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CAT 2025 Slot 1 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 · 20 MCQ · 4 TITA

  • Reading Comprehension · 16
  • Verbal Ability · 8

DILR

Data Interpretation & Logical Reasoning

22 questions · 11 MCQ · 11 TITA

  • Logical Reasoning · 18
  • Data Interpretation · 4

QA

Quantitative Ability

22 questions · 15 MCQ · 7 TITA

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

Often the well intentioned music lover or the traditionally-minded professional composer asks two basic questions when faced with the electronic music phenomena: (1) . . . is this type of artistic creation music at all? and, (2) given that the product is accepted as music of a new type or order, is not such music “inhuman”? . . . As Lejaren Hiller points out in his book Experimental Music (coauthor Leonard M. Isaacson), two questions which often arise when music is discussed are: (a) the substance of musical communication and its symbolic and semantic significance, if any, and (b) the particular processes, both mental and technical, which are involved in creating and responding to musical composition. The ever-present popular concept of music as a direct, open, emotional expression and as a subjective form of communication from the composer, is, of course still that of the nineteenth century, when composers themselves spoke of music in those terms . . . But since the third decade of our century many composers have preferred more objective definitions of music, epitomized in Stravinsky's description of it as “a form of speculation in terms of sound and time”. An acceptance of this more characteristic twentieth-century view of the art of musical composition will of course immediately bring the layman closer to an understanding of, and sympathetic response to, electronic music, even if the forms, sounds and approaches it uses will still be of a foreign nature to him.

A communication problem however will still remain. The principal barrier that electronic music presents at large, in relation to the communication process, is that composers in this medium are employing a new language of forms . . . where terms like 'densities', 'indefinite pitch relations', 'dynamic serialization', 'permutation', etc., are substitutes (or remote equivalents) for the traditional concepts of harmony, melody, rhythm, etc. . . . When the new structural procedures of electronic music are at last fully understood by the listener the barriers between him and the work he faces will be removed. . . .

The medium of electronic music has of course tempted many kinds of composers to try their hand at it . . . But the serious-minded composer approaches the world of electronic music with a more sophisticated and profound concept of creation. Although he knows that he can reproduce and employ melodic, rhythmic patterns and timbres of a traditional nature, he feels that it is in the exploration of sui generis languages and forms that the aesthetic magic of the new medium lies. And, conscientiously, he plunges into this search.

The second objection usually levelled against electronic music is much more innocent in nature. When people speak—sometimes very vehemently—of the 'inhuman' quality of this music they seem to forget that the composer is the one who fires the machines, collects the sounds, manipulates them, pushes the buttons, programs the computer, filters the sounds, establishes pitches and scales, splices tape, thinks of forms, and rounds up the over-all structure of the piece, as well as every detail of it.

Question 2 · MCQ

The goal of the author over the course of this passage is to:
  1. A.
    differentiate the modern composer from the nineteenth century composer
  2. B.
    differentiate between electronic music and other forms of music.
  3. C.
    defend the “serious-minded composer” from Lejaren Hill and Stravinsky.
  4. D.
    defend electronic music from certain common charges.
    ✓ Correct
Solution
The passage addresses two main objections/questions raised against electronic music: (1) whether it is music at all, and (2) whether it is "inhuman". The author systematically refutes these objections by redefining music through a modern lens, explaining the communication barrier, and highlighting the active human role of the composer. Thus, the primary goal is to defend electronic music from these common charges.

Question 3 · MCQ

What relation does the “communication problem” mentioned in paragraph 2 have to the questions that the author recounts at the beginning of the passage?
  1. A.
    Unfamiliar forms and terms might get in the way of our seeing electronic music as music, but this can be overcome.
    ✓ Correct
  2. B.
    Its unfamiliar “language of forms” and novel terms mean that we cannot see electronic music as music since it does not employ traditional musical concepts.
  3. C.
    None; they are unrelated to one another and form parts of different discussions.
  4. D.
    The communication problem is what allows us to see electronic music as music because music must be difficult to understand.
Solution
The first paragraph introduces the question of whether electronic music is "music at all". The second paragraph explains that the "communication problem" arises because composers use a new language of forms (like 'densities' and 'indefinite pitch relations') instead of traditional harmony and melody. However, the author notes that once these new structural procedures are "fully understood by the listener the barriers between him and the work he faces will be removed," meaning this obstacle to recognizing it as music can be overcome.

