CATALYST

Official paper · included in Plus & Pro

CAT 2020 Slot 3 Question Paper with Solutions

68 questions in 120 minutes, in three timed sections. Below: how the paper is built, the topics each section tested, and a solved sample from every section. Take the whole paper in the simulator to get your Score Waterfall, Topic ROI Map and Strategic IQ.

Paper structure and topics

VARC

Verbal Ability & Reading Comprehension

24 questions · 21 MCQ · 3 TITA

  • Reading Comprehension · 18
  • Verbal Ability · 6

DILR

Data Interpretation & Logical Reasoning

22 questions · 15 MCQ · 7 TITA

  • Logical Reasoning · 14
  • Data Interpretation · 8

QA

Quantitative Ability

22 questions · 15 MCQ · 7 TITA

  • Arithmetic · 8
  • Algebra · 7
  • Number System · 4
  • Geometry · 3

Sample questions with solutions

14 of the 68 questions: the first passage, the first DILR set and the first QA questions of the paper.

VARC · Verbal Ability & Reading Comprehension

Passage

[There is] a curious new reality: Human contact is becoming a luxury good. As more screens appear in the lives of the poor, screens are disappearing from the lives of the rich. The richer you are, the more you spend to be off-screen....

The joy — at least at first — of the internet revolution was its democratic nature. Facebook is the same Facebook whether you are rich or poor. Gmail is the same Gmail. And it's all free. There is something mass market and unappealing about that. And as studies show that time on these advertisement-support platforms is unhealthy, it all starts to seem déclassé, like drinking soda or smoking cigarettes, which wealthy people do less than poor people. The wealthy can afford to opt out of having their data and their attention sold as a product. The poor and middle class don't have the same kind of resources to make that happen.

Screen exposure starts young. And children who spent more than two hours a day looking at a screen got lower scores on thinking and language tests, according to early results of a landmark study on brain development of more than 11,000 children that the National Institutes of Health is supporting. Most disturbingly, the study is finding that the brains of children who spend a lot of time on screens are different. For some kids, there is premature thinning of their cerebral cortex. In adults, one study found an association between screen time and depression....

Tech companies worked hard to get public schools to buy into programs that required schools to have one laptop per student, arguing that it would better prepare children for their screenbased future. But this idea isn't how the people who actually build the screen-based future raise their own children. In Silicon Valley, time on screens is increasingly seen as unhealthy. Here, the popular elementary school is the local Waldorf School, which promises a back-to nature, nearly screen-free education. So as wealthy kids are growing up with less screen time, poor kids are growing up with more. How comfortable someone is with human engagement could become a new class marker.

Human contact is, of course, not exactly like organic food.... But with screen time, there has been a concerted effort on the part of Silicon Valley behemoths to confuse the public. The poor and the middle class are told that screens are good and important for them and their children. There are fleets of psychologists and neuroscientists on staff at big tech companies working to hook eyes and minds to the screen as fast as possible and for as long as possible. And so human contact is rare....

There is a small movement to pass a "right to disconnect" bill, which would allow workers to turn their phones off, but for now a worker can be punished for going offline and not being available. There is also the reality that in our culture of increasing isolation, in which so many of the traditional gathering places and social structures have disappeared, screens are filling a crucial void.

Question 1 · MCQ

The author is least likely to agree with the view that the increase in screen-time is fuelled by the fact that:
  1. A.
    there is a growth in computer-based teaching in public schools.
  2. B.
    some workers face punitive action if they are not online.
  3. C.
    with falling costs, people are streaming more content on their devices.
    ✓ Correct
  4. D.
    screens provide social contact in an increasingly isolating world.
Solution
The passage cites three forces increasing screen time: aggressive school-based computer promotion, workers punished for being offline, and screens filling a social void. Falling costs for streaming are never mentioned. Hence, the author is least likely to agree with that as a driver.

Question 2 · MCQ

The author claims that Silicon Valley tech companies have tried to “confuse the public" by:
  1. A.
    promoting screen time in public schools while opting for a screen-free education for their own children.
    ✓ Correct
  2. B.
    pushing for greater privacy while working with advertisement-support platforms to mine data.
  3. C.
    concealing the findings of psychologists and neuroscientists on screen-time use from the public.
  4. D.
    developing new work-efficiency programmes while lobbying for the "right to disconnect" bill.
Solution
The author notes that Silicon Valley firms pushed schools toward one-laptop-per-child programmes while educating their own children at largely screen‑free Waldorf schools. This contradiction is cited directly as the way they confuse the public.

