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CAT 2022 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 · 21 MCQ · 3 TITA

  • Reading Comprehension · 16
  • Verbal Ability · 8

DILR

Data Interpretation & Logical Reasoning

20 questions · 14 MCQ · 6 TITA

  • Logical Reasoning · 20

QA

Quantitative Ability

22 questions · 14 MCQ · 8 TITA

  • Arithmetic · 9
  • Algebra · 6
  • Geometry · 3
  • Modern Math · 2
  • Number System · 2

Sample questions with solutions

14 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

The passage below is accompanied by a set of questions. Choose the best answer to each question.

Stories concerning the Undead have always been with us. From out of the primal darkness of Mankind’s earliest years, come whispers of eerie creatures, not quite alive (or alive in a way which we can understand), yet not quite dead either. These may have been ancient and primitive deities who dwelt deep in the surrounding forests and in remote places, or simply those deceased who refused to remain in their tombs and who wandered about the countryside, physically tormenting and frightening those who were still alive. Mostly they were ill-defined—strange sounds in the night beyond the comforting glow of the fire, or a shape, half-glimpsed in the twilight along the edge of an encampment. They were vague and indistinct, but they were always there with the power to terrify and disturb. They had the power to touch the minds of our early ancestors and to fill them with dread. Such fear formed the basis of the earliest tales although the source and exact nature of such terrors still remained very vague.

And as Mankind became more sophisticated, leaving the gloom of their caves and forming themselves into recognizable communities—towns, cities, whole cultures—so the Undead travelled with them, inhabiting their folklore just as they had in former times. Now they began to take on more definite shapes. They became walking cadavers; the physical embodiment of former deities and things which had existed alongside Man since the Creation. Some still remained vague and ill-defined but, as Mankind strove to explain the horror which it felt towards them, such creatures emerged more readily into the light.

In order to confirm their abnormal status, many of the Undead were often accorded attributes, which defied the natural order of things—the power to transform themselves into other shapes, the ability to sustain themselves by drinking human blood, and the ability to influence human minds across a distance. Such powers—described as supernatural—only [lent] an added dimension to the terror that humans felt regarding them.

And it was only natural, too, that the Undead should become connected with the practice of magic. From very early times, Shamans and witchdoctors had claimed at least some power and control over the spirits of departed ancestors, and this has continued down into more “civilized” times. Formerly, the invisible spirits and forces that thronged around men’s earliest encampments, had spoken “through” the tribal Shamans but now, as entities in their own right, they were subject to magical control and could be physically summoned by a competent sorcerer. However, the relationship between the magician and an Undead creature was often a very tenuous and uncertain one. Some sorcerers might have even become Undead entities once they died, but they might also have been susceptible to the powers of other magicians when they did.

From the Middle Ages and into the Age of Enlightenment, theories of the Undead continued to grow and develop. Their names became more familiar—werewolf, vampire, ghoul—each one certain to strike fear into the hearts of ordinary humans.

Question 1 · MCQ

All of the following statements, if false, could be seen as being in accordance with the passage, EXCEPT:
  1. A.
    the transition from the Middle Ages to the Age of Enlightenment saw new theories of the Undead.
    ✓ Correct
  2. B.
    the Undead remained vague and ill-defined, even as Mankind strove to understand the horror they inspired.
  3. C.
    the relationship between Shamans and the Undead was believed to be a strong and stable one.
  4. D.
    the growing sophistication of Mankind meant that humans stopped believing in the Undead.
Solution
The question asks for the option which, if false, would NOT be in accordance with the passage (i.e., its falsehood contradicts the passage, meaning the statement itself must be true according to the passage, EXCEPT one which is false or not supported). Let's evaluate the statements:
  • Statement 1: 'the transition from the Middle Ages to the Age of Enlightenment saw new theories of the Undead.' The passage says: 'From the Middle Ages and into the Age of Enlightenment, theories of the Undead continued to grow and develop.' If this statement is false, it contradicts the passage. Thus, its falsehood is NOT in accordance with the passage. This makes it the correct exception.
  • Statement 2: 'the Undead remained vague and ill-defined...' The passage states they emerged more readily into the light and took on more definite shapes. If Statement 2 is false (meaning they did NOT remain vague), it is in accordance with the passage.
  • Statement 3: 'the relationship between Shamans and the Undead was believed to be a strong and stable one.' The passage says it was 'tenuous and uncertain'. If Statement 3 is false, it is in accordance with the passage.
  • Statement 4: 'the growing sophistication of Mankind meant that humans stopped believing in the Undead.' The passage says they traveled with them. If Statement 4 is false, it is in accordance with the passage.

