Amount of money spent by Eshwar cannot be equal to the amount of money spent by 2 other friends.
Thus, only 4 possible combinations now remain.
Out of these 4, the amount of money spent by Anay and Bhola on each of Rent, Groceries and Travel is greater than the amount spent by Dinu on each of Rent, Groceries and Travel
Thus, Amount of money spent by Dinu cannot be equal to the amount of money spent by 2 other friends.
Thus, the amount spent by Anay, Bhola and Chintu is equal.
Thus, 0.26R+0.24G+0.22T=0.22R+0.24G+0.24T
=> 0.04R = 0.02T
Thus, 2R=T
Also, 0.22R+0.24G+0.24T=0.18R+0.28G+0.24T
=> R=G
Thus, the table becomes:-

Thus the amount spent on traveling is 100% is more than the amount spent on rent by all the friends combined 
Hence, the Option A is the correct option.

CAT Mock Test- 9 (November 11) - Question 16

Directions: Read the following passage and answer the questions that follow:
Below data is given regarding the number of soft toys of three different types (Pikachu, Teddy bear, and Doraemon) made by three soft toys companies S, T and U.
Company S: The number of Teddy bears made by S is 31.25% of total Teddy bears made by three companies and the number of Pikachu made by S is equal to the number of Doraemon made by T. The ratio of the number of Pikachu, Teddy bear and Doraemon made by three companies together are 8: 8: 9 respectively and the ratio of the number of Doraemon made by S, T and U are 3: 2:1 respectively.
Company T: The number of Teddy bears made by T is 40 more than the number of Doraemon made by T. The number of Pikachu made by T is 20 less than the number of Teddy bears made by S.
Company U: The number of Pikachu made by S is 20 more than the number of Pikachu made by U and the number of Teddy bears made by U is 160.

Q. The number of Doraemon and Pikachu made by U is what percentage more or less than the number of Teddy bear and Doraemon made by T?

Detailed Solution for CAT Mock Test- 9 (November 11) - Question 16

Detailed Explanation:
Let the total number of Pikachu, Teddy bear, and Doraemon made by all three companies are 8a, 8a and 9a respectively.
And the number of Doraemon made by S, T and U are 3b, 2b and b respectively. The number of Teddy bear made by S = 31.25% of 8a = 2.5a
The number of Pikachu made by S = 2b
The number of Doraemon made by S = 3b
The number of Teddy bear made by T = (2b + 40)
The number of Pikachu made by T = 2.5a – 20
The number of Doraemon made by T = 2b
The number of Teddy bear made by U = 160 
The number of Pikachu made by U = (2b – 20)
The number of Doraemon made by U = b
Total number of Doraemon made by all three companies = 9a
=> 3b + 2b + b = 9a
=> 6b = 9a
=> b = 3a/2
=> b = 1.5a
And total number of Teddy bear made by all three companies = 8a
=> 2.5a + (2b + 40) + 160 = 8a
=> 2.5a + 2 × 1.5a + 200 = 8a
=> 2.5a = 200
=> a = 80
So, b = 1.5 × 80
=> b = 120
Tabulating the above data:

The number of Doraemon and Pikachu made by U = 120 + 220 = 340
The number of Teddy bear and Doraemon made by T = 280 + 240 = 520
So, required % 

*Answer can only contain numeric values
CAT Mock Test- 9 (November 11) - Question 17

A person travels from A to B and returns. He has two stops (C and D) to reach his destination and AC = CD = DB. In onward journey, his speed from A to C is 20 kmph, from C to D is 25 kmph, and from D to B is 10 kmph. While returning to A, his speed from B to D is 20 kmph; from D to C, he takes a different route which increases his driving distance by 10 km but allows him to drive at 40 kmph along his route; and from C to A, his speed is 25 kmph. If his return journey takes 3 minutes less than his onward journey, find the distance (in km) between A and B.


