CAT 50 Day Streak Day 35

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CAT 50 Day Streak – Day 35

30 questions across VARC, DILR & QA · +3 for a correct answer · −1 for a wrong MCQ · no negative marking for TITA

0/30Attempted

0Correct

0Wrong

0Score / 90

VARC · Verbal Ability & Reading Comprehension

Q1 – Q10 0/10

Passage · Q1 – Q4

In a blog on ‘Epistemic Relativism’ (2021), Francis Fukuyama writes: ‘We who live in modern liberal societies have necessarily accepted a certain degree of moral relativism.’ Fukuyama does not comment on whether this is a good or bad thing, but chastises postmodernist writers who espouse relativism regarding ‘assertions of fact concerning the outside world’. Fukuyama identifies the rise of epistemic relativism with writers who followed Friedrich Nietzsche, but these themes are present in Outlines of Pyrrhonism. Bracketing from the question of chronology, is Fukuyama right that relativism is a problem?

A quick reply is that sceptics eschew the term relativism. Sceptics do not maintain that truth changes depending on time or place. In 1933, the German philosopher Martin Heidegger believed in the inner truth and greatness of the National Socialist cause. Heidegger is a relativist but not a sceptic.

To the larger point that epistemic relativism is a problem, sceptics maintain that they do have criteria to make decisions about facts in the world or how to treat other people. These are, according to Sextus, ‘the guidance of nature, the compulsion of the feelings, the tradition of laws and customs, and the instruction of the arts’. For Sextus, nature and culture are the soil from which our ethical dispositions grow. Sceptics may be kind to children, help their neighbours, and build institutions that reflect the values of their culture.

And there are many examples of cruel dogmatists.

In one of Sextus’ surviving manuscripts titled Against the Ethicists, he addresses the question of what a sceptic will do if a tyrant commands a forbidden act. The sceptic ‘will choose one thing, perhaps, and avoid the other by the preconception which accords with his ancestral laws and customs’ and will ‘bear the harsh situation more easily compared with the dogmatist’. Aha! For critics of scepticism such as Martha Nussbaum, this seems like evidence that sceptics are passive in the face of injustice. They don’t even know whether they will fight tyrants!

Rising to Sextus’ defence, the political scientist John Christian Laursen argues that sceptics can grow up in cultures that believe in watering the tree of liberty with the blood of tyrants, and sceptics can have a burning hatred for tyrants. Sceptics can possess energy, commitment, and concern about the political order. ‘One can be committed without a chain of truths to support one’s actions.’ And, of course, dogmatists can also support tyrants who murder people who disagree with them.

Fukuyama wants people to agree on facts about the outside world. But intelligent people can look at those supposed facts in a variety of ways. Grass is green. Except at night, when it appears black. Sceptics can make arguments like that for a long time. Sceptics encourage us to live our lives in less frustrating ways than demanding something that humans do not and may not ever possess: truth.

Q1MCQ

According to the passage, what is the fundamental difference between epistemic relativism and scepticism?

AScepticism maintains that truth is constant, while epistemic relativism maintains that truth is relative.

BEpistemic relativism is about the assertion of facts about the outside world, while scepticism does not believe in facts.

CScepticism opposes the idea of truth, while epistemic relativism believes that something can be true only within a particular individual’s or culture’s perspective, but not absolutely or universally.

DEpistemic relativism and scepticism have no fundamental difference since both believe that truth is not absolute or universal but according to an individual’s culture.

Solution Answer: C

A relativist holds that truth varies with time, place or perspective; Heidegger believed in the “inner truth” of a cause. Sceptics reject that view and doubt that humans can possess truth at all, which the closing line makes clear. C captures this difference.

A: sceptics don’t claim truth is constant; they doubt we can have it. B: sceptics do have criteria for deciding about facts in the world. D: the passage separates the two explicitly (“Heidegger is a relativist but not a sceptic”).

Q2MCQ

The author of the passage is likely to support which one of the following statements?