Question 2 · MCQ

Which one of the following observations is a valid conclusion to draw from the statement, “From out of the primal darkness of Mankind’s earliest years, come whispers of eerie creatures, not quite alive (or alive in a way which we can understand), yet not quite dead either.”?
  1. A.
    Mankind’s primal years were marked by creatures alive with eerie whispers, but seen only in the darkness.
  2. B.
    We can understand the lives of the eerie creatures in Mankind’s early years through their whispers in the darkness.
  3. C.
    Mankind’s early years were marked by a belief in the existence of eerie creatures that were neither quite alive nor dead.
    ✓ Correct
  4. D.
    Long ago, eerie creatures used to whisper in the primal darkness that they were not quite dead.
Solution
The quoted statement describes the early beliefs of mankind regarding eerie creatures that were 'not quite alive... yet not quite dead either' emerging from the 'primal darkness of Mankind's earliest years'. This directly supports Option 3, which states that Mankind's early years were marked by a belief in the existence of eerie creatures that were neither quite alive nor dead. Other options misinterpret the metaphorical 'whispers' and 'darkness' as literal physical whispers or sights.

Question 3 · MCQ

Which one of the following statements best describes what the passage is about?
  1. A.
    The passage describes the failure of human beings to fully comprehend their environment.
  2. B.
    The writer discusses the transition from primitive thinking to the Age of Enlightenment.
  3. C.
    The passage discusses the evolution of theories of the Undead from primitive thinking to the Age of Enlightenment.
    ✓ Correct
  4. D.
    The writer describes the ways in which the Undead come to be associated with Shamans and the practice of magic.
Solution
The passage traces the evolution of the concept of the Undead chronologically: starting from mankind's earliest primal years (vague, ill-defined shapes), moving to more sophisticated communities where they took definite shapes, then to their association with magic and shamans, and finally to the Middle Ages and the Age of Enlightenment where specific theories and names (werewolf, vampire, ghoul) developed. Thus, Option 3 best describes the main idea of the passage.

Question 4 · MCQ

“In order to confirm their abnormal status, many of the Undead were often accorded attributes, which defied the natural order of things . . .” Which one of the following best expresses the claim made in this statement?
  1. A.
    The Undead are deified in nature’s order by giving them divine attributes.
  2. B.
    Human beings conceptualise the Undead as possessing abnormal features.
    ✓ Correct
  3. C.
    According the Undead an abnormal status is to reject the natural order of things.
  4. D.
    The natural attributes of the Undead are rendered abnormal by changing their status.
Solution
The sentence states that 'in order to confirm their abnormal status, many of the Undead were often accorded attributes, which defied the natural order of things'. This means that human beings attributed abnormal, supernatural features (like shape-shifting or blood-drinking) to these creatures to define and confirm their abnormal status. This is best expressed by Option 2.

DILR · Data Interpretation & Logical Reasoning

Set

Adhara, Bithi, Chhaya, Dhanavi, Esther, and Fathima are the interviewers in a process that awards funding for new initiatives. Every interviewer individually interviews each of the candidates individually and awards a token only if she recommends funding. A token has a face value of 2, 3, 5, 7, 11, or 13. Each interviewer awards tokens of a single face value only.

Once all six interviews are over for a candidate, the candidate receives a funding that is Rs.1000 times the product of the face values of all the tokens. For example, if a candidate has tokens with face values 2, 5, and 7, then they get a funding of Rs.1000 × (2 × 5 × 7) = Rs.70,000.

Pragnyaa, Qahira, Rasheeda, Smera, and Tantra were five candidates who received funding. The funds they received, in descending order, were Rs.390,000, Rs.210,000, Rs.165,000, Rs.77,000, and Rs.66,000.