Detailed Solution for CAT Mock Test- 9 (November 11) - Question 17

Let the distance between A and B be 3x.
AC = CD = DB = x km
Time taken for going from A to C in onward journey = x/20
Time taken for going from C to D in onward journey = x/25
Time taken for going from D to B in onward journey = x/10
Time taken for going back from B to D in return journey = x/20
Time taken for going back from D to C in return journey = (x + 10)/40
Time taken for going back from C to A in return journey = x/25
It is given that he takes 3 minutes (1/20 hours) less in the return journey.
Hence, according to the question:

Thus, distance between A and B = 3x = 12 km

CAT Mock Test- 9 (November 11) - Question 18

There are three solutions, A, B and C containing alcohol and water. The strength of the three solutions are 80%, 90% and 70% respectively. When 1 litre each of A and B is mixed with C, the strength of C increases to 75%. What would be the strength of C if two litres of A and 0.5 litres of B were mixed with C?

Detailed Solution for CAT Mock Test- 9 (November 11) - Question 18

Let the volume of C be x litres.
As the strengths of A and B are 80% and 90%, by mixing 1 litre each of A and B with C, we are adding 800 ml and 900 ml respectively of alcohol to C.
The strength of C is 70% which increases to 75%.
So, the new strength = 75%

On solving, we get x = 4 litres
So, alcohol present in C = 70% of 4 litres = 2.8 litres
In the second case, total alcohol added = (1.6 + 0.45) litres = 2.05 litres

Hence, option A is the correct answer.

CAT Mock Test- 9 (November 11) - Question 19

A cube is painted and then cut into 1000 smaller cubes of equal size. What is the number of small cubes which have exactly one face painted?

Detailed Solution for CAT Mock Test- 9 (November 11) - Question 19

The number of small cubes on one face of the big cube = 10*10 = 100. Out of these, the number of cubes which do not belong to the boundary = 100-(10+10+8+8) = 100-36 = 64. All these 64 cubes on one face of the big cube have exactly one face painted. The total number of such cubes on all the faces is 64*6 = 384.

CAT Mock Test- 9 (November 11) - Question 20

If A,B and C are the angles of a triangle and a,b,c are the corresponding sides, then the equations (sin A + sin B)x+(sin B + sin C)y+sin C + sin A = 0 and (a+b)x + (b+c)y+c+a = 0 have

Detailed Solution for CAT Mock Test- 9 (November 11) - Question 20

(sin A + sin B)x+(sin B + sin C)y+sin C + sin A = 0 -- Eq (1)
(a+b)x+(b+c)y+c+a = 0 -- Eq (2)
In a triangle, a/sin A = b/sin B = c/sin C = 2R where R is the circumradii
sin A = a/2R, sin B = b/2R, sin C = c/2R
On substituting the values in (sin A + sin B)x+(sin B + sin C)y+sin C + sin A = 0, we get
(a+b)x+(b+c)y+c+a = 0          
which is same as Eq 2
Hence the equations will have infinite solutions.

*Answer can only contain numeric values
CAT Mock Test- 9 (November 11) - Question 21

What is the maximum number of acute interior angles that a 12 sided closed figure can enclose?


Detailed Solution for CAT Mock Test- 9 (November 11) - Question 21

The total angle enclosed by a closed polygon is (n-2)*180.
Hence, a 12 sided polygon will enclose 1800.
For an angle to be acute, it has to be less than 90. Hence, we will use 90∘ for the ease of calculation.
If all 12 are acute angles, then the sum of angles will be 12*90∘ = 1080.
This case is not possible.
If 11 of them are acute and 1 is obtuse, then 11*90∘ + obtuse angle = 1800.
⇒ The measure of the obtuse angle is 810. But, angle enclosed by a polygon cannot be greater than 360. Hence, this case is also not possible.
If 10 angles are acute, the sum of the 2 obtuse angles will be 900. The measure of the obtuse angle = 450.
Hence, this case is also not possible.
If 9 angles are acute, the sum of the remaining 3 obtuse angles will be 1800∘ - 810∘ = 990.
The measure of the obtuse angle can be 990 /3 = 330.
Hence, this case is possible.
Hence, the maximum number of acute angles possible is 9.