AFukuyama is opposed to the moral relativism found in liberal modern societies.

BSceptics can make arguments about the truth for which there is no definitive answer.

CSceptics can tackle harsh situations better than dogmatists can.

DSceptics can be acquiescent in the face of inequity or unfairness.

Solution Answer: B

The grass example (green by day, black at night) shows a sceptic arguing over a supposed fact with no definitive resolution. The author adds that sceptics “can make arguments like that for a long time”.

A: Fukuyama “does not comment on whether this is a good or bad thing”. C is Sextus’ claim, which the author reports rather than endorses. D is the critics’ charge, which the author rebuts through Laursen.

Q3MCQ

From the passage, we can infer that the author is in favour of

Amore scepticism

Bmorals according to culture

Ca belief in the fact that truth can be objective

Da belief in some cause or ideology

Solution Answer: A

The author defends sceptics against the charges of relativism and passivity, and closes by saying sceptics help us live “in less frustrating ways”. That is an endorsement of scepticism.

B: culture appears as one of Sextus’ criteria, not as the author’s stated position. C contradicts the closing doubt about truth. D: committed belief in a cause is what the dogmatist examples illustrate.

Q4MCQ

Regarding which one of the following quotes could we argue that the author overemphasises the importance of scepticism?

AA quick reply is that sceptics eschew the term relativism.

BSceptics do not maintain that truth changes depending on time or place.

CThe sceptic ‘will choose one thing, perhaps, and avoid the other by the preconception which accords with his ancestral laws and customs’ and will ‘bear the harsh situation more easily compared with the dogmatist.

DSceptics encourage us to live our lives in less frustrating ways than demanding something that humans do not and may not ever possess: truth.

Solution Answer: D

D is the author’s own sweeping claim that scepticism offers a less frustrating way to live. It also asserts that humans may never possess truth. This broad, value-laden conclusion is where the author could be accused of overselling scepticism.

A and B are neutral descriptions of what sceptics hold. C quotes Sextus, not the author’s own claim.

Q5TITA

Sentences given in the questions below, when properly sequenced, form a coherent paragraph. The first and last sentences are A and F, and the four in between are labelled 1, 2, 3, and 4. Choose the most logical order of these four sentences to construct a coherent paragraph from sentences A to F.

Imagine setting off a single domino and watching as one by one, each piece tumbles effortlessly.
This idea might sound simple, yet it’s incredibly potent when applied to understanding new words and phrases.
It’s a principle that not only applies to physical dominos but also to our everyday language and interactions.
Just as one domino can initiate a chain reaction, learning a new term can unlock a series of connections and insights in your language journey.
This simple action captures the essence of the domino effect, a powerful concept that shows how one small move can lead to significant changes.
And today, we’re focusing on one such term: the domino effect.

Solution Answer: 4213

The order runs like this:

4: “This simple action” (toppling the domino in A) captures the domino effect.
2: “It’s a principle” that also applies to language.
1: “This idea” is potent for learning new words.
3: Just as one domino starts a chain, one new term unlocks connections, which leads into F’s “one such term”.

Q6MCQ

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 Similarly, disorienting is the fact that these visions and pontifications are driving change in the real world.

Paragraph What exactly is a person, listening in their car on the way to the grocery store, to make of conversations like this? ___(1)___. Surely, there’s a cohort that finds covering the Earth or atmosphere with data centers very exciting. ___(2)___. But what about those of us who don’t? Altman and lesser personalities in the AI space often talk this way, making extreme, matter-of-fact proclamations about the future and sounding like kids playing a strategy game. ___(3)___. This isn’t a business plan; it’s an idle daydream. ___(4)___.

AOption 1

BOption 2

COption 3

DOption 4

Solution Answer: D (Option 4)

“These visions and pontifications” needs an antecedent, and that is the “extreme, matter-of-fact proclamations about the future” called “an idle daydream”. After that dismissal, the sentence adds a second unsettling point: these daydreams are actually changing the real world.

