Official paper · included in Plus & Pro

CAT 2020 Slot 2 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 · 13
Data Interpretation · 9

QA

Quantitative Ability

22 questions · 15 MCQ · 7 TITA

Arithmetic · 10
Algebra · 8
Geometry · 3
Number System · 1

Sample questions with solutions

13 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

Aggression is any behavior that is directed toward injuring, harming, or inflicting pain on another living being or group of beings. Generally, the victim(s) of aggression must wish to avoid such behavior in order for it to be considered true aggression. Aggression is also categorized according to its ultimate intent. Hostile aggression is an aggressive act that results from anger, and is intended to inflict pain or injury because of that anger. Instrumental aggression is an aggressive act that is regarded as a means to an end other than pain or injury. For example, an enemy combatant may be subjected to torture in order to extract useful intelligence, though those inflicting the torture may have no real feelings of anger or animosity toward their subject. The concept of aggression is very broad, and includes many categories of behavior (e.g., verbal aggression, street crime, child abuse, spouse abuse, group conflict, war, etc.). A number of theories and models of aggression have arisen to explain these diverse forms of behavior, and these theories/models tend to be categorized according to their specific focus. The most common system of categorization groups the various approaches to aggression into three separate areas, based upon the three key variables that are present whenever any aggressive act or set of acts is committed. The first variable is the aggressor him/herself. The second is the social situation or circumstance in which the aggressive act(s) occur. The third variable is the target or victim of aggression.

Regarding theories and research on the aggressor, the fundamental focus is on the factors that lead an individual (or group) to commit aggressive acts. At the most basic level, some argue that aggressive urges and actions are the result of inborn, biological factors. Sigmund Freud (1930) proposed that all individuals are born with a death instinct that predisposes us to a variety of aggressive behaviors, including suicide (self directed aggression) and mental illness (possibly due to an unhealthy or unnatural suppression of aggressive urges). Other influential perspectives supporting a biological basis for aggression conclude that humans evolved with an abnormally low neural inhibition of aggressive impulses (in comparison to other species), and that humans possess a powerful instinct for property accumulation and territorialism. It is proposed that this instinct accounts for hostile behaviors ranging from minor street crime to world wars. Hormonal factors also appear to play a significant role in fostering aggressive tendencies. For example, the hormone testosterone has been shown to increase aggressive behaviors when injected into animals. Men and women convicted of violent crimes also possess significantly higher levels of testosterone than men and women convicted of nonviolent crimes. Numerous studies comparing different age groups, racial/ethnic groups, and cultures also indicate that men, overall, are more likely to engage in a variety of aggressive behaviors (e.g., sexual assault, aggravated assault, etc.) than women. One explanation for higher levels of aggression in men is based on the assumption that, on average, men have higher levels of testosterone than women.

Question 1 · MCQ

The author identifies three essential factors according to which theories of aggression are most commonly categorised. Which of the following options is closest to the factors identified by the author?

A.
Psychologically – Sociologically – Medically.
B.
Aggressor – Circumstances of aggression – Victim.
✓ Correct
C.
Extreme – Moderate – Mild.
D.
Hostile – Instrumental – Hormonal.

Solution

The passage states: 'The most common system of categorization groups the various approaches to aggression into three separate areas, based upon the three key variables … The first variable is the aggressor him/herself. The second is the social situation or circumstance … The third variable is the target or victim of aggression.' This directly matches option 2.

Question 2 · MCQ

The author discusses all of the following arguments in the passage EXCEPT that:

A.
men in general are believed to be more hormonally driven to exhibit violence than women.
B.
several studies indicate that aggression may have roots in the biological condition of humanity.
C.
the nature of aggression can vary depending on several factors, including intent.
D.
aggression in most societies is kept under control through moderating the death instinct identified by Freud.
✓ Correct

Solution

Options 1, 2, and 3 are discussed: hormone-driven violence in men (testosterone), biological roots (low neural inhibition), and varying nature by intent (hostile vs instrumental). Option 4 is not discussed. The passage mentions Freud's death instinct and suppression of aggressive urges only in the context of mental illness, not societal control through moderating the death instinct.

Question 3 · MCQ

All of the following statements can be seen as logically implied by the arguments of the passage EXCEPT:

A.
the Freudian theory of suicide as self-inflicted aggression implies that an aggressive act need not be sought to be avoided in order for it to be considered aggression.
B.
a common theory of aggression is that it is the result of an abnormally low neural regulation of testosterone.
✓ Correct
C.
if the alleged aggressive act is not sought to be avoided, it cannot really be considered aggression.
D.
Freud’s theory of aggression proposes that aggression results from the suppression of aggressive urges.

Solution

Option 2 is not implied. The passage separately mentions 'abnormally low neural inhibition of aggressive impulses' and the role of testosterone, but never combines them into a theory about low neural regulation of testosterone. Options 1, 3, and 4 are logically implied: 1 follows from Freud's inclusion of suicide as aggression despite the victim’s possible non-avoidance; 3 restates the passage’s definition; 4 is implied by the discussion of suppression and mental illness.