CAT Mock Test- 9 (November 11) - Question 22

What is the total number of positive integral solution of [x/7] = [x/9], where [a] denotes the greatest integer less than or equal to a?

Detailed Solution for CAT Mock Test- 9 (November 11) - Question 22

Consider [x/7] = [x/9] = 0 
[x/7] = 0  ⇒ 0  ≤ x/7 < 1  ⇒ 0 ≤ x < 7 and [x/9] = 0 ⇒ 0 ≤ x/9 < 1  ⇒ 0 ≤ x < 9
x ϵ [0,7) ∩ [0,9) i.e.1,2,3,4,5,6 (6 integral values)
Consider [x/7] = [x/9] = 1 
[x/7] = 1 ⇒ 1 ≤ x/7 < 2  ⇒ 7 ≤ x < 14 and [x/9] = 1 ⇒ 1 ≤ x/9 < 2  ⇒ 9 ≤ x < 18
x ϵ [7,14) ∩ [9,18) i.e. 9,10,11,12,13 (5 integral values)
Consider [x/7] = [x/9] = 2
[x/7] = 2  ⇒ 2 ≤ x/7 < 3  ⇒ 14 ≤ x <21 and  [x/9] = 0 ⇒ 2 ≤ x/9 < 3  ⇒ 18 ≤ x < 27
x ϵ [14,21) ∩ [18,27) i.e. 18,19,20 (3 integral values)
Consider [x/7] = [x/9] = 3
[x/7] = 3  ⇒ 3 ≤ x/7 < 4  ⇒ 21 ≤ x < 28 and  [x/9] = 0  ⇒ 3 ≤ x/9 < 4  ⇒ 27 ≤ x < 36
x ϵ [21,28) ∩ [27,36) i.e. 27 (1 integral values)
Consider [x/7] = [x/9] = 4
[x/7] = 4  ⇒ 4 ≤ x/7 < 5  ⇒ 28 ≤ x < 35 and  [x/9] = 4  ⇒ 36 ≤ x/9 < 45  ⇒ 36≤x<45
x ϵ [28,35) ∩ [36,45)  (No integral values)
Total values = 6+5+3+1=15

CAT Mock Test- 9 (November 11) - Question 23

If |x + 1| < 6 and |y - 1| < 6 where x, y are integers, what can be the maximum value of x2 + y2 - xy

Detailed Solution for CAT Mock Test- 9 (November 11) - Question 23

We have, |x + 1| < 6 and |y - 1| < 6
|x + 1| < 6   ⇒ -6 < x + 1 < 6  ⇒  -7 < x < 5
|y - 1| < 6 ⇒ -6 < y - 1 < 6 ⇒ -5 < y < 7.
Since x2 + yis positive, the value will be maximized when xy is negative.
The highest negative value of x = -6 and highest positive value of y is 6.
Hence the maximum value of x2 + y2 - xy will be (-6)2 + (6)2 - (-6) = 108 

CAT Mock Test- 9 (November 11) - Question 24

Determine the value of a x b if log27 a + log9 b3 = 13 and log27 b + log9 a3 = 9.

Detailed Solution for CAT Mock Test- 9 (November 11) - Question 24

Using logarithm formula,



⇒ Multiplying (1) and (2), we get
(ab)11/6 = 322  
⇒ ab = 312 = 81*81*81 = 531441 (Using cyclicity, among given options, A is the answer)

*Answer can only contain numeric values
CAT Mock Test- 9 (November 11) - Question 25

The cost of 4 pens, 10 pencils and 14 erasers at a stationery shop is Rs 120. At the same shop, the cost of 6 pens and 10 erasers is Rs 60 more than 12 pencils. By how much amount (in Rs.) does the cost of 78 pencils and 2 erasers exceed the cost of 12 pens?


