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CAT 2021 Slot 1 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 · 20 MCQ · 4 TITA

  • Reading Comprehension · 16
  • Verbal Ability · 8

DILR

Data Interpretation & Logical Reasoning

20 questions · 15 MCQ · 5 TITA

  • Logical Reasoning · 12
  • Data Interpretation · 8

QA

Quantitative Ability

22 questions · 14 MCQ · 8 TITA

  • Arithmetic · 10
  • Algebra · 6
  • Geometry · 3
  • Number System · 2
  • Modern Math · 1

Sample questions with solutions

15 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

We cannot travel outside our neighbourhood without passports. We must wear the same plainclothes. We must exchange our houses every ten years. We cannot avoid labour. We all go to bed at the same time . . . We have religious freedom, but we cannot deny that the soul dies with the body, since ‘but for the fear of punishment, they would have nothing but contempt for the laws and customs of society'. . . . In More's time, for much of the population, given the plenty and security on offer, such restraints would not have seemed overly unreasonable. For modern readers, however, Utopia appears to rely upon relentless transparency, the repression of variety, and the curtailment of privacy. Utopia provides security: but at what price? In both its external and internal relations, indeed, it seems perilously dystopian.

Such a conclusion might be fortified by examining selectively the tradition which follows more on these points. This often portrays societies where. . .'it would be almost impossible for man to be depraved, or wicked'. . . . This is achieved both through institutions and mores, which underpin the common life. ... The passions are regulated and inequalities of wealth and distinction are minimized. Needs, vanity, and emulation are restrained, often by prizing equality and holding riches in contempt. The desire for public power is curbed. Marriage and sexual intercourse are often controlled: in Tommaso Campanella's The City of the Sun (1623), the first great literary utopia after More's, relations are forbidden to men before the age of twenty-one and women before nineteen. Communal child-rearing is normal; for Campanella this commences at age two. Greater simplicity of life, 'living according to nature', is often a result: the desire for simplicity and purity are closely related. People become more alike in appearance, opinion, and outlook than they often have been. Unity, order, and homogeneity thus prevail at the cost of individuality and diversity. This model, as J. C. Davis demonstrates, dominated early modern utopianism. . . . And utopian homogeneity remains a familiar theme well into the twentieth century.

Given these considerations, it is not unreasonable to take as our starting point here the hypothesis that utopia and dystopia evidently share more in common than is often supposed. Indeed, they might be twins, the progeny of the same parents. Insofar as this proves to be the case, my linkage of both here will be uncomfortably close for some readers. Yet we should not mistake this argument for the assertion that all utopias are, or tend to produce, dystopias. Those who defend this proposition will find that their

association here is not nearly close enough. For we have only to acknowledge the existence of thousands of successful intentional communities in which a cooperative ethos predominates and where harmony without coercion is the rule to set aside such an assertion. Here the individual's submersion in the group is consensual (though this concept is not unproblematic). It results not in enslavement but voluntary submission to group norms. Harmony is achieved without . . .harming others.

Question 1 · MCQ

All of the following statements can be inferred from the passage EXCEPT that:
  1. A.
    utopian and dystopian societies are twins, the progeny of the same parents.
    ✓ Correct
  2. B.
    utopian societies exist in a long tradition of literature dealing with imaginary people practicing imaginary customs, in imaginary worlds.
  3. C.
    many conceptions of utopian societies emphasise the importance of social uniformity and cultural homogeneity.
  4. D.
    it is possible to see utopias as dystopias, with a change in perspective, because one person's utopia could be seen as another's dystopia.
Solution
The passage presents the twinhood of utopia and dystopia as a hypothesis (“they might be twins”), not as a definite fact. Option 1 asserts it as a fact (“are twins”), so it cannot be validly inferred. The other options are supported: option 2 by references to the long literary tradition (More, Campanella, etc.), option 3 by the emphasis on unity, order, and homogeneity, and option 4 by the shift in perspective between More’s contemporaries and modern readers.

Question 2 · MCQ

Following from the passage, which one of the following may be seen as a characteristic of a utopian society?
  1. A.
    The regulation of homogeneity through promoting competitive heterogeneity.
  2. B.
    A society where public power is earned through merit rather than through privilege.
  3. C.
    Institutional surveillance of every individual to ensure his/her security and welfare.
    ✓ Correct
  4. D.
    A society without any laws to restrain one's individuality.
Solution
The passage describes More’s Utopia as relying on “relentless transparency” and “curtailment of privacy” to provide security. This implies institutional surveillance for security and welfare. Option 1 contradicts the passage’s emphasis on homogeneity, option 2 is not supported (the desire for public power is curbed, not merit‑based), and option 4 is the opposite of the repressive nature of utopian laws.