At blanks 1 and 2 the proclamations haven’t been mentioned yet. At blank 3 the sentence would split the proclamations from the author’s verdict on them (“This isn’t a business plan”).

Q7TITA

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.

There is, however, a third type of reason why philosophical writing is often inaccessible, and it is that the author consciously intends it to be so.
These commentators did accept that intentional obscurity can be commendable if it is designed to stimulate the reader to learn through grappling with the text.
This was recognised by the scholars of Ancient Greece and Rome, and those of the Middle Ages, who commented on the treatises of Plato and Aristotle.
They symbolised this sort of obscurantism with the cuttlefish, which discharges ink to cloud the water around it.
These commentators criticised writing in which the intentional obscurity was designed to prevent readers from understanding or refuting it.

Solution Answer: 2

The coherent paragraph is 1 → 3 → 5 → 4:

1: A third reason for inaccessible writing: deliberate obscurity.
3: “This was recognised” by ancient and medieval commentators.
5: “These commentators criticised” obscurity meant to block understanding or refutation.
4: “They symbolised this sort of obscurantism” with the cuttlefish.

Sentence 2 praises a commendable kind of obscurity. The paragraph is a single line of criticism, and “this sort of obscurantism” in 4 has to point straight back to the criticised kind in 5.

Q8TITA

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.

The shift suggests that gathering people’s online data for targeted advertising is not going away.
The internet industry shuddered last year when Apple introduced privacy measures for the iPhone that threatened to upend online tracking and cripple digital advertising and Google pledged similar privacy actions.
And it is having the unintended effect of reinforcing the power of some of tech’s biggest titans.
But in less than a year, another type of internet tracking has started taking over.

Solution Answer: 2431

The order runs like this:

2: Apple’s and Google’s privacy moves threatened online tracking.
4: “But in less than a year”, a new kind of tracking took over.
3: “And it” (the new tracking) is reinforcing the big tech titans.
1: “The shift” shows that data gathering for ads isn’t going away.

Q9MCQ

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

Passage Hollywood representation—the idea that people from marginalised communities should have a place in mass pop culture—has never been particularly high up on my list of political priorities. Let me first get the caveats out of the way: I think it’s nice to have an underrepresented name on the marquees. I do believe a person’s stake in this country is tied, in some part, to whether they see themselves in the broader culture. And I agree that it would also be great if awards shows in the past had done a better job of celebrating the work of minority artists. My objection is mostly one of proportion. I just think we probably make too big a deal out of Hollywood representation.

AThe representation of marginalised communities in mass pop culture has been given undue importance.

BToo much importance has been given to the representation of marginalised communities in mass pop culture, although this representation is required.

CAlthough it is nice to have a representation of marginalised communities in Hollywood, this representation of minorities in mass pop culture has gone too far.

DAlthough it would be nice to have representation from marginalised communities in mass pop culture, it is not a political priority.

Solution Answer: B

The author grants that representation matters (a person’s stake in the country is tied to seeing themselves in the culture) but objects “mostly” on proportion: we make “too big a deal” of it. B keeps both the main point and the concession.

A drops the caveats. C says representation itself “has gone too far”, but the complaint is about how much we fuss over it. D focuses on the author’s personal priority list and misses the proportion argument.

Q10TITA

Instead, most students, I believe, want to search for moments of solidarity with people from different backgrounds despite the pressures placed upon them to turn their life stories into cultural capital.
But I do not understand how the trauma algorithms that currently exist at elite institutions advance any of these conversations.
I just think there is a way in which the denial of one’s hardships constitutes a far more insidious form of dishonesty.
We should talk about privilege and systemic racism and the ways in which the history of violence against Black, Latino, Native American, and Asian people in this country still shapes their lives today.
A compassionate society, especially one with as much inequality as the United States, should talk about discrimination and the very real ways some people’s lives are harder than others.

Solution Answer: 3

The coherent paragraph is 5 → 4 → 2 → 1:

5: A compassionate society should talk about discrimination.
4: “We should talk about” privilege and systemic racism.
2: “But” trauma algorithms at elite institutions don’t advance “these conversations”.
1: “Instead”, students want moments of solidarity.

