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CAT 2023 Slot 2: Past Year Question Paper - CAT MCQ


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30 Questions MCQ Test - CAT 2023 Slot 2: Past Year Question Paper

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CAT 2023 Slot 2: Past Year Question Paper - Question 1

The central idea of the passage would be undermined if:

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 1
  • The central idea of the passage is the promotion of sustainable shopping practices, particularly second-hand shopping, as a means to combat the detrimental environmental effects of the fashion industry. But, the passage also discusses the need for consumers to be mindful of the environmental impact of their clothing choices, opting for high-quality items that last longer and shed fewer microfibers.
  • The passage argues that opting for second clothing might not always be beneficial for the environment by highlighting the microfibre pollution that they can potentially cause. Now, if the second-hand clothes being sold were only of higher quality, it would take care of this problem ([They would be well advised to buy] high-quality items that shed less and last longer [as this] combats both microfibre pollution and excess garments ending up in landfills”)
  • So, the correct answer is Option C.
  • Option A is more about the purchasing channel than the nature of the clothes so it does not necessarily undermine the central idea of the passage.
  • Option B supports the central idea by reducing environmental harm.
  • Option D could align with the sustainability goal and support the central idea, so it doesn't necessarily undermine it.
CAT 2023 Slot 2: Past Year Question Paper - Question 2

The act of "thrifting", as described in the passage, can be considered ironic because it:

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 2

From the context in which the word 'thrifting' is used in the passage, we can conclude that it refers to the purchase of second-hand items at low costs, a practice which is now a trend as consumers get to be 'cool' while also caring for the planet. However, as explained in the passage, the act of thrifting can be considered ironic if, instead of saving the planet, it actually contributes to microfibre pollution of the rivers and oceans. Option A is the correct choice.

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CAT 2023 Slot 2: Past Year Question Paper - Question 3

Based on the passage, we can infer that the opposite of fast fashion, ‘slow fashion’, would most likely refer to clothes that:

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 3
  • Option A is the correct answer because the passage emphasizes the environmental issues associated with fast fashion, including the wasteful disposal of garments in landfills. The opposite of this disposable and rapid turnover nature of fast fashion would be a more sustainable and durable approach, which aligns with the idea of "slow fashion."
  • The passage suggests that buying high-quality items that last longer is a way to combat the negative environmental impact of the fashion industry. Therefore, 'slow fashion' can be inferred to refer to clothes that are of high quality and long-lasting, promoting a more sustainable and environmentally friendly approach to fashion consumption.
CAT 2023 Slot 2: Past Year Question Paper - Question 4

According to the author, companies like ThredUP have not caught on in the UK for all of the following reasons EXCEPT that:

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 4

Option D is the correct answer because the passage does not mention or suggest that the British don't buy second-hand clothing. Instead, the passage discusses challenges related to luxury brands and their reluctance to circulate their latest season stock globally at a cheaper price. The reasons mentioned include the financial aspect(Option A), concerns about brand image(Option B), and the desire to avoid devaluing their products(Option D). Therefore, the passage does not attribute the slow adoption of companies like ThredUP in the UK to the British not buying second-hand clothing.

CAT 2023 Slot 2: Past Year Question Paper - Question 5

The author of the passage faults Deneen's conclusions for all of the following reasons, EXCEPT:

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 5
  • In considering whether Deneen's argument on liberalism is convincing, the author points out Deneen's narrow definition of liberalism is limited to individual freedoms: ' He argues that the essence of liberalism lies in freeing individuals from constraints. In fact, liberalism contains a wide range of intellectual traditions which provide different answers to the question of how to trade off the relative claims of rights and responsibilities, individual expression and social ties..'
  • The author also says Deneen fails to recognise liberalism's ability to reform itself: 'Mr Deneen's fixation on the essence of liberalism leads to the second big problem of his book: his failure to recognise liberalism's ability to reform itself and address its internal problems.'
  • Finally, in the last two lines of the passage, the author states Deneen is wrong in his extreme pessimism about the future of liberalism.
  • Options B, C and D are true.
  • The author does not say that Deneen harks back to premodern notions of liberty. So, option A is the correct answer choice.
CAT 2023 Slot 2: Past Year Question Paper - Question 6