Question 3 · MCQ

Which sequence of words below best captures the narrative of the passage?
  1. A.
    Relentless transparency – Homogeneity – Utopia – Dystopia.
  2. B.
    Utopia - Security – Dystopia – Coercion.
  3. C.
    Curtailment of privacy – Dystopia – Utopia – Intentional community.
  4. D.
    Utopia - Security – Homogeneity – Intentional community.
    ✓ Correct
Solution
The narrative begins with a description of More’s Utopia, then turns to the security it offers at a price, moves to the tradition of homogeneity in early modern utopianism, and concludes with the counterexample of intentional communities that achieve harmony without coercion. This sequence matches “Utopia – Security – Homogeneity – Intentional community”. The other options misorder or misrepresent the flow.

Question 4 · MCQ

All of the following arguments are made in the passage EXCEPT that:
  1. A.
    in More's time, there was plenty and security, so people did not need restraints that could appear unreasonable.
    ✓ Correct
  2. B.
    there have been thousands of communities where homogeneity and stability have been achieved through choice, rather than by force.
  3. C.
    in early modern utopianism, the stability of utopian societies was seen to be achieved only with individuals surrendering their sense of self.
  4. D.
    the tradition of utopian literature has often shown societies in which it would be nearly impossible for anyone to be sinful or criminal.
Solution
The passage says that in More’s time, given the plenty and security, such restraints “would not have seemed overly unreasonable”. It does NOT claim that people therefore did not need restraints—the restraints existed and were accepted. Option 1 misinterprets this. Options 2, 3, and 4 are directly or indirectly supported (thousands of voluntary communities, stability at the cost of individuality, and the impossibility of being depraved in utopian literature).

DILR · Data Interpretation & Logical Reasoning

Set

A journal plans to publish 18 research papers, written by eight authors (A, B, C, D, E, F, G, and H) in four issues of the journal scheduled in January, April, July and October. Each of the research papers was written by exactly one of the eight authors. Five papers were scheduled in each of the first two issues, while four were scheduled in each of the last two issues. Every

author wrote at least one paper and at most three papers. The total number of papers written by A, D, G and H was double the total number of papers written by the other four authors. Four of the authors were from India and two each were from Japan and China. Each author belonged to exactly one of the three areas Manufacturing, Automation and Logistics. Four of the authors were from the Logistics area and two were from the Automation area. As per the journal policy, none of the authors could have more than one paper in any issue of the journal.

The following facts are also known.
  1. F, an Indian author from the Logistics area, wrote only one paper. It was scheduled in the October issue.
  2. A was from the Automation area and did not have a paper scheduled in the October issue.
  3. None of the Indian authors were from the Manufacturing area and none of the Japanese or Chinese authors were from the Automation area.
  4. A and H were from different countries, but had their papers scheduled in exactly the same issues.
  5. C and E, both Chinese authors from different areas, had the same number of papers scheduled. Further, E had papers scheduled in consecutive issues of the journal but C did not.
  6. B, from the Logistics area, had a paper scheduled in the April issue of the journal.
  7. B and G belonged to the same country. None of their papers were scheduled in the same issue of the journal.
  8. D, a Japanese author from the Manufacturing area, did not have a paper scheduled in the July issue.
  9. C and H belonged to different areas.

Question 1 · MCQ

What is the correct sequence of number of papers written by B, C, E and G, respectively?
  1. A.
    1, 2, 2, 3
    ✓ Correct
  2. B.
    1, 3, 3, 1
  3. C.
    3, 1, 1, 3
  4. D.
    1, 2, 2, 1
Solution
After assigning countries and areas, we find: A (Indian, Automation, 3 papers), B (Indian, Logistics, 1 or 3), C (Chinese, Manufacturing, 1 or 2), D (Japanese, Manufacturing, 3), E (Chinese, Logistics, 1 or 2), F (Indian, Logistics, 1), G (Indian, Automation, 3), H (Japanese, Logistics, 3). Total papers = 18. Group (A,D,G,H) = 12 ⇒ each must be 3. Group (B,C,E,F) = 6 ⇒ B+C+E+1 = 6 ⇒ B+C+E = 5.
C and E have same count. If C=E=1 ⇒ B=3, but E must have papers in consecutive issues ⇒ requires at least 2 papers. Thus C=E=2, B=1. So B=1, C=2, E=2. G=3. Sequence: 1,2,2,3.

