Official paper · included in Plus & Pro

CAT 2021 Slot 2 Question Paper with Solutions

66 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 · 19 MCQ · 5 TITA

Reading Comprehension · 16
Verbal Ability · 8

DILR

Data Interpretation & Logical Reasoning

20 questions · 15 MCQ · 5 TITA

Logical Reasoning · 16
Data Interpretation · 4

QA

Quantitative Ability

22 questions · 14 MCQ · 8 TITA

Arithmetic · 10
Algebra · 7
Geometry · 3
Modern Math · 1
Number System · 1

Sample questions with solutions

13 of the 66 questions: the first passage, the first DILR set and the first QA questions of the paper.

VARC · Verbal Ability & Reading Comprehension

Passage

Many people believe that truth conveys power. . . . Hence sticking with the truth is the best strategy for gaining power. Unfortunately, this is just a comforting myth. In fact, truth and power have a far more complicated relationship, because in human society, power means two very different things.

On the one hand, power means having the ability to manipulate objective realities: to hunt animals, to construct bridges, to cure diseases, to build atom bombs. This kind of power is closely tied to truth. If you believe a false physical theory, you won’t be able to build an atom bomb. On the other hand, power also means having the ability to manipulate human beliefs, thereby getting lots of people to cooperate effectively. Building atom bombs requires not just a good understanding of physics, but also the coordinated labor of millions of humans. Planet Earth was conquered by Homo sapiens rather than by chimpanzees or elephants, because we are the only mammals that can cooperate in very large numbers. And large-scale cooperation depends on believing common stories. But these stories need not be true. You can unite millions of people by making them believe in completely fictional stories about God, about race or about economics. The dual nature of power and truth results in the curious fact that we humans know many more truths than any other animal, but we also believe in much more nonsense. . . .

When it comes to uniting people around a common story, fiction actually enjoys three inherent advantages over the truth. First, whereas the truth is universal, fictions tend to be local. Consequently if we want to distinguish our tribe from foreigners, a fictional story will serve as a far better identity marker than a true story. . . . The second huge advantage of fiction over truth has to do with the handicap principle, which says that reliable signals must be costly to the signaler. Otherwise, they can easily be faked by cheaters. . . . If political loyalty is signalled by believing a true story, anyone can fake it. But believing ridiculous and outlandish stories exacts greater cost, and is therefore a better signal of loyalty. . . . Third, and most important, the truth is often painful and disturbing. Hence if you stick to unalloyed reality, few people will follow you. An American presidential candidate who tells the American public the truth, the whole truth and nothing but the truth about American history has a 100 percent guarantee of losing the elections. . . . An uncompromising adherence to the truth is an admirable spiritual practice, but it is not a winning political strategy. . . .

Even if we need to pay some price for deactivating our rational faculties, the advantages of increased social cohesion are often so big that fictional stories routinely triumph over the truth in human history. Scholars have known this for thousands of years, which is why scholars often had to decide whether they served the truth or social harmony. Should they aim to unite people by making sure everyone believes in the same fiction, or should they let people know the truth even at the price of disunity?

Question 1 · MCQ

The central theme of the passage is about the choice between:

A.
truth and power.
B.
leaders who unknowingly spread fictions and those who intentionally do so.
C.
stories that unite people and those that distinguish groups from each other.
D.
attaining social cohesion and propagating objective truth.
✓ Correct

Solution

The central theme of the passage is the tension between propagating objective truth and achieving social cohesion (which relies on shared fictions). The author discusses how fictions are highly effective at uniting people and creating social cohesion, forcing scholars and societies to choose between serving the truth or social harmony. Option 4 perfectly captures this central choice.

Question 2 · MCQ

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

A.
"In fact, truth and power have a far more complicated relationship, because in human society, power means two very different things."
B.
“Hence sticking with the truth is the best strategy for gaining power. Unfortunately, this is just a comforting myth.”
C.
“On the one hand, power means having the ability to manipulate objective realities: to hunt animals, to construct bridges, to cure diseases, to build atom bombs.”
D.
“. . . scholars often had to decide whether they served the truth or social harmony. Should they aim to unite people by making sure everyone believes in the same fiction, or should they let people know the truth . . .?”
✓ Correct

Solution

In Option 4, the author presents a stark binary choice for scholars: either unite people by making sure everyone believes in the same fiction, or let people know the truth at the price of disunity. This overemphasizes the role of fiction by presenting it as the sole means of achieving social harmony and unity, ignoring other potential bases for cohesion.