Question 4 · MCQ

The mention of Stravinsky's description of music in the first paragraph does all the following EXCEPT:
  1. A.
    help us determine which sounds are musical and which are not.
    ✓ Correct
  2. B.
    respond to and expand upon earlier understandings of music.
  3. C.
    complicate our notion of what is communicated through music.
  4. D.
    allow us to classify electronic music as music.
Solution
Stravinsky's definition of music as "a form of speculation in terms of sound and time" is used to shift the definition away from 19th-century emotional expression (responding to/expanding earlier understandings, complicating communication notions) and to help laymen accept electronic music as music. It does not, however, provide a mechanism or criteria to determine which specific sounds are musical and which are not.

Question 5 · MCQ

From the context in which it is placed, the phrase “sui generis” in paragraph 3 suggests which one of the following?
  1. A.
    Particular
    ✓ Correct
  2. B.
    Generic
  3. C.
    Unaesthetic
  4. D.
    Indescribable
Solution
In paragraph 3, the author states that the serious composer seeks to explore "sui generis languages and forms" unique to the new medium rather than reproducing traditional patterns. "Sui generis" means unique, of its own kind, or "particular" to itself, which directly contrasts with "generic" or "traditional".

DILR · Data Interpretation & Logical Reasoning

Set

A round table has seven chairs around it. The chairs are numbered 1 through 7 in a clockwise direction. Four friends, Aslam, Bashir, Chhavi, and Davies, sit on four of the chairs. In the starting position, Aslam and Chhavi are sitting next to each other, while for Bashir as well as Davies, there are empty chairs on either side of the chairs that are sitting on.
The friends take turns moving either clockwise or counterclockwise from their chair. The friend who has to move in a turn occupies the first empty chair in whichever direction (s)he chooses to move. Aslam moves first (Turn 1), followed by Bashir, Chhavi, and Davies (Turns 2, 3, and 4, respectively). Then Aslam moves again followed by Bashir, and Chhavi (Turns 5, 6, and 7, respectively).
The following information is known
  1. The four friends occupy adjacent chairs only at the end of Turn 2 and Turn 6.
  2. Davies occupies Chair 2 after Turn 1 and Chair 4 after Turn 5, and Chhavi occupies Chair 7 after Turn 2.

Question 1 · TITA (type in the answer)

What is the number of the chair initially occupied by Bashir?

Answer: 4

Solution
Davies doesn't move in Turn 1 but is at chair 2 after Turn 1, so he is initially at 2. Chhavi doesn't move in Turns 1 or 2 but is at 7 after Turn 2, so she is initially at 7. Aslam and Chhavi are initially adjacent, so Aslam is at 1 or 6. If Aslam is at 1, Davies (at 2) would not have empty chairs on both sides. Thus, Aslam is at 6. The occupied chairs are 2, 6, and 7. Bashir must also have empty chairs on both sides, which is only possible if he is at chair 4 (leaving 3 and 5 empty).
TurnAslamBashirChhaviDaviesEmpty
Start64721, 3, 5
1 (A)14723, 5, 6
2 (B)13724, 5, 6
3 (C)13624, 5, 7
4 (D)13642, 5, 7
5 (A)73641, 2, 5
6 (B)75641, 2, 3
7 (C)751 or 34-

Question 2 · MCQ

Who sits on the chair numbered 4 at the end of Turn 3?
  1. A.
    Bashir
  2. B.
    Chhavi
  3. C.
    Davies
  4. D.
    No one
    ✓ Correct
Solution
From the initial state (A=6, B=4, C=7, D=2):
In Turn 1, Aslam moves to 1 (moving to 5 would prevent an adjacent block in Turn 2).
In Turn 2, Bashir moves to 3, forming the adjacent block 7-1-2-3.
In Turn 3, Chhavi (at 7) must move to 6. Moving to 4 would form the block 1-2-3-4, violating the rule that they are adjacent only after Turns 2 and 6.
At the end of Turn 3, the occupied chairs are 1, 2, 3, and 6. Chair 4 is empty, so no one sits on it.
TurnAslamBashirChhaviDaviesEmpty
Start64721, 3, 5
1 (A)14723, 5, 6
2 (B)13724, 5, 6
3 (C)13624, 5, 7

Question 3 · MCQ

Which of the chairs are occupied at the end of Turn 6?
  1. A.
    Chairs numbered 4, 5, 6, and 7
    ✓ Correct
  2. B.
    Chairs numbered 1, 2, 3, and 4
  3. C.
    Chairs numbered 2, 3, 4, and 5
  4. D.
    Chairs numbered 1, 2, 6, and 7
Solution
Continuing from Turn 3 (A=1, B=3, C=6, D=2):
In Turn 4, Davies moves to 4 (since he must be at 4 after Turn 5 and doesn't move in Turn 5).
In Turn 5, Aslam moves to 7 (moving to 2 would prevent an adjacent block in Turn 6).
In Turn 6, Bashir moves to 5, forming the adjacent block 4-5-6-7.
Thus, chairs 4, 5, 6, and 7 are occupied at the end of Turn 6.
TurnAslamBashirChhaviDaviesEmpty
3 (C)13624, 5, 7
4 (D)13642, 5, 7
5 (A)73641, 2, 5
6 (B)75641, 2, 3