The author of the passage is likely to disagree with all of the following statements, EXCEPT:

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 6
  • Consider option A. The author is likely to disagree with this. Note the lines, 'He argues that the essence of liberalism lies in freeing individuals from constraints. In fact, liberalism contains a wide range of intellectual traditions which provide different answers to the question of how to trade off the relative claims of rights and responsibilities, individual expression and social ties.'
  • Consider option B. The author starts the passage by saying, 'Over the past four centuries liberalism has been so successful that it has driven all its opponents off the battlefield'. He also argues in the penultimate paragraph that liberalism has the ability to reform itself to remain dominant. So, the author is likely to agree with this option. Option B is the correct choice.
  • Let us also consider options C and D to rule them out.
  • The author is likely to disagree with the statement that claims about liberalism's disintegration are exaggerated and misunderstand its core features. Note the lines, 'Mr Deneen is right to point out that the record of liberalism in recent years has been dismal. He is also right to assert that the world has much to learn from the premodern notions of liberty as self-mastery and self-denial.'
  • The author is also likely to disagree with the idea that if we accept that liberalism is a dying ideal, we must work to find a viable substitute. The author argues against liberation from liberalism and states the liberalism must heed the call to action and reform itself.
  • So, option B is the correct answer choice.
CAT 2023 Slot 2: Past Year Question Paper - Question 7

All of the following statements are evidence of the decline of liberalism today, EXCEPT:

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 7

All options except B relate to liberalism and the problems caused by its disintegration. Technological advances cannot be considered evidence of the decline of liberalism.

CAT 2023 Slot 2: Past Year Question Paper - Question 8

The author of the passage refers to "the Davos elite" to illustrate his views on:

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 8

Note the context in which the author talks about the 'Davos elite': 'The biggest enemy of liberalism is not so much atomisation but old-fashioned greed, as members of the Davos elite pile their plates ever higher with perks and share options.' Only option D relates to the greed of the Davos elite. This is the correct answer choice.

CAT 2023 Slot 2: Past Year Question Paper - Question 9

All of the following, if true, can weaken the passage's claim that facts do not speak for themselves, EXCEPT:

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 9
  • If option B is true, that is, if facts are relative and subject to interpretation, then that strengthens the passage's claim that facts do not speak for themselves. So, option B is the right answer choice.
  • The passage claims that facts do not speak for themselves by arguing that while facts are objective and universal and hold true irrespective of the historian who expresses it, it is the historian who decides to which facts to give the floor, and in what order or context, thereby influencing their interpretation. So, all options except B, if true, weaken the passage's claim.
CAT 2023 Slot 2: Past Year Question Paper - Question 10

If the author of the passage were to write a book on the Battle of Hastings along the lines of his/her own reasoning, the focus of the historical account would be on:

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 10
  • The main idea of the passage is that facts speak only when the historian calls on them. The author says that it is because historians regard the Battle of Hastings as a major historical event that we are interested in knowing about it. It is the historian's interpretation of facts that we are interested in. So, if the author were to write a book on the Battle of Hastings, the focus of the account would be on subjective interpretations, like exploring the socio-political and economic factors that led to the Battle.
  • Options A and D are easily ruled out as they focus on the importance of facts.
  • Option B is close, as 'nuanced interpretation' is what the author says historians have to focus on. But option B, unlike option C, emphasizes the role of auxillary sciences in helping a historian do his work. The author says relying on facts that can be gathered from auxiliary sciences of history is "a necessary condition" of a historians' work, "but not his essential function". So, option C is better than B.
CAT 2023 Slot 2: Past Year Question Paper - Question 11

According to this passage, which one of the following statements best describes the significance of archaeology for historians?