Question 3 · MCQ

The author would support none of the following statements about political power EXCEPT that:

A.
manipulating people’s beliefs is politically advantageous, but a leader who propagates only myths is likely to lose power.
B.
there are definite advantages to promoting fiction, but there needs to be some limit to a pervasive belief in myths.
C.
while unalloyed truth is not recommended, leaders should stay as close as possible to it.
D.
people cannot handle the unvarnished truth, so leaders retain power by deviating from it.
✓ Correct

Solution

The question asks which statement the author would support (i.e., "support none... EXCEPT"). The passage explicitly states that "the truth is often painful and disturbing" and that a candidate who tells the whole truth has a "100 percent guarantee of losing the elections." Thus, the author supports the idea that people cannot handle the unvarnished truth, and leaders retain power by deviating from it (Option 4).

Question 4 · MCQ

The author implies that, like scholars, successful leaders:

A.
know how to balance truth and social unity.
✓ Correct
B.
use myths to attain the first type of power.
C.
today know how to create social cohesion better than in the past.
D.
need to leverage both types of power to remain in office.

Solution

The passage states that scholars often had to decide whether they served the truth or social harmony. Successful leaders, like scholars, must navigate this tension. To remain successful, they must balance the need for objective truth (to manipulate physical reality, like building weapons or infrastructure) with the need for social unity (which often relies on shared fictions). Thus, they must know how to balance truth and social unity (Option 1).

DILR · Data Interpretation & Logical Reasoning

Set

The different bars in the diagram provide information about different orders in various categories (Art, Binders, ….) that were booked in the first two weeks of September of a store for one client. The colour and pattern of a bar denotes the ship mode (First Class / Second Class / Standard Class). The left end point of a bar indicates the booking day of the order, while the right end point indicates the dispatch day of the order. The difference between the dispatch day and the booking day (measured in terms of the number of days) is called the processing time of the order. For the same category, an order is considered for booking only after the previous order of the same category is dispatched. No two consecutive orders of the same category had identical ship mode during this period.

For example, there were only two orders in the furnishing category during this period. The first one was shipped in the Second Class. It was booked on Sep 1 and dispatched on Sep 5. The second order was shipped in the Standard class. It was booked on Sep 5 (although the order might have been placed before that) and dispatched on Sep 12. So the processing times were 4 and 7 days respectively for these orders. [See diagram in image for data on categories: Art, Binders, Paper, Phones, Appliances, Bookcases, Fasteners, Furnishings, Labels, Tables, Chairs, Accessories, Envelopes, Storage].

Question 1 · TITA (type in the answer)

How many days between Sep 1 and Sep 14 (both inclusive) had no booking from this client considering all the above categories?

Answer: 6

Solution

Based on the chart, we need to find the days between Sep 1 and Sep 14 where no left end point of any bar exists.
Looking at the left end points of all bars across all categories:
Bookings occurred on Sep 1, 2, 3, 5, 6, 8, 9, 11.
No bookings occurred on Sep 4, 7, 10, 12, 13, 14.
Thus, there are 6 days with no bookings.

Question 2 · TITA (type in the answer)

What was the average processing time of all orders in the categories which had only one type of ship mode?

Answer: 5

Solution

Categories with only one type of ship mode (same pattern/color for all bars) are Fasteners (1 order), Labels (1 order), and Envelopes (1 order).
Processing times:
Fasteners: Sep 1 to Sep 6 = 5 days.
Labels: Sep 1 to Sep 2 = 1 day.
Envelopes: Sep 1 to Sep 10 = 9 days.
Average processing time = \( \frac{5 + 1 + 9}{3} = 5 \) days.