Question 2 · TITA (type in the answer)

How many papers were written by Indian authors?

Answer: 8

Solution
Indian authors are A, B, F, G. Their paper counts: A=3, B=1, F=1, G=3. Total = 3+1+1+3 = 8.

Question 3 · MCQ

Which of the following statement(s) MUST be true?

Statement A: Every issue had at least one paper by author(s) from each country.

Statement B: Every issue had at most two papers by author(s) from each area.
  1. A.
    Both the statements
  2. B.
    Only Statement B
  3. C.
    Only Statement A
    ✓ Correct
  4. D.
    Neither of the statements
Solution
From the final schedule:
Jan: D(JP,Man), G(IN,Auto), A(IN,Auto), H(JP,Log), C(CN,Man)
Apr: B(IN,Log), D(JP,Man), A(IN,Auto), H(JP,Log), E(CN,Log)
Jul: G(IN,Auto), A(IN,Auto), H(JP,Log), E(CN,Log)
Oct: D(JP,Man), F(IN,Log), G(IN,Auto), C(CN,Man)

Statement A: Every issue has at least one paper from each country. True (Jan: IN,JP,CN; Apr: IN,JP,CN; Jul: IN,JP,CN; Oct: IN,JP,CN).
Statement B: Every issue has at most two papers from each area. April has three Logistics papers (B, H, E) → false.
Hence, only Statement A is true.

Question 4 · MCQ

Which of the following statements is FALSE?
  1. A.
    Every issue had at least one paper by author(s) from Automation area.
  2. B.
    Every issue had exactly one paper by a Chinese author.
  3. C.
    Every issue had exactly two papers by authors from Logistics area.
    ✓ Correct
  4. D.
    Every issue had exactly two papers by Indian authors.
Solution
Full schedule derived from constraints:
AuthorCountryAreaPapersIssues
AIndiaAuto3Jan, Apr, Jul
BIndiaLog1Apr
CChinaManu2Jan, Oct
DJapanManu3Jan, Apr, Oct
EChinaLog2Apr, Jul
FIndiaLog1Oct
GIndiaAuto3Jan, Jul, Oct
HJapanLog3Jan, Apr, Jul
Area-wise paper counts per issue:
  • Automation: Jan 2, Apr 1, Jul 2, Oct 1 → every issue has ≥1. True.
  • Chinese (C & E): Jan 1, Apr 1, Jul 1, Oct 1 → exactly 1 per issue. True.
  • Logistics: Jan 1, Apr 3, Jul 2, Oct 1 → not exactly 2 per issue. False.
  • Indian (A,B,F,G): Jan 2, Apr 2, Jul 2, Oct 2 → exactly 2 per issue. True.
Thus statement 3 is false.

Question 5 · MCQ

Which of the following statements is FALSE?
  1. A.
    There were exactly two papers by authors from Manufacturing area in the January issue.
  2. B.
    There was exactly one paper by an author from Manufacturing area in the April issue.
  3. C.
    There was exactly one paper by an author from Logistics area in the October issue.
  4. D.
    There were exactly two papers by authors from Manufacturing area in the July issue.
    ✓ Correct
Solution
From the schedule, Manufacturing papers (D and C) appear in:
  • Jan: D, C → 2
  • Apr: D only → 1
  • Jul: none → 0
  • Oct: D, C → 2
Checking options:
  1. Jan Manu = 2 → True
  2. Apr Manu = 1 → True
  3. Oct Logistics = 1 (only F) → True
  4. Jul Manu = 2 → False (it is 0)
Hence statement 4 is false.

Question 6 · MCQ

Which of the following is the correct sequence of number of papers by authors from Automation, Manufacturing and Logistics areas, respectively?
  1. A.
    6, 5, 7
    ✓ Correct
  2. B.
    6, 6, 6
  3. C.
    6, 7, 5
  4. D.
    5, 6, 7
Solution
Total papers by area:
  • Automation: A (3) + G (3) = 6
  • Manufacturing: D (3) + C (2) = 5
  • Logistics: B (1) + E (2) + F (1) + H (3) = 7
Sequence: Automation 6, Manufacturing 5, Logistics 7 → matches option 1.