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 11
  • Note the context in which the author talks about archaeology and other the "auxiliary sciences" of history: 'But [to] praise a historian for his accuracy is like praising an architect for using well-seasoned timber or properly mixed concrete in his building. It is a necessary condition of his work, but not his essential function. It is precisely for matters of this kind that the historian is entitled to rely on what have been called the "auxiliary sciences" of history-archaeology, epigraphy, numismatics, chronology, and so forth...'
  • The author states auxiliary sciences like archaeology only help historians to ascertain the accuracy of facts. They do not help in the essential function of his work, which is to interpret the facts.
  • Option C is the correct choice.
CAT 2023 Slot 2: Past Year Question Paper - Question 12

All of the following describe the "common-sense view" of history, EXCEPT:

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 12
  • According to the passage, the "common-sense" view of history is influenced by the positivist view and so it places great weight on facts. In this view, facts are available to the historian in documents, inscriptions, and so on and history can be objective like the sciences if it is derived from historical facts.
  • The author's view is in contrast to the common-sense view. The author believes history is a 'selective' system of cognitive orientations to reality. Facts only speak as the historian interprets them. Option A is the correct answer choice.
CAT 2023 Slot 2: Past Year Question Paper - Question 13

Based on information provided in the passage, all of the following are true, EXCEPT:

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 13
  • Option A is true, based on the lines, 'The economics of European productions are more appealing, too. American audiences are more willing than before to give dubbed or subtitled viewing a chance. This means shows such as "Lupin", a French crime caper on Netflix, can become global hits.'
  • Option B is true, too: 'In 2015, about 75% of Netflix's original content was American; now the figure is half, according to Ampere, a media-analysis company.'
  • Option C is clearly stated in the passage:'A bigger problem is that national broadcasters still dominate. Streaming services, such as Netflix or Disney+, account for about a third of all viewing hours, even in markets where they are well-established.'
  • Only option D is incorrect: 'Now Netflix has offices across Europe. But ultimately the big decisions rest with American executives.'
CAT 2023 Slot 2: Past Year Question Paper - Question 14

The author sees the rise of Netflix in Europe as:

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 14

The author clearly sees Netflix as a unifying force in Europe: 'Now Netflix and friends pump the same content into homes across a continent, making culture a cross-border endeavour, too. If Europeans are to share a currency, bail each other out in times of financial need and share vaccines in a pandemic, then they need to have something in common-even if it is just bingeing on the same series.'

CAT 2023 Slot 2: Past Year Question Paper - Question 15

Which one of the following research findings would weaken the author's conclusion in the final paragraph?

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 15
  • In the last paragraph, the author concludes that Netflix is a unifying force in Europe, making culture "a cross-border endeavour". If there were a wide variance in the popularity and viewing of Netflix shows across different EU countries, then the author's assumption that Netflix is popular across Europe, giving Europeans something to share across borders, is weakened. Option B is the correct answer choice.
  • All other options are unrelated to the author's conclusion in the final paragraph.
CAT 2023 Slot 2: Past Year Question Paper - Question 16

Based only on information provided in the passage, which one of the following hypothetical Netflix shows would be most successful with audiences across the EU?

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 16
  • Talking about which shows have better appeal, the passage states, 'Not everything works across borders. Comedy sometimes struggles. Whodunits and bloodthirsty maelstroms between arch Romans and uppity tribesmen have a more universal appeal...'. So, a murder mystery drama set in North Africa and France is likely, according to the passage, to be successful with audiences across the EU.
  • Based on the lines above, option D is easily eliminated. The passage declares 'German television is not always built for export', so option B is also ruled out. The passage focuses on translations of European productions and their success. Option A does not relate to this.
CAT 2023 Slot 2: Past Year Question Paper - Question 17

There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4) the following sentence would best fit.

Sentence: And probably much earlier, moving the documentation for kissing back 1,000 years compared to what was acknowledged in the scientific community.

Paragraph: Research has hypothesised that the earliest evidence of human lip kissing originated in a very specific geographical location in South Asia 3,500 years ago.___(1)___. From there it may have spread to other regions, simultaneously accelerating the spread of the herpes simplex virus 1. According to Dr Troels Pank Arbøll and Dr Sophie Lund Rasmussen, who in a new article in the journal Science draw on a range of written sources from the earliest Mesopotamian societies, kissing was already a well-established practice 4,500 years ago in the Middle East.___(2)___. In ancient Mesopotamia, people wrote in cuneiform script on clay tablets.___(3)___. Many thousands of these clay tablets have survived to this day, and they contain clear examples that kissing was considered a part of romantic intimacy in ancient times.___(4)___. "Kissing could also have been part of friendships and family members' relations," says Dr Troels Pank Arbøll, an expert on the history of medicine in Mesopotamia.