Question 3 · MCQ

The sequence of categories -- Art, Binders, Paper and Phones -- in decreasing order of average processing time of their orders in this period is:

A.
Art, Binders, Paper, Phones
B.
Phones, Art, Binders, Paper
C.
Phones, Binders, Art, Paper
D.
Paper, Binders, Art, Phones
✓ Correct

Solution

Calculate average processing times for the given categories:
Art: 5 orders. Total time = (3-1) + (5-3) + (8-5) + (11-8) + (14-11) = 13 days. Average = 13/5 = 2.6 days.
Binders: 4 orders. Total time = (2-1) + (6-2) + (10-6) + (14-10) = 13 days. Average = 13/4 = 3.25 days.
Paper: 3 orders. Total time = (3-1) + (8-3) + (14-8) = 13 days. Average = 13/3 = 4.33 days.
Phones: 4 orders. Total time = (3-1) + (5-3) + (7-5) + (9-7) = 8 days. Average = 8/4 = 2 days.
Decreasing order: Paper, Binders, Art, Phones.

Question 4 · MCQ

Approximately what percentage of orders had a processing time of one day during the period Sep 1 to Sep 22 (both dates inclusive)?

A.
22%
B.
16%
C.
20%
✓ Correct
D.
25%

Solution

Count the total number of orders and those with a processing time of 1 day.
Total orders across all categories = 5 (Art) + 4 (Binders) + 3 (Paper) + 4 (Phones) + 2 (Appliances) + 2 (Bookcases) + 1 (Fasteners) + 2 (Furnishings) + 1 (Labels) + 2 (Tables) + 2 (Chairs) + 2 (Accessories) + 1 (Envelopes) + 2 (Storage) = 33 orders.
Orders with 1 day processing time: Art (1), Binders (1), Phones (1), Labels (1), Tables (1), Chairs (1), Accessories (1) = 7 orders.
Percentage = \( \frac{7}{33} \times 100 \approx 21.21% \), which is approximately 20%.

QA · Quantitative Ability

Question 1 · TITA (type in the answer)

For all possible integers n satisfying \(2.25 \le 2 + 2^{n+2} \le 202\), then the number of integer values of \(3 + 3^{n+1}\) is:

Answer: 7

Solution

Subtracting 2 from all parts of the inequality gives \(0.25 \le 2^{n+2} \le 200\).

Expressing \(0.25\) as a power of 2, we get \(2^{-2} \le 2^{n+2} \le 200\).

Since \(n\) is an integer, \(n+2\) must be an integer. The possible values for \(n+2\) are \(-2, -1, 0, 1, 2, 3, 4, 5, 6, 7\) (since \(2^7 = 128\) and \(2^8 = 256\)).

This gives \(n \in \{-4, -3, -2, -1, 0, 1, 2, 3, 4, 5\}\).

For \(3 + 3^{n+1}\) to be an integer, \(3^{n+1}\) must be an integer, which requires the exponent \(n+1 \ge 0\), meaning \(n \ge -1\).

Filtering our possible values, the valid integers for \(n\) are \(-1, 0, 1, 2, 3, 4, 5\).

There are exactly 7 such values.

Question 2 · MCQ

Three positive integers x, y and z are in arithmetic progression. If \(y - x > 2\) and \(xyz = 5(x + y + z)\), then z-x equals

A.
8
B.
12
C.
14
✓ Correct
D.
10

Solution

Let the three positive integers in the arithmetic progression be \(x = y - d\), \(y\), and \(z = y + d\), where \(d\) is the common difference.

The sum of the terms is \(x + y + z = 3y\), and their product is \(xyz = y(y - d)(y + d) = y(y^2 - d^2)\).

Given \(xyz = 5(x + y + z)\), we have \(y(y^2 - d^2) = 15y\).

Since \(y\) is a positive integer, dividing by \(y\) yields \(y^2 - d^2 = 15\), which factors as \((y - d)(y + d) = 15\).

Since \(x = y - d\) is a positive integer, the possible factor pairs for \((y - d, y + d)\) are \((3, 5)\) and \((1, 15)\).

If \((y - d, y + d) = (3, 5)\), then \(y = 4\) and \(d = 1\). This is rejected because we are given \(y - x = d > 2\).

If \((y - d, y + d) = (1, 15)\), then \(y = 8\) and \(d = 7\), which satisfies \(d > 2\).

Therefore, \(z - x = 2d = 14\).