Question 4 · MCQ

“[A]n enemy combatant may be subjected to torture in order to extract useful intelligence, though those inflicting the torture may have no real feelings of anger or animosity toward their subject.” Which one of the following best explicates the larger point being made by the author here?

A.
Information revealed by subjecting an enemy combatant to torture is not always reliable because of the animosity involved.
B.
When an enemy combatant refuses to reveal information, the use of torture can sometimes involve real feelings of hostility.
C.
In certain kinds of aggression, inflicting pain is not the objective, and is no more than a utilitarian means to achieve another end.
✓ Correct
D.
The use of torture to extract information is most effective when the torturer is not emotionally involved in the torture.

Solution

The author uses the example to illustrate instrumental aggression, where 'an aggressive act is regarded as a means to an end other than pain or injury.' Thus, inflicting pain is not the objective but a utilitarian means to extract intelligence, which aligns with option 3.

DILR · Data Interpretation & Logical Reasoning

Set

Twenty five coloured beads are to be arranged in a grid comprising of five rows and five columns. Each cell in the grid must contain exactly one bead. Each bead is coloured either Red, Blue or Green.

While arranging the beads along any of the five rows or along any of the five columns, the rules given below are to be followed:

Two adjacent beads along the same row or column are always of different colours.
There is at least one Green bead between any two Blue beads along the same row or column.
There is at least one Blue and at least one Green bead between any two Red beads along the same row or column.

Every unique, complete arrangement of twenty five beads is called a configuration.

Question 1 · TITA (type in the answer)

The total number of possible configuration using beads of only two colours is:

Answer: 2

Solution

Only two‑colour combinations allowed by the rules are examined. Red cannot appear with only one other colour because Rule 3 requires at least one Blue and one Green between any two Reds. Hence the only viable two‑colour choice is Blue–Green. With only Blue and Green, Rule 1 (adjacent different) forces every row and column to alternate colours, i.e. a chessboard pattern. On a 5×5 board there are exactly two such global colourings: one where the top‑left cell is Blue and one where it is Green. Both satisfy Rule 2 because between any two Blues there is always at least one Green. Thus the total number of configurations using exactly two colours is 2.

Question 2 · TITA (type in the answer)

What is the maximum possible number of Red beads that can appear in any configuration?

Answer: 9

Solution

In any row or column of length 5, Rule 3 forces at least two cells between any two Reds, so the maximum Reds per line is 2. To reach the absolute maximum of 10 Reds, every row and every column would need exactly 2 Reds. This forces column 3 to contain 2 Reds as well. However, if a row has a Red in column 3, the only possible second Red would be in column 1, but then the gap (column 2 alone) cannot contain both a Blue and a Green. Hence a row with a Red in column 3 can have at most one Red. Therefore column 3 can contain at most one Red overall, making a total of 10 Reds impossible.

A valid configuration with 9 Reds is attainable. One such arrangement (R = Red, B = Blue, G = Green) is tabulated below.

	C1	C2	C3	C4	C5
R1	R	G	B	R	G
R2	B	R	G	B	R
R3	G	B	R	G	B
R4	R	G	B	R	G
R5	G	R	G	B	R

Every row and column satisfies all three rules. Hence the maximum possible number of Red beads is 9.

Question 3 · TITA (type in the answer)

What is the minimum number of Blue beads in any configuration?

Answer: 6

Solution

Each row/column must contain at least one Blue (0‑Blue rows impossible because they would force alternating R‑G with at least two Reds and no Blue between them, violating rule 3). If total Blues = 5, they form a permutation (one per row and column). In any such permutation, some row must have its Blue in column 1 or 5. A row with Blue at column 1 forces the sequence B, X, Y, X, Y (X,Y ∈ {R,G}), which inevitably has two Reds with no Blue between them – invalid. Thus 5 Blues is impossible. A configuration with exactly 6 Blues is possible; for example:

	C1	C2	C3	C4	C5
R1	R	G	B	G	R
R2	G	B	G	R	G
R3	B	G	R	G	B
R4	G	R	G	B	G
R5	R	G	B	G	R

Every row and column satisfies all three rules. Hence minimum Blue beads = 6.

Question 4 · TITA (type in the answer)

Two Red beads have been placed in ‘second row, third column’ and ‘third row, second column’. How many more Red beads can be placed so as to maximise the number of Red beads used in the configuration?

Answer: 6

Solution

With Red at (2,3) and (3,2) fixed:

Row 2 has Red at col 3; any second Red in row 2 would be at col 1 or 5, both giving only one cell between and thus no room for the required Blue and Green → row 2 can have at most 1 Red.
Column 2 has Red at row 3; similarly it can hold at most 1 Red.
In any column, two Reds must be separated by at least two cells (distance ≥ 3). Thus column 3 may get a second Red at row 5, and column 5 may get a second Red at row 3, but not all rows can simultaneously have two Reds without exceeding column limits.

Maximising Reds subject to these constraints yields exactly 8 Reds (2 more than the given two). One such arrangement is:

	C1	C2	C3	C4	C5
R1	R	B	G	R	B
R2	B	G	R	B	G
R3	G	R	B	G	R
R4	R	B	G	R	G
R5	B	G	R	G	B

Total Reds = 8, so we can place 8 – 2 = 6 more Red beads.