The following additional facts are known:
  1. Fathima awarded tokens to everyone except Qahira, while Adhara awarded tokens to no one except Pragnyaa.
  2. Rashida received the highest number of tokens that anyone received, but she did not receive one from Esther.
  3. Bithi awarded a token to Smera but not to Qahira, while Dhanavi awarded a token to Qahira but not to Smera.

Question 1 · TITA (type in the answer)

How many tokens did Qahira receive?

Answer: 2

Solution
The funding amounts correspond to the product of the token face values (which are prime numbers: 2, 3, 5, 7, 11, 13).
Factoring the given funding amounts (divided by 1000):
  • 390 = 2 × 3 × 5 × 13 (4 tokens)
  • 210 = 2 × 3 × 5 × 7 (4 tokens)
  • 165 = 3 × 5 × 11 (3 tokens)
  • 77 = 7 × 11 (2 tokens)
  • 66 = 2 × 3 × 11 (3 tokens)
Fathima awarded tokens to everyone except Qahira, meaning she awarded exactly 4 tokens. The only prime factor present in exactly 4 amounts is 3. Thus, Fathima's token is 3, and the only amount without a 3 is 77. Therefore, Qahira received Rs. 77,000.
Since 77 = 7 × 11, Qahira received exactly 2 tokens.
CandidateFunding (Rs.)Token Values (Prime Factors)Total Tokens
Pragnyaa390,0002, 3, 5, 134
Rasheeda210,0002, 3, 5, 74
Smera165k or 66k(3, 5, 11) or (2, 3, 11)3
Tantra66k or 165k(2, 3, 11) or (3, 5, 11)3
Qahira77,0007, 112

Question 2 · MCQ

Who among the following definitely received a token from Bithi but not from Dhanavi?
  1. A.
    Qahira
  2. B.
    Tantra
  3. C.
    Pragnyaa
    ✓ Correct
  4. D.
    Rasheeda
Solution
From our initial deductions, Pragnyaa received Rs. 390,000 (tokens: 2, 3, 5, 13) because Adhara awarded a token to no one except Pragnyaa (Adhara = 13).
Rasheeda received the highest number of tokens (4), so she received Rs. 210,000 (tokens: 2, 3, 5, 7).
Since Rasheeda did not receive a token from Esther, Esther's token cannot be 2, 3, 5, or 7. Thus, Esther = 11.
Dhanavi awarded a token to Qahira (7, 11) but not to Smera. Since Esther is 11, Dhanavi must be 7.
Bithi awarded a token to Smera but not Qahira. The remaining tokens are 2 and 5, so Bithi is either 2 or 5.
Pragnyaa's tokens are 2, 3, 5, 13. She has both 2 and 5, so she definitely received a token from Bithi. She does not have a 7, so she did not receive one from Dhanavi.
InterviewerToken ValueCandidates Awarded To
Adhara13Pragnyaa
Bithi2 or 5Pragnyaa, Rasheeda, Smera
Chhaya5 or 2Pragnyaa, Rasheeda, Tantra
Dhanavi7Rasheeda, Qahira
Esther11Smera, Tantra, Qahira
Fathima3Pragnyaa, Rasheeda, Smera, Tantra

Question 3 · TITA (type in the answer)

How many tokens did Chhaya award?

Answer: 3

Solution
As established, the token values for Adhara, Dhanavi, Esther, and Fathima are 13, 7, 11, and 3 respectively.
This leaves the token values 2 and 5 for Bithi and Chhaya.
Regardless of whether Chhaya's token is 2 or 5, both 2 and 5 appear in exactly 3 funding amounts:
  • 2 appears in 390, 210, and 66.
  • 5 appears in 390, 210, and 165.
Therefore, Chhaya awarded exactly 3 tokens.
InterviewerToken ValueCandidates Awarded To
Adhara13Pragnyaa
Bithi2 or 5Pragnyaa, Rasheeda, Smera
Chhaya5 or 2Pragnyaa, Rasheeda, Tantra
Dhanavi7Rasheeda, Qahira
Esther11Smera, Tantra, Qahira
Fathima3Pragnyaa, Rasheeda, Smera, Tantra

Question 4 · TITA (type in the answer)

How many tokens did Smera receive?