Sentence 3 is about denying one’s own hardships as a form of dishonesty. The paragraph is about how institutions handle conversations about inequality, and nothing in it sets up that point.

DILR · Data Interpretation & Logical Reasoning

Q11 – Q20 0/10

Set 1 · Q11 – Q15

Glassy, a bar in a city, serves beers of only 3 brands - Kingfisher, Budweiser and Carlsberg. Last Friday, not all the customers necessarily drank beers, but those who did had at least one of the 3 brands. Further, some of the observations were as follows:

The number of customers who drank only Carlsberg was twice the number of customers who drank only Budweiser.
The number of customers who drank both Carlsberg and Budweiser was 24 more than twice the number of customers who drank only Budweiser and Kingfisher.
The number of customers who drank only Kingfisher and Carlsberg was 28.
For every 3 customers who drank only Kingfisher, there was 1 customer who drank only Carlsberg and Budweiser.
For every 3 customers who drank Carlsberg, there was 1 customer who drank Budweiser and Carlsberg.
For every 3 customers who drank Budweiser, there was 1 customer who drank Kingfisher and Budweiser.

Q11TITA

What can be the minimum number of customers who visited the bar on Friday?

Solution Answer: 133

Variables. Only K = k, only B = b, only C = 2b, only C&B = x, only B&K = y, only K&C = 28, all three = t. From the ratio clue, k = 3x.
Carlsberg ratio. 2b + x + 28 + t = 3(x + t), which gives b = x + t − 14.
C&B clue. x + t = 24 + 2y, so b = 10 + 2y.
Budweiser ratio. b + x + y + t = 3(y + t), which gives x = 2t − 10, and then y = (3t − 34)/2.
Everything in terms of t. k = 6t − 30, b = 3t − 24, only C = 6t − 48, and beer drinkers = (39t − 202)/2. For y to be a non-negative whole number, t must be even and at least 12.

t (all 3)	Only K	Only B	Only C	Only C&B	Only B&K	Only K&C	Drinkers
12	42	12	24	14	1	28	133
14	54	18	36	18	4	28	172
16	66	24	48	22	7	28	211
18	78	30	60	26	10	28	250

With t = 12 and no non-drinkers, the minimum number of customers is 133.

Q12MCQ

If 172 customers visited the bar on Friday, how many people had only Kingfisher?

A42

B45

C54

D60

Solution Answer: C

Detailed solution coming soon.

Q13MCQ

If 250 customers visited the bar on Friday, what could be the minimum number of customers who did not drink any of the 3 beers?

Solution Answer: A

From the table in Q11, t = 18 gives exactly 250 beer drinkers. Everyone could have drunk beer, so the minimum number of non-drinkers is 0.

Q14MCQ

Which of the following could be a possible number of customers who drank exactly 2 of the 3 brands of beers?

A40

B50

C60

D70

Solution Answer: B

From the table in Q11, exactly two brands = only C&B + only B&K + only K&C. That is 43 (t = 12), 50 (t = 14), 57 (t = 16), 64 (t = 18), 71 (t = 20), and so on. Of the options, only 50 appears.

Q15MCQ

What is the difference between the number of customers who drank only Kingfisher and the number of customers who drank only Carlsberg?

A18

B16

C24

DCannot be determined

Solution Answer: A

From Q11, only K − only C = (6t − 30) − (6t − 48) = 18, whatever the value of t.

Set 2 · Q16 – Q20

Tendulkar played 10 innings in which his scores were 27, 32, 37, 46, 52, 57, 62, 76, 78, and 143, not in this order. An interesting thing was noticed, that after each innings, his average was an integer. When asked about the hints to figure out the runs scored by him in different innings, he gave just two more hints:

His average after 7th and 9th innings was the same. After no other innings, he had that same average.
He did not score more than 50 in his first two innings.

Q16MCQ

What is his average after the 6th innings?