Detailed Solution for CAT Mock Test- 9 (November 11) - Question 25

Let the cost of a pen be x, the cost of a pencil be y and the cost of an eraser be z.
4x + 10y + 14z = 120
⇒ 2x + 5y + 7z = 60 → (1)
6x + 10z = 60 + 12y
⇒ 6x - 12y + 10z = 60
⇒ 3x - 6y + 5z = 30 → (2)
We need the value of 78y + 2z - 12x = 2*(-6x + 39y + z)
3*(1) - 4*(2) gives 6x + 15y + 21z - 12x + 24y - 20z = 180 - 120
⇒ -6x + 39y + z = 60
So, the required value is 2*60 = 120

CAT Mock Test- 9 (November 11) - Question 26

Milkman Indravadan is planning to sell Rabdi. He bought milk at the rate of Rs 30/kg and sugar at the rate of Rs 50/kg and mixed them in a ratio of 5:4. He then cooks the mixture for several hours during which some of the water got evaporated. In the new mixture ’Rabdi’, the ratio of milk to sugar is 4:5. At approximately what price (per kg) should he sell this Rabdi so as to earn a profit of 20% on the whole transaction?

Detailed Solution for CAT Mock Test- 9 (November 11) - Question 26

In the initial mixture, milk: water = 5:4 which becomes 4:5 after cooking. Assume that he mixed 25 kg of milk with 20 kg of sugar initially.
The cost price for this 45 kg mixture to Indravadan= 25 x 30 + 50 x 20 = Rs1750
To earn 20% discount on this investment, his total selling amount should be 1.2 x 1750 = Rs 2100
Now after cooking, the new ratio is 4:5. Since the sugar amount remains the same i.e. 20 kg, the milk content after reduction will be 16 kg.
Thus, the total weight will be 36kg.
He wants to sell this 36kg for Rs 2100.
Thus, the selling price per kg is 2100/36 = Rs 58.33.

*Answer can only contain numeric values
CAT Mock Test- 9 (November 11) - Question 27

What is the number of perfect cubes that can be represented as a 4-digit number in base 5?


Detailed Solution for CAT Mock Test- 9 (November 11) - Question 27

The smallest 4 digit number in base 5 = (1000)5 = (125)10
The largest 4 digit number in base 5 = (4444)5 = (624)10
The number of perfect cubes between 125 and 624 is 4 i.e 125, 216, 343, 512
4 is the correct answer.,

*Answer can only contain numeric values
CAT Mock Test- 9 (November 11) - Question 28

An arithmetic progression consists of an even number of terms. The sum of its odd terms is 50 whereas the sum of its even terms is 56. Find the number of terms in the series if the last term of the series exceeds the first term by 11.25.


Detailed Solution for CAT Mock Test- 9 (November 11) - Question 28

Let '2n', 'd' be the total number of terms and common difference in the series then,

By subtracting equation (1) from equation (2)

⇒ n*d = 6 ... (3)  

It is given that T2n - T1 = 11.25

From equations (3) and(4),

Hence total number of terms in the given series = 2n = 2*8 = 16. 

*Answer can only contain numeric values
CAT Mock Test- 9 (November 11) - Question 29

The selling price of 16 pens is the same the cost price of 25 pens. If the total discount offered on 50 pens is the same as the selling price of 14 pens then find out the markup percentage.


Detailed Solution for CAT Mock Test- 9 (November 11) - Question 29

Let '100x' be the seeing price of 1 pen. It is given that selling price of 16 pens is the same the cost price of 25 pens.
Hence, the cost price of 1 pen

Total discount offered on 50 pens is the same as the selling price of 14 pens. 
Hence, the discount offered on 1 pen 

Therefore, the marked up price of 1 pen = 100x + 28x = 128x 
Hence, markup percentage

*Answer can only contain numeric values
CAT Mock Test- 9 (November 11) - Question 30

How many factors of 840 are multiples of 5 but not of 8?


Detailed Solution for CAT Mock Test- 9 (November 11) - Question 30

840=23 x 31 x 51 x 71
The required factor should
not contain 23 and must contain 5.
The numbers of ways of using 2 are 20, 21, 22
The numbers of ways of using 3 are 30, 31
The number of ways of using 5 is 51
The numbers of ways of using 7 are 70, 71
Hence required number of factors = 3 x 2 x 1 x 2 = 12

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