QA · Quantitative Ability

Question 1 · MCQ

If \(x_0 = 1,x_1 = 2\), and \(x_{n+2} = \frac{1+x_{n+1}}{x_n}\), \(n = 0,1,2,3,...,\) then \(x_{2021}\) is equal to
  1. A.
    3
  2. B.
    4
  3. C.
    2
    ✓ Correct
  4. D.
    1
Solution
Compute terms: \(x_0=1\), \(x_1=2\), \(x_2=3\), \(x_3=2\), \(x_4=1\), \(x_5=1\), \(x_6=2\), \(x_7=3\), \(x_8=2\), \(x_9=1\), \(x_{10}=1\).
From \(n=1\), the sequence repeats every 5: \(2,3,2,1,1\).
\(2021 \bmod 5 = 1\), so \(x_{2021}=2\).

Question 2 · MCQ

If the area of a regular hexagon is equal to the area of an equilateral triangle of side 12 cm, then the length, (in cm), of each side of the hexagon is
  1. A.
    \(2\sqrt{6}\)
    ✓ Correct
  2. B.
    \(4\sqrt{6}\)
  3. C.
    \(\sqrt{6}\)
  4. D.
    \(6\sqrt{6}\)
Solution
Area of equilateral triangle with side 12 cm: \(\frac{\sqrt{3}}{4} \times 12^2 = 36\sqrt{3}\).
Regular hexagon area: \(6 \times \frac{\sqrt{3}}{4} a^2 = \frac{3\sqrt{3}}{2} a^2\).
Equate: \(\frac{3\sqrt{3}}{2} a^2 = 36\sqrt{3} \Rightarrow a^2 = 24 \Rightarrow a = 2\sqrt{6}\).

Question 3 · TITA (type in the answer)

Amal purchases some pens at ₹ 8 each. To sell these, he hires an employee at a fixed wage. He sells 100 of these pens at ₹ 12 each. If the remaining pens are sold at ₹ 11 each, then he makes a net profit of ₹300, while he makes a net loss of ₹ 300 if the remaining pens are sold at ₹ 9 each. The wage of the employee, in INR, is

Answer: 1000

Solution
Let \(n\) be total pens, wage \(W\). Cost = \(8n + W\).
Sell 100 at ₹\(12\) each, rest at ₹\(11\): Revenue = \(1200 + 11(n-100) = 11n+100\).
Profit 300 ⇒ \(11n+100 - (8n+W) = 300\) ⇒ \(3n - W = 200\) (1)
Sell 100 at ₹\(12\), rest at ₹\(9\): Revenue = \(1200 + 9(n-100) = 9n+300\).
Loss 300 ⇒ \(8n+W - (9n+300) = 300\) ⇒ \(W - n = 600\) ⇒ \(W = n+600\) (2)
Substitute (2) in (1): \(3n - (n+600) = 200\) ⇒ \(2n = 800\) ⇒ \(n=400\), \(W=1000\).
Wage of employee = ₹\(1000\).

Question 4 · MCQ

\(f(x) = \frac{x^2+2x-15}{x^2-7x-18}\) is negative if and only if
  1. A.
    \(-2 < x <3\) or \(x > 9\)
  2. B.
    \(x <-5\) or \(-2 < x <3\)
  3. C.
    \(x <-5\) or \(3 < x < 9\)
  4. D.
    \(-5<x<-2\) or \(3 < x < 9\)
    ✓ Correct
Solution
\(f(x) = \frac{x^2+2x-15}{x^2-7x-18} = \frac{(x+5)(x-3)}{(x-9)(x+2)}\).
Zeros: \(x=-5,3\); undefined at \(x=-2,9\).
Sign chart:
IntervalSign of \(f(x)\)
\((-\infty,-5)\)\(+\)
\((-5,-2)\)\(-\)
\((-2,3)\)\(+\)
\((3,9)\)\(-\)
\((9,\infty)\)\(+\)
Hence \(f(x)<0\) exactly for \(-5 < x < -2\) or \(3 < x < 9\).
That matches option 4.

Question 5 · MCQ

Two trains cross each other in 14 seconds when running in opposite directions along parallel tracks. The faster train is 160 m long and crosses a lamp post in 12 seconds. If the speed of the other train is 6 km/hr less than the faster one, its length, in m, is
  1. A.
    180
  2. B.
    192
  3. C.
    190
    ✓ Correct
  4. D.
    184
Solution
Faster train speed = 160 m / 12 s = \( \frac{40}{3} \) m/s = 48 km/hr.
Other train speed = 48 \(-\) 6 = 42 km/hr = \( \frac{35}{3} \) m/s.
Relative speed (opposite) = \( \frac{40}{3} + \frac{35}{3} = 25 \) m/s.
Total length crossed in 14 s = \( 25 \times 14 = 350 \) m.
Length of other train = 350 \(-\) 160 = 190 m.

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