A62

B68

C65

D67

Solution Answer: D

Innings 10. The total is 610. The sum after 9 innings must be divisible by 9, and 610 ≡ 7 (mod 9), so innings 10 ≡ 7 (mod 9). That makes it 52. S₉ = 558, average 62.
Innings 8 and 9. S₇ = 7 × 62 = 434, so innings 8 + 9 = 124 = 46 + 78. Both orders work: 480/8 = 60 and 512/8 = 64.
Innings 7. S₆ = 434 − s₇ must be divisible by 6, so s₇ is 32 or 62. If s₇ = 62, the 6th-innings average would also be 62, which breaks hint (i). So s₇ = 32 and S₆ = 402.
Innings 1–6. By hint (ii), innings 1 and 2 are 27 and 37 (S₂ = 64). Then s₃ must make S₃ divisible by 3, so s₃ = 143. Divisibility by 4 gives s₄ = 57, by 5 gives s₅ = 76, and s₆ = 62.

Innings	1	2	3	4	5	6	7	8	9	10
Score	27 / 37	37 / 27	143	57	76	62	32	46 / 78	78 / 46	52
Average	27 / 37	32	69	66	68	67	62	60 / 64	62	61

Average after the 6th innings = 402/6 = 67.

Q17TITA

For how many innings can we uniquely determine his score?

Solution Answer: 6

From the table in Q16, innings 3, 4, 5, 6, 7 and 10 are fixed. Innings 1–2 and 8–9 can each be swapped. The answer is 6.

Q18MCQ

What was his score in the 4th innings?

A76

B57

C62

DCannot be determined

Solution Answer: B

From the table in Q16, the 4th innings score is 57.

Q19MCQ

In which innings did he get the highest score?

A3rd

B4th

C5th

D6th

Solution Answer: A

From the table in Q16, his highest score of 143 came in the 3rd innings.

Q20MCQ

What could be his maximum average at the end of the 8th innings?

A60

B61

C64

D65

Solution Answer: C

From Q16, the 8th innings is 46 or 78. With 78: (434 + 78)/8 = 512/8 = 64.

QA · Quantitative Ability

Q21 – Q30 0/10

Q21MCQ

What is the length of the common chord of two circles whose radii are 18 cm and 24 cm and whose centres are 30 cm apart?

A28.8 cm

B25.6 cm

C26.4 cm

D27.2 cm

Solution Answer: A

18² + 24² = 900 = 30², so the two radii drawn to an intersection point meet at a right angle. The half-chord is the altitude of this right triangle onto the hypotenuse: 18 × 24/30 = 14.4.

Common chord = 2 × 14.4 = 28.8 cm.

Q22TITA

A teacher asked the students to find the average of the first ‘N’ natural numbers. Mridul got an average of 60524, which was incorrect as he had missed a number. Find the difference between ‘N’ and the number he missed.

Solution Answer: 85

Mridul divided (sum − missed number) by N and got 1445/24, so N is a multiple of 24. The true average (N + 1)/2 must be a little above 60, so N = 120.

The true sum is 120 × 121/2 = 7260. His sum is 120 × 1445/24 = 7225. The missed number is 35.

N − 35 = 120 − 35 = 85.

Q23MCQ

If the solutions of the equation x² + 2x − 24 = 0 are factors of the equation 3x³ − ax² − 74x + p = 0, find the sum a + p.

A16

B19

C29

D37

Solution Answer: B

The roots of x² + 2x − 24 = 0 are 4 and −6.

At x = 4: 192 − 16a − 296 + p = 0, so p − 16a = 104. At x = −6: −648 − 36a + 444 + p = 0, so p − 36a = 204.

Subtracting: 20a = −100, so a = −5 and p = 24. a + p = 19.

Q24MCQ

There are three taps, A, B, and C, which are attached to a tank. Each tap fills the tank in 12 minutes, 15 minutes, and 18 minutes, respectively. The mechanism of the taps is set in such a way that each tap, starting with A, is turned on exactly for a minute. B is then turned on for a minute, then C, and the cycle repeats. Find the delay in the time if C acts as a draining tap instead of a filling tap.