QA · Quantitative Ability

Question 1 · MCQ

The sum of the perimeters of an equilateral triangle and a rectangle is 90 cm. The area, T, of the triangle and the area, R, of the rectangle, both in sq cm, satisfy the relationship \(R = T^2\). If the sides of the rectangle are in the ratio 1: 3, then the length, in cm, of the longer side of the rectangle, is

A.
24
B.
27
✓ Correct
C.
21
D.
18

Solution

Let side of equilateral triangle = a cm. Perimeter = 3a. Area T = \(\frac{\sqrt{3}}{4}a^2\).
Rectangle sides x and 3x. Perimeter = 8x. Area R = 3x².
Given: 3a + 8x = 90 and R = T² → 3x² = \(\frac{3}{16}a^4\) → x = \(\frac{a^2}{4}\).
Substituting: 3a + 2a² = 90 → 2a² + 3a – 90 = 0 → a = 6 (positive).
Then x = 9, longer side = 3x = 27 cm.
Answer: 27.

Question 2 · MCQ

In May, John bought the same amount of rice and the same amount of wheat as he had bought in April, but spent ₹ 150 more due to price increase of rice and wheat by 20% and 12%, respectively. If John had spent ₹ 450 on rice in April, then how much did he spend on wheat in May?

A.
₹ 580
B.
₹ 570
C.
₹ 560
✓ Correct
D.
₹ 590

Solution

Let April wheat spending = ₹W.
April: rice ₹450, wheat ₹W.
May prices: rice +20% → ₹540; wheat +12% → ₹1.12W.
Total increase: ₹150 → 540 + 1.12W = (450 + W) + 150 = 600 + W.
0.12W = 60 → W = 500.
May wheat spending = 1.12 × 500 = ₹560.
Answer: ₹560.

Question 3 · MCQ

In a car race, car A beats car B by 45 km, car B beats car C by 50 km, and car A beats car C by 90 km. The distance (in km) over which the race has been conducted is

A.
500
B.
475
C.
550
D.
450
✓ Correct

Solution

Let race distance = \(D\) km. When A finishes, B has covered \(D - 45\), C has covered \(D - 90\). When B finishes, C has covered \(D - 50\).
Speed ratios: \(\frac{v_A}{v_B} = \frac{D}{D-45}\), \(\frac{v_B}{v_C} = \frac{D}{D-50}\), \(\frac{v_A}{v_C} = \frac{D}{D-90}\).
Multiplying first two: \(\frac{D^2}{(D-45)(D-50)} = \frac{D}{D-90}\).
Simplify (cancel \(D\)): \(D(D-90) = (D-45)(D-50)\)
Expand: \(D^2 - 90D = D^2 - 95D + 2250\) → \(5D = 2250\) → \(D = 450\).
Answer: 450 km.

Question 4 · TITA (type in the answer)

John takes twice as much time as Jack to finish a job. Jack and Jim together take one-thirds of the time to finish the job than John takes working alone. Moreover, in order to finish the job, John takes three days more than that taken by three of them working together. In how many days will Jim finish the job working alone?

Answer: 4

Solution

Let Jack’s time = \(x\) days → John’s time = \(2x\).
Let Jim’s time = \(y\) days. Jack & Jim together take \(\frac{1}{3}\) of John’s time = \(\frac{2x}{3}\) days.
So \(\frac{1}{x} + \frac{1}{y} = \frac{3}{2x}\) → \(\frac{1}{y} = \frac{3}{2x} - \frac{1}{x} = \frac{1}{2x}\) → \(y = 2x\).
All three together: rate = \(\frac{1}{x} + \frac{1}{2x} + \frac{1}{2x} = \frac{2}{x}\), time = \(\frac{x}{2}\).
John’s time = \(2x = \frac{x}{2} + 3\) → \(\frac{3x}{2} = 3\) → \(x = 2\).
Jim’s time = \(2x = 4\) days.

Question 5 · MCQ

Let the m-th and n-th terms of a geometric progression be \(\frac{3}{4}\) and 12, respectively, where m < n. If the common ratio of the progression is an integer r, then the smallest possible value of r + n - m is

A.
-2
✓ Correct
B.
2
C.
6
D.
-4

Solution

Let first term = \(a\) and common ratio = \(r\) (integer). Then:
\(T_m = a r^{m-1} = \frac{3}{4}\)
\(T_n = a r^{n-1} = 12\)
Dividing: \(r^{n-m} = 12 / (3/4) = 16\).

We need the smallest possible value of \(r + (n-m)\).
Find integer \(r\) and positive integer \(d = n-m\) with \(r^d = 16\):

\(r\)	\(d\)	\(r+d\)
16	1	17
4	2	6
2	4	6
−2	4	2
−4	2	−2

The smallest is \(-2\). (Checking: \(r=-4, d=2\) gives \(T_n = T_m \cdot r^2 = \frac{3}{4}\cdot 16 = 12\), valid.)

The other 55 questions are in the simulator

Sit CAT 2020 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