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 17

The given sentence begins with 'and probably much earlier...', so the sentence before must have some reference to time. This narrows down the options to 1 and 2. Of these options 2 makes better sense as the given sentence talks about documentation for kissing and the sentence before 2 talks about written sources that confirm new research findings.

CAT 2023 Slot 2: Past Year Question Paper - Question 18

There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4) the following sentence would best fit.

Sentence: Dualism was long held as the defining feature of developing countries in contrast to developed countries, where frontier technologies and high productivity were assumed to prevail.

Paragraph: ___(1)___. At the core of development economics lies the idea of 'productive dualism': that poor countries' economies are split between a narrow 'modern' sector that uses advanced technologies and a larger 'traditional' sector characterized by very low productivity.___(2)___. While this distinction between developing and advanced economies may have made some sense in the 1950s and 1960s, it no longer appears to be very relevant. A combination of forces have produced a widening gap between the winners and those left behind.___(3)___. Convergence between poor and rich parts of the economy was arrested and regional disparities widened.___(4)___. As a result, policymakers in advanced economies are now grappling with the same questions that have long preoccupied developing economies: mainly how to close the gap with the more advanced parts of the economy.

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 18

The given sentence is about dualism, long held as a distinction between developing and developed countries. The sentence before option 2 introduces dualism and the sentence after it begins with 'while this distinction between developing and advanced economies..', making option 2 the best choice for fitting in the given sentence.

CAT 2023 Slot 2: Past Year Question Paper - Question 19

Five jumbled up sentences (labelled 1, 2, 3, 4 and 5), related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd sentence and key in the number of that sentence as your answer.

1. Self-care particularly links to loneliness, behavioural problems, and negative academic outcomes.
2. "Latchkey children" refers to children who routinely return home from school to empty homes and take care of themselves for extended periods of time.
3. Although self-care generally points to negative outcomes, it is important to consider that the bulk of research has yet to track long-term consequences.
4. In research and practice, the phrase "children in self-care" has come to replace latchkey in an effort to more accurately reflect the nature of their circumstances.
5. Although parents might believe that self-care would be beneficial for development, recent research has found quite the opposite.

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 19
  • Sentence 3 is the odd one out because it introduces a different perspective. While the other sentences discuss the negative outcomes associated with self-care in children, Sentence 3 suggests a need to consider that the bulk of research has yet to track long-term consequences. This sentence introduces a more neutral or balanced viewpoint that doesn't align with the general theme of the other sentences, which focus on the negative aspects of self-care for children.
  • The remaining sentences (1, 2, 4, and 5) can be put together to form a coherent paragraph discussing the concept of self-care in relation to children, particularly those referred to as "Latchkey children."
CAT 2023 Slot 2: Past Year Question Paper - Question 20

Five jumbled up sentences (labelled 1, 2, 3, 4 and 5), related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd sentence and key in the number of that sentence as your answer.

  1. The banning of Northern Lights could be considered a precursor to censoring books for “moral”, world view or religious reasons.
  2. Attempts to ban books are attempts to silence authors who have summoned immense courage in telling their stories.
  3. Now the banning and challenging of books in the US has escalated to an unprecedented level.
  4. The widely acclaimed fantasy novel Northern Lights was banned in some parts of the US, and was the second most challenged book in the US.
  5. The American Library Association documented an unparalleled number of reported book challenges in 2022, about 2,500 unique titles.
Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 20

Sentence 2 is the odd one out because it introduces a broader statement about attempts to ban books and silence authors, while the other sentences are specifically focused on the banning and challenging of books in the US. Sentences 1, 3, 4, and 5 collectively form a coherent paragraph discussing the banning of Northern Lights and the escalation of book challenges in the US, while Sentence 2 introduces a different perspective that doesn't directly contribute to the flow of the paragraph regarding the specific incidents and trends mentioned in the other sentences.