A14 minutes

B14.5 minutes

C15 minutes

D15.5 minutes

Solution Answer: B

Take the tank as 180 units: A = 15, B = 12 and C = 10 units per minute.

All filling: 37 units per 3-minute cycle. After 4 cycles (12 min) the tank holds 148. A brings it to 163 and B to 175, and C needs half a minute for the last 5 units. Time = 14.5 min.

C draining: 17 units per cycle. After 9 cycles (27 min) the tank holds 153. A brings it to 168 and B fills it exactly at 29 min. (Earlier cycles never reach 180, since the peak in cycle 9 is 163.)

Delay = 29 − 14.5 = 14.5 minutes.

Q25TITA

A devotee is climbing a flight of steps to reach a hilltop temple. She climbs 54 steps in the first minute, but her speed decreases by 2 steps per minute thereafter. If she has completed 60% of the total ascent in 10 minutes, after how many minutes will she have completed 80% of the total steps?

Solution Answer: 15

Steps in 10 minutes = 10/2 × (108 − 18) = 450, which is 60% of the total, so the total is 750. 80% is 600 steps.

Steps in n minutes = n/2 × (108 − 2(n − 1)) = n(55 − n) = 600. So n² − 55n + 600 = 0, giving n = 15 or 40. She first reaches 80% at 15 minutes.

Q26MCQ

Which of the following statements is/are true?

Four consecutive integers can add up to a perfect square.
Four consecutive integers can add up to a perfect cube.

ABoth I and II

BOnly I

COnly II

DNeither I nor II

Solution Answer: D

n + (n + 1) + (n + 2) + (n + 3) = 4n + 6, which leaves remainder 2 on division by 4.

A perfect square leaves remainder 0 or 1 on division by 4. A perfect cube is either odd or a multiple of 8, so it leaves 0, 1 or 3. Neither can leave 2, so neither I nor II is possible.

Q27MCQ

A state has 20 cities and 130 roads, where each road directly connects precisely two cities. What is the largest possible number of cities that are directly connected to every other city?

A10

Solution Answer: C

If k cities connect to every other city, they need C(k, 2) roads among themselves plus k(20 − k) roads to the rest.

k = 8: 28 + 96 = 124 ≤ 130 ✓. k = 9: 36 + 99 = 135 > 130 ✗. The largest possible number is 8.

Q28TITA

In the figure given below, ABCDEF is a regular hexagon and ∠AOF = 90°. How many triangles of size AOF can fit into trapezium ABCF?

Regular hexagon ABCDEF with O on the line from F toward C, directly below A, so that AO is perpendicular to FO and triangle AOF is right-angled at O

Solution Answer: 6

Let the side be s. In triangle AOF, ∠AFO = 60°, so FO = s/2 and AO = (√3/2)s. Area of AOF = ½ × s/2 × (√3/2)s = √3s²/8.

Trapezium ABCF is half the hexagon: ½ × (3√3/2)s² = 3√3s²/4.

Ratio = (3/4) ÷ (1/8) = 6.

Q29MCQ

Savita can knit sweaters of 2 sizes. She can knit a sweater of the smaller size in 5 days. The bigger sweater is 40% bigger than the smaller sweater. If she gets an order of 40 smaller sweaters and 30 bigger sweaters, then find the percentage of more/less time required by Savita to knit the bigger sweaters than the smaller sweaters.

A4% less

B5% more

C8% more

D10% less

Solution Answer: B

A bigger sweater takes 5 × 1.4 = 7 days. Smaller order: 40 × 5 = 200 days. Bigger order: 30 × 7 = 210 days.

The bigger sweaters take 10/200 × 100 = 5% more time.

Q30MCQ

If log₁₀ x + 2 log₁₀ y = 1, and x − 3y² = 13, find the product xy.

A4√5

B2√13

C5√6