Answer: 3

Solution
The funding amounts correspond to the product of the token face values.
Factoring the given funding amounts (divided by 1000):
  • 390 = 2 × 3 × 5 × 13 (4 tokens)
  • 210 = 2 × 3 × 5 × 7 (4 tokens)
  • 165 = 3 × 5 × 11 (3 tokens)
  • 77 = 7 × 11 (2 tokens)
  • 66 = 2 × 3 × 11 (3 tokens)
We know Pragnyaa received 390, Rasheeda received 210, and Qahira received 77.
This leaves the amounts 165 and 66 for Smera and Tantra.
Both 165 and 66 are products of exactly 3 prime factors. Thus, Smera received exactly 3 tokens.
CandidateFunding (Rs.)Token Values (Prime Factors)Total Tokens
Pragnyaa390,0002, 3, 5, 134
Rasheeda210,0002, 3, 5, 74
Smera165k or 66k(3, 5, 11) or (2, 3, 11)3
Tantra66k or 165k(2, 3, 11) or (3, 5, 11)3
Qahira77,0007, 112

Question 5 · MCQ

Which of the following could be the amount of funding that Tantra received?
(a) Rs. 66,000
(b) Rs. 165,000
  1. A.
    Both (a) and (b)
    ✓ Correct
  2. B.
    Neither (a) nor (b)
  3. C.
    Only (a)
  4. D.
    Only (b)
Solution
We know Smera and Tantra received the funding amounts Rs. 165,000 and Rs. 66,000 in some order.
Bithi's token is either 2 or 5.
If Bithi's token is 2, Smera must have received the amount with a factor of 2 (Rs. 66,000), making Tantra's amount Rs. 165,000.
If Bithi's token is 5, Smera must have received the amount with a factor of 5 (Rs. 165,000), making Tantra's amount Rs. 66,000.
Both scenarios perfectly satisfy all given conditions. Therefore, Tantra could have received either Rs. 66,000 or Rs. 165,000.
CandidateFunding (Rs.)Token Values (Prime Factors)Total Tokens
Pragnyaa390,0002, 3, 5, 134
Rasheeda210,0002, 3, 5, 74
Smera165k or 66k(3, 5, 11) or (2, 3, 11)3
Tantra66k or 165k(2, 3, 11) or (3, 5, 11)3
Qahira77,0007, 112

QA · Quantitative Ability

Question 1 · MCQ

Let \(a\) and \(b\) be natural numbers. If \(a^2 + ab + a = 14\) and \(b^2 + ab + b = 28\), then \((2a + b)\) equals
  1. A.
    10
  2. B.
    7
  3. C.
    8
    ✓ Correct
  4. D.
    9
Solution
Given equations:
\(a(a + b + 1) = 14\)
\(b(a + b + 1) = 28\)

Adding both equations gives:
\((a + b)(a + b + 1) = 42\)

Let \(x = a + b\). The equation becomes \(x(x + 1) = 42\).
Since \(a\) and \(b\) are natural numbers, \(x > 0\), which gives \(x = 6\).

Substitute \(a + b = 6\) into the first equation:
\(a(6 + 1) = 14 \implies 7a = 14 \implies a = 2\)

Substitute \(a + b = 6\) into the second equation:
\(b(6 + 1) = 28 \implies 7b = 28 \implies b = 4\)

We need to find \(2a + b\):
\(2(2) + 4 = 8\)

Question 2 · TITA (type in the answer)

For any real number \(x\), let \([x]\) be the largest Integer less than or equal to \(x\). If \(\sum_{n=1}^{N} [\frac{1}{5} + \frac{n}{25}] = 25\) then \(N\) is

Answer: 44

Solution
The given sum is \(\sum_{n=1}^{N} \left[\frac{5 + n}{25}\right] = 25\).

Let's evaluate the terms \(\left[\frac{5 + n}{25}\right]\) for different values of \(n\):
For \(1 \le n \le 19\), \(6 \le 5 + n \le 24\), so \(\left[\frac{5 + n}{25}\right] = 0\).
For \(20 \le n \le 44\), \(25 \le 5 + n \le 49\), so \(\left[\frac{5 + n}{25}\right] = 1\).

The sum of the first 19 terms is \(0\).
The next terms are all equal to \(1\). To reach a total sum of \(25\), we need exactly 25 terms that equal \(1\).
These terms correspond to \(n = 20, 21, \dots, 44\).