Question 3 · TITA (type in the answer)

For a 4-digit number, the sum of its digits in the thousands, hundreds and tens places is 14, the sum of its digits in the hundreds, tens and units places is 15, and the tens place digit is 4 more than the units place digit. Then the highest possible 4-digit number satisfying the above conditions is

Answer: 4195

Solution

Let the 4-digit number be \(abcd\).
Given conditions:

\(a + b + c = 14\)
\(b + c + d = 15\)
\(c = d + 4\)

Substitute \(d = c - 4\) into the second equation:
\(b + c + c - 4 = 15 \implies b + 2c = 19\)

Since \(b\) is a single digit (\(b \le 9\)), \(2c = 19 - b \ge 10 \implies c \ge 5\).
To maximize the number \(abcd\), we must maximize the thousands digit \(a\).
From the first equation, \(a = 14 - (b + c)\).

\(c\)	\(b\)	\(a\)	\(d\)	Number
9	1	4	5	4195
8	3	3	4	3384
7	5	2	3	2573
6	7	1	2	1762

(Note: \(c = 5\) gives \(b = 9\) and \(a = 0\), which is invalid for a 4-digit number).

The highest possible 4-digit number satisfying all conditions is 4195.

Question 4 · MCQ

Raj invested ₹ 10000 in a fund. At the end of first year, he incurred a loss but his balance was more than ₹ 5000. This balance, when invested for another year, grew and the percentage of growth in the second year was five times the percentage of loss in the first year. If the gain of Raj from the initial investment over the two year period is 35%, then the percentage of loss in the first year is

A.
5
B.
15
C.
17
D.
10
✓ Correct

Solution

Let the percentage of loss in the first year be \(x%\).
The balance at the end of the first year is \(10000 \times \left(1 - \frac{x}{100}\right)\).
Since this balance is more than ₹ 5000, \(1 - \frac{x}{100} > 0.5 \implies x < 50\).

The percentage of growth in the second year is \(5x%\).
The final balance after two years reflects a 35% overall gain, so it is \(10000 \times 1.35 = 13500\).
\(\left(1 - \frac{x}{100}\right)\left(1 + \frac{5x}{100}\right) = 1.35\)

Let \(y = \frac{x}{100}\):
\((1 - y)(1 + 5y) = 1.35\)
\(1 + 4y - 5y^2 = 1.35\)
\(5y^2 - 4y + 0.35 = 0\)

Multiply by 100 to clear decimals:
\(500y^2 - 400y + 35 = 0 \implies 100y^2 - 80y + 7 = 0\)

Solving the quadratic equation:
\(y = \frac{80 \pm \sqrt{6400 - 2800}}{200} = \frac{80 \pm 60}{200}\)
\(y = 0.7\) or \(y = 0.1\)

Thus, \(x = 70\) or \(x = 10\).
Since \(x < 50\), we must have \(x = 10\).
The percentage of loss in the first year is 10%.

Question 5 · TITA (type in the answer)

The number of ways of distributing 15 identical balloons, 6 identical pencils and 3 identical erasers among 3 children, such that each child gets at least four balloons and one pencil, is

Answer: 1000

Solution

To find the total number of ways, we calculate the number of ways to distribute each type of item independently and multiply them.

Balloons: 15 identical balloons among 3 children, each gets at least 4.

Let \( b_1, b_2, b_3 \) be the number of balloons each child receives.
\( b_1 + b_2 + b_3 = 15 \) with \( b_i \ge 4 \).
Substitute \( b_i' = b_i - 4 \ge 0 \):
\( b_1' + b_2' + b_3' = 15 - 12 = 3 \).
The number of non-negative integer solutions is \( \binom{3+3-1}{3-1} = \binom{5}{2} = 10 \).

Pencils: 6 identical pencils among 3 children, each gets at least 1.

\( p_1 + p_2 + p_3 = 6 \) with \( p_i \ge 1 \).
Substitute \( p_i' = p_i - 1 \ge 0 \):
\( p_1' + p_2' + p_3' = 6 - 3 = 3 \).
The number of non-negative integer solutions is \( \binom{3+3-1}{3-1} = \binom{5}{2} = 10 \).

Erasers: 3 identical erasers among 3 children, no restrictions.

\( e_1 + e_2 + e_3 = 3 \) with \( e_i \ge 0 \).
The number of non-negative integer solutions is \( \binom{3+3-1}{3-1} = \binom{5}{2} = 10 \).

Total number of ways = \( 10 \times 10 \times 10 = 1000 \).

The other 53 questions are in the simulator

Sit CAT 2021 Slot 2 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