CAT 2023 Slot 2: Past Year Question Paper - Question 21

The four sentences (labelled 1, 2, 3 and 4) given 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. Contemporary African writing like ‘The Bottled Leopard’ voices this theme using two children and two backgrounds to juxtapose two varying cultures.
  2. Chukwuemeka Ike explores the conflict, and casts the Western tradition as condescending, enveloping and unaccommodating towards local African practice.
  3. However, their views contradict the reality, for a rich and sustaining local African cultural ethos exists for all who care, to see and experience.
  4. Western Christian concepts tend to deny or feign ignorance about the existence of a genuine and enduring indigenous African tradition.
Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 21
  • Sentence 4 introduces the conflict between Western Christian concepts and indigenous African tradition.This gives context for the discussion to be followed.
  • Now we can see that Sentence 3 starts with “However….” which implies that this sentence is challenging the views presented in Sentence 4 by asserting the existence of a rich indigenous African cultural ethos. Therefore Sentence 3 must be following Sentence 4.
  • Sentence 2 introduces Chuwkuemeka Ike and provides additional information about Chukwuemeka Ike's exploration of the conflict, adding depth to the discussion. Sentence 1 introduces an example of contemporary African writing that explores the conflict. It makes sense that first we give an example and then elaborate on it. Sentence 1 introduces the book; it is a logical inferences that Ike must be the author of this book.
  • Therefore Sentence 2 must be following Sentence 1.

Therefore the correct order is 4-3-1-2.

CAT 2023 Slot 2: Past Year Question Paper - Question 22

The four sentences (labelled 1, 2, 3 and 4) given 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. Like the ants that make up a colony, no single neuron holds complex information like self-awareness, hope or pride.
  2. Although the human brain is not yet understood enough to identify the mechanism by which emergence functions, most neurobiologists agree that complex interconnections among the parts give rise to qualities that belong only to the whole.
  3. Nonetheless, the sum of all neurons in the nervous system generate complex human emotions like fear and joy, none of which can be attributed to a single neuron.
  4. Human consciousness is often called an emergent property of the human brain.
Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 22
  • Sentence 4 introduces the main idea that human consciousness is often referred to as an emergent property of the human brain. This gives context for the discussion to be followed.
  • Now if we consider Sentences 1 and 3 we can see that Sentence 1 ends with “no single neuron holds complex information like self-awareness, hope or pride.” Sentence 3 builds on the idea in Sentence 1 by stating that, nonetheless, the collective activity of all neurons in the nervous system generates complex human emotions like fear and joy “Nonetheless, the sum of all neurons …..”. So we can infer that Sentence 3 must be following Sentence 1. Sentence 3 also supports the notion that emergent properties arise from the interaction of individual components.
  • Finally, Sentence 2 concludes the paragraph by explaining that although the exact mechanism of emergence in the human brain is not fully understood, neurobiologists agree that complex interconnections among the parts give rise to qualities specific to the whole. This sentence wraps up the discussion and reinforces the concept introduced Sentence 4.
  • Therefore the correct order is 4-1-3-2.
CAT 2023 Slot 2: Past Year Question Paper - Question 23

The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.

Heatwaves are becoming longer, frequent and intense due to climate change. The impacts of extreme heat are unevenly experienced; with older people and young children, those with pre-existing medical conditions and on low incomes significantly more vulnerable. Adaptation to heatwaves is a significant public policy concern. Research conducted among at-risk people in the UK reveals that even vulnerable people do not perceive themselves as at risk of extreme heat; therefore, early warnings of extreme heat events do not perform as intended. This suggests that understanding how extreme heat is narrated is very important. The news media play a central role in this process and can help warn people about the potential danger, as well as about impacts on infrastructure and society.

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 23
  • The passage discusses the increasing frequency and intensity of heatwaves due to climate change, with vulnerable groups experiencing uneven impacts. It emphasizes that adaptation to heatwaves is a significant public policy concern. The research findings suggest that even vulnerable individuals may not perceive themselves as at risk of extreme heat, highlighting the importance of understanding how extreme heat is narrated. The passage specifically mentions the central role of the news media in warning people about the potential danger of heatwaves and their impacts on infrastructure and society. Option C effectively conveys the primary focus on heatwaves posing a substantial risk and the critical role of the media in alerting the public to this danger.
  • Option A implies a general importance of protection without specifically highlighting the role of the media in alerting people to the risks of heatwaves.
  • Option B acknowledges the vulnerability to heatwaves but it does not emphasize the role of the media in alerting people and suggests a broader critique of measures taken.
  • Option D mentions the need for news stories to become more effective but does not emphasize the central role of the media in alerting people to the risk of heatwaves, as the passage does.
CAT 2023 Slot 2: Past Year Question Paper - Question 24

The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.