Question 3 · MCQ

The statement “The richer you are, the more you spend to be off-screen” is supported by which other line from the passage?
  1. A.
    "Gmail is the same Gmail. And it's all free."
  2. B.
    "... screens are filling a crucial void."
  3. C.
    "How comfortable someone is with human engagement could become a new class marker."
    ✓ Correct
  4. D.
    “... studies show that time on these advertisement-support platforms is unhealthy.
Solution
The opening statement that wealth buys distance from screens is later echoed by the idea that ease with human engagement—rather than screen‑dependence—will become a new class marker. That line best supports the original claim.

Question 4 · MCQ

Which of the following statements about the negative effects of screen time is the author least likely to endorse?
  1. A.
    It is designed to be addictive.
  2. B.
    It is shown to have adverse effects on young children's learning.
  3. C.
    It increases human contact as it fills an isolation void.
    ✓ Correct
  4. D.
    It can cause depression in viewers.
Solution
The passage describes screen time as purposely addictive, harmful to children’s cognition, and linked to depression. It does not say screens increase human contact; instead it says they fill an isolation void. The author would reject the idea that screen time genuinely boosts human contact.

DILR · Data Interpretation & Logical Reasoning

Set

The Hi-Lo game is a four-player game played in six rounds. In every round, each player chooses to bid Hi or Lo. The bids are made simultaneously. If all four bid Hi, then all four lose 1 point each. If three players bid Hi and one bids Lo, then the players bidding Hi gain 1 point each and the player bidding Lo loses 3 points. If two players bid Hi and two bid Lo, then the players bidding Hi gain 2 points each and the players bidding Lo lose 2 points each. If one player bids Hi and three bid Lo, then the player bidding Hi gains 3 points and the players bidding Lo lose 1 point each. If all four bid Lo, then all four gain 1 point each.

Four players Arun, Bankim, Charu, and Dipak played the Hi-Lo game. The following facts are known about their game:
  1. At the end of three rounds, Arun had scored 6 points, Dipak had scored 2 points, Bankim and Charu had scored -2 points each.
  2. At the end of six rounds, Arun had scored 7 points, Bankim and Dipak had scored -1 point each, and Charu had scored -5 points.
  3. Dipak's score in the third round was less than his score in the first round but was more than his score in the second round.
  4. In exactly two out of the six rounds, Arun was the only player who bid Hi.

Question 1 · MCQ

What were the bids by Arun, Bankim, Charu and Dipak, respectively in the first round?
  1. A.
    Hi, Lo, Lo, Lo
  2. B.
    Lo, Lo, Lo, Hi
  3. C.
    Hi, Hi, Lo, Lo
  4. D.
    Hi, Lo, Lo, Hi
    ✓ Correct
Solution
The first three rounds are uniquely determined:
RoundArunBankimCharuDipakPoints gained
1HiLoLoHiA+2, B–2, C–2, D+2
2HiLoLoLoA+3, B–1, C–1, D–1
3LoLoLoLoall +1
Thus in the first round the bids were Hi, Lo, Lo, Hi.

Question 2 · TITA (type in the answer)

In how many rounds did Arun bid Hi?

Answer: 4

Solution
Arun’s bids across the six rounds:
• Round 1: Hi
• Round 2: Hi
• Round 3: Lo
In the last three rounds we have one all‑Hi (Arun Hi), one round where only Arun bids Hi (Arun Hi), and one round where only Bankim bids Hi (Arun Lo).
So two more Hi bids in R4–R6. Total = 4.

Question 3 · TITA (type in the answer)

In how many rounds did Bankim bid Lo?

Answer: 4

Solution
Bankim’s bids:
• Round 1: Lo
• Round 2: Lo
• Round 3: Lo
In the last three rounds: all‑Hi (Bankim Hi), Arun‑only‑Hi (Bankim Lo), Bankim‑only‑Hi (Bankim Hi).
Thus exactly one more Lo. Total Lo bids = 4.

Question 4 · TITA (type in the answer)

In how many rounds did all four players make identical bids?

Answer: 2

Solution
Identical bids occur only in all‑Lo or all‑Hi rounds.
After 3 rounds total points = 4 → exactly one all‑Lo round in the first 3 rounds and no all‑Hi.
After 6 rounds total points = 0 → number of all‑Lo = number of all‑Hi overall.
Hence the all‑Hi round must be in the last 3 rounds.
Thus there is 1 all‑Lo + 1 all‑Hi = 2 rounds with all four players making identical bids.

Question 5 · TITA (type in the answer)

In how many rounds did Dipak gain exactly 1 point?

Answer: 1

Solution
Dipak’s round‑wise scores from the deduced order:
RoundTypeDipak’s score
1Arun & Dipak Hi (type 2)+2
2Arun sole Hi (type 1)−1
3All Lo (type 0)+1
4–6All Hi / Arun sole Hi / Bankim sole Hi−1 each
He gains exactly 1 point only in round 3.
Hence the answer is 1 round.