Thus, \(N = 44\).

Question 3 · MCQ

Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X is
  1. A.
    6
  2. B.
    10
  3. C.
    15
    ✓ Correct
  4. D.
    12
Solution
Let the time taken by the trains to meet be \(t\) minutes.
Train A travels for \(t\) minutes before meeting and \(10 - t\) minutes after meeting.
Train B travels for \(t\) minutes before meeting and \(9\) minutes after meeting.
The distance covered by A before meeting equals the distance covered by B after meeting: \(v_A \times t = v_B \times 9\).
The distance covered by B before meeting equals the distance covered by A after meeting: \(v_B \times t = v_A \times (10 - t)\).
Dividing the first equation by the second gives: \(\frac{v_A}{v_B} = \frac{9 v_B}{v_A (10 - t)} \implies \frac{v_A^2}{v_B^2} = \frac{9}{10 - t}\).
From the first equation, we also have \(\frac{v_A}{v_B} = \frac{9}{t}\).
Equating the two expressions for \(\frac{v_A^2}{v_B^2}\): \(\frac{81}{t^2} = \frac{9}{10 - t}\).
\(9(10 - t) = t^2 \implies t^2 + 9t - 90 = 0\).
Solving this quadratic equation yields \((t + 15)(t - 6) = 0\), so \(t = 6\) minutes (since \(t > 0\)).
Total time taken by train B = Time before meeting + Time after meeting = \(6 + 9 = 15\) minutes.

Question 4 · TITA (type in the answer)

A trapezium ABCD has side AD parallel to BC, \(\angle BAD = 90^\circ\), BC = 3 cm and AD = 8 cm. If the perimeter of this trapezium is 36 cm, then its area, in sq. cm, is

Answer: 66

Solution
Let \(AB = h\) be the height of the trapezium. Since \(AD \parallel BC\) and \(\angle BAD = 90^\circ\), \(\angle ABC = 90^\circ\).
Draw a perpendicular from \(C\) to \(AD\) meeting at \(E\). Then \(ABCE\) is a rectangle with \(AE = BC = 3\) cm and \(CE = AB = h\).
The remaining part of \(AD\) is \(ED = AD - AE = 8 - 3 = 5\) cm.
In right-angled \(\triangle CED\), the hypotenuse \(CD = \sqrt{CE^2 + ED^2} = \sqrt{h^2 + 25}\).
The perimeter of the trapezium is \(AB + BC + CD + DA = 36\).
Substituting the known values: \(h + 3 + \sqrt{h^2 + 25} + 8 = 36 \implies \sqrt{h^2 + 25} = 25 - h\).
Squaring both sides: \(h^2 + 25 = 625 - 50h + h^2 \implies 50h = 600 \implies h = 12\) cm.
The area of the trapezium is \(\frac{1}{2} \times (AD + BC) \times AB = \frac{1}{2} \times (8 + 3) \times 12 = 66\) sq. cm.

Question 5 · TITA (type in the answer)

For natural numbers \(x, y\), and \(z\), if \(xy + yz = 19\) and \(yz + xz = 51\), then the minimum possible value of \(xyz\) is

Answer: 34

Solution
Given \(xy + yz = 19\), we can factor this as \(y(x + z) = 19\).
Since \(x, y, z\) are natural numbers, \(y\) and \(x + z\) must be positive integers that are factors of 19.
As 19 is prime and \(x + z \ge 2\) (since \(x \ge 1\) and \(z \ge 1\)), we must have \(y = 1\) and \(x + z = 19\).
The second equation is \(yz + xz = 51\), which factors as \(z(y + x) = 51\).
Substituting \(y = 1\) and \(x = 19 - z\), we get \(z(20 - z) = 51\), or \(z^2 - 20z + 51 = 0\).
Factoring the quadratic yields \((z - 3)(z - 17) = 0\), so \(z = 3\) or \(z = 17\).
If \(z = 3\), then \(x = 16\), and \(xyz = 16 \times 1 \times 3 = 48\).
If \(z = 17\), then \(x = 2\), and \(xyz = 2 \times 1 \times 17 = 34\).
The minimum possible value of \(xyz\) is 34.

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