People spontaneously create counterfactual alternatives to reality when they think “if only” or “what if” and imagine how the past could have been different. The mind computes counterfactuals for many reasons. Counterfactuals explain the past and prepare for the future, they implicate various relations including causal ones, and they affect intentions and decisions. They modulate emotions such as regret and relief, and they support moral judgments such as blame. The ability to create counterfactuals develops throughout childhood and contributes to reasoning about other people's beliefs, including their false beliefs.

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 24
  • The passage discusses the phenomenon of counterfactual thinking, highlighting that people spontaneously create counterfactual alternatives to reality for various reasons. These reasons include explaining the past, preparing for the future, implicating various relations (including causal ones), affecting emotions, and supporting moral judgments. Additionally, the passage mentions that the ability to create counterfactuals develops throughout childhood and contributes to reasoning about other people's beliefs. Option C effectively encompasses these key points, making it the most accurate summary of the passage.
  • Option A focuses primarily on the preparation for the future aspect, neglecting the broader reasons for creating counterfactual alternatives.
  • Option B does not emphasize the developmental aspect and various reasons for creating
  • Option D inaccurately suggests that counterfactual thinking helps reverse past and future actions, which is not the main point of the passage, and it oversimplifies the role of counterfactuals.
CAT 2023 Slot 2: Past Year Question Paper - Question 25

Let a, b, m and n be natural numbers such that a > 1 and b > 1. If ambn = 144145, then the largest possible value of n - m is

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 25

CAT 2023 Slot 2: Past Year Question Paper - Question 26

The sum of all possible values of x satisfying the equation 24x2 - 22x2 + x + 16 + 22x + 30 = 0, is

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 26

CAT 2023 Slot 2: Past Year Question Paper - Question 27

For any natural numbers m, n, and k, such that k divides both m + 2n and 3m + 4n, k must be a common divisor of

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 27

It is given that k divides m+2n and 3m+4n.

Since k divides (m+2n), it implies k will also divide 3(m+2n). Therefore, k divides 3m+6n.

Similarly, we know that k divides 3m+4n.

We know that if two numbers a, and b both are divisible by c, then their difference (a-b) is also divisible by c.

By the same logic, we can say that {(3m+6n)-(3m+4n)} is divisible by k. Hence, 2n is also divisible by k.

Now, (m+2n) is divisible by k, it implies 2(m+2n) =2m+4n is also divisible by k.

Hence, {(3m+4n)-(2m+4n)} = m is also divisible by k.

Therefore, m, and 2n are also divisible by k.

The correct option is C

CAT 2023 Slot 2: Past Year Question Paper - Question 28

Any non-zero real numbers x, y such that y ≠ 3 and will satisfy the condition

Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 28

*Answer can only contain numeric values
CAT 2023 Slot 2: Past Year Question Paper - Question 29

For some positive real number x, if  then the value of 


Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 29

*Answer can only contain numeric values
CAT 2023 Slot 2: Past Year Question Paper - Question 30

The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is


Detailed Solution for CAT 2023 Slot 2: Past Year Question Paper - Question 30

A positive integer less than 50, having exactly two distinct factors other than 1 and itself, is either a perfect cube below 50 or an integer that is a product of exactly two distinct primes.
Case i)
Perfect cubes below 50 are 23 and 33. So, two numbers here
Case ii)
For the product of two primes to be below 50, the individual primes should be below 25.
(Because, the smallest prime is 2 and multiplying 2 with anything greater than or equal to 25 yields a number greater than or equal to 50.)
2, 3, 5, 7, 11, 13, 17, 19, 23 are prime numbers less than 25.

2, 3, 5, 7 are the primes less than √50, any product of two numbers among them yields a product less than 50.
So, there are 4C2 = 6 pairs here.
11, 13, 17, 19, 23 are the primes greater than √50, any product of two numbers among them yields a product greater than 50.
So, there are 0 pairs here.
Between the two lists 11 and 13 can pair with 2 and 3, while 17, 19, and 23 can only pair with 2.
So, there are 7 pairs here.
So, totally, there are 2 + 6 + 0 + 7 = 15 such numbers.

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