QA · Quantitative Ability

Question 1 · MCQ

If \(\log_2 30 = A\), \(\log_a (5 / 3) = -B\) and \(\log_2 a = 1/3\), then \(\log_3 a\) equals
  1. A.
    \(\frac{2}{A+B-3}\)
  2. B.
    \(\frac{A+B-3}{2}\)
  3. C.
    \(\frac{2}{3A+B-3}\)
    ✓ Correct
  4. D.
    \(\frac{A+B-3}{2}\)
Solution
Let \(a = 2^{1/3}\).
From \(\log_a (5/3) = -B\), we get \(2^{-B/3} = 5/3\).
\(\log_2 30 = A\) gives \(2^{A-1} = 3 \cdot 5\).
Substitute \(5 = 3 \cdot 2^{-B/3}\) into the previous:
\(2^{A-1} = 3 \cdot (3 \cdot 2^{-B/3}) = 3^2 \cdot 2^{-B/3}\)
\(\Rightarrow 2^{A-1+B/3} = 3^2 \Rightarrow 2^{\frac{A-1+B/3}{2}} = 3\).
Hence \(\log_2 3 = \frac{A-1+B/3}{2}\).
Then \(\log_3 a = \frac{\log_2 a}{\log_2 3} = \frac{1/3}{(A-1+B/3)/2} = \frac{2}{3A+B-3}\).

Question 2 · TITA (type in the answer)

Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick's age is 1 year less than the average age of all three, then Harry's age, in years, is

Answer: 18

Solution
Let Tom’s age = \(T\).
Dick = \(3T\), Harry = \(6T\).
Average = \((T + 3T + 6T)/3 = 10T/3\).
Given: \(3T = \frac{10T}{3} - 1 \Rightarrow 9T = 10T - 3 \Rightarrow T = 3\).
Harry = \(6 \times 3 = 18\).

Question 3 · MCQ

A and B are two railway stations 90 km apart. A train leaves A at 9:00 am, heading towards B at a speed of 40 km/hr. Another train leaves B at 10:30 am, heading towards A at a speed of 20 km/hr. The trains meet each other at
  1. A.
    11:45 am
  2. B.
    10:45 am
  3. C.
    11:20 am
  4. D.
    11:00 am
    ✓ Correct
Solution
Train from A starts at 9:00 am, speed = 40 km/hr.
By 10:30 am, it travels for 1.5 hr, covering 40 × 1.5 = 60 km.
Remaining distance between trains at 10:30 am = 90 – 60 = 30 km.
Relative speed when moving towards each other = 40 + 20 = 60 km/hr.
Time to meet after 10:30 am = 30/60 = 0.5 hr = 30 min.
Meeting time = 10:30 am + 30 min = 11:00 am.

Question 4 · MCQ

Let k be a constant. The equations \(kx + y = 3\) and \(4x + ky = 4\) have a unique solution if and only if
  1. A.
    \(|k| \ne 2\)
    ✓ Correct
  2. B.
    \(|k| = 2\)
  3. C.
    \(k \ne -2\)
  4. D.
    \(k = 2\)
Solution
For the system to have a unique solution, the determinant must be non-zero:
\( \begin{vmatrix} k & 1 \\ 4 & k \end{vmatrix} = k^2 - 4 \neq 0 \)
\(\Rightarrow k \neq 2\) and \(k \neq -2\).
Thus, the correct condition is \(k \neq \pm 2\).
Option 1 (\(|k| \neq 2\)) is correct; option 3 (\(k \neq -2\)) is incomplete; option 2 (\(|k| = 2\)) is the opposite; option 4 (\(k = 2\)) is incorrect.

Question 5 · MCQ

If \(x_1 = -1\) and \(x_m = x_{m+1} + (m +1)\) for every positive integer \(m\), then \(x_{100}\) equals
  1. A.
    -5151
  2. B.
    -5150
  3. C.
    -5051
  4. D.
    -5050
    ✓ Correct
Solution
Rewrite recurrence: \(x_{m} = x_{m+1} + (m+1) \implies x_{m+1} = x_m - (m+1)\).

Then \(x_n = x_1 - (2+3+\cdots+n) = -1 - \left[\frac{n(n+1)}{2} - 1\right] = -\frac{n(n+1)}{2}\).

For \(n=100\): \(x_{100} = -\frac{100 \times 101}{2} = -5050\).

The other 54 questions are in the simulator

Sit CAT 2020 Slot 3 with the real exam's timer and interface, then see where your marks went: silly slips, traps, topics that cost you time, and the questions you should have skipped. Start with the free mock test: no payment needed.

Unlock this paper