Question 4 · MCQ

Which of the following BEST describes the friends sitting on chairs adjacent to the one occupied by Bashir at the end of Turn 7?
  1. A.
    Chhavi only
  2. B.
    Davies only
    ✓ Correct
  3. C.
    Chhavi and Davies
  4. D.
    Aslam and Chhavi
Solution
After Turn 6, the positions are A=7, B=5, C=6, D=4.
In Turn 7, Chhavi moves from chair 6 to the first empty chair in either direction (chair 1 or 3).
Bashir remains at chair 5. The chairs adjacent to 5 are 4 and 6.
Chair 4 is occupied by Davies, and chair 6 is now empty. Therefore, only Davies is adjacent to Bashir.
TurnAslamBashirChhaviDaviesEmpty
6 (B)75641, 2, 3
7 (C)751 or 34-

QA · Quantitative Ability

Question 1 · MCQ

A value of c for which the minimum value of \(f(x) = x^2 - 4cx + 8c\) is greater than the maximum value of \(g(x) = -x^2 + 3cx - 2c\), is
  1. A.
    2
  2. B.
    \(\frac{1}{2}\)
    ✓ Correct
  3. C.
    \(-\frac{1}{2}\)
  4. D.
    -2
Solution
The minimum value of a quadratic \(ax^2+bx+c\) (for \(a>0\)) occurs at \(x = -\frac{b}{2a}\).
For \(f(x) = x^2 - 4cx + 8c\), the minimum occurs at \(x = 2c\).
\(f_{min} = (2c)^2 - 4c(2c) + 8c = 8c - 4c^2\).
For \(g(x) = -x^2 + 3cx - 2c\), the maximum occurs at \(x = \frac{3c}{2}\).
\(g_{max} = -\left(\frac{3c}{2}\right)^2 + 3c\left(\frac{3c}{2}\right) - 2c = \frac{9c^2}{4} - 2c\).
Given \(f_{min} > g_{max}\):
\(8c - 4c^2 > \frac{9c^2}{4} - 2c \implies 10c > \frac{25c^2}{4} \implies 25c^2 - 40c < 0\).
\(5c(5c - 8) < 0 \implies 0 < c < 1.6\).
Among the given options, only \(\frac{1}{2}\) lies in the interval \((0, 1.6)\).

Question 2 · MCQ

Shruti travels a distance of 224 km in four parts for a total travel time of 3 hours. Her speeds in these four parts follow an arithmetic progression, and the corresponding time taken to cover these four parts follow another arithmetic progression. If she travels at a speed of 960 meters per minute for 30 minutes to cover the first part, then the distance, in meters, she travels in the fourth part is
  1. A.
    76800
  2. B.
    112000
  3. C.
    96000
  4. D.
    86400
    ✓ Correct
Solution
Total distance = \(224 \text{ km} = 224,000 \text{ m}\). Total time = \(3 \text{ hours} = 180 \text{ min}\).
Let the times be \(t_1, t_2, t_3, t_4\) in an arithmetic progression (AP). Given \(t_1 = 30\), the sum of the 4 terms is \(\frac{4}{2} [2(30) + 3d_t] = 180 \implies 60 + 3d_t = 90 \implies d_t = 10\).
The times are \(30, 40, 50, 60\) minutes.
Let the speeds be \(s_1, s_2, s_3, s_4\) in AP. Given \(s_1 = 960\), the speeds are \(960, 960+d_s, 960+2d_s, 960+3d_s\).
Total distance = \(\sum s_i t_i = 960(30) + (960+d_s)(40) + (960+2d_s)(50) + (960+3d_s)(60) = 224000\).
\(172800 + 320d_s = 224000 \implies 320d_s = 51200 \implies d_s = 160\).
The distance traveled in the fourth part is \(s_4 t_4 = (960 + 3 \times 160) \times 60 = 1440 \times 60 = 86400 \text{ m}\).

Question 3 · TITA (type in the answer)

In a 3-digit number N, the digits are non-zero and distinct such that none of the digits is a perfect square, and only one of the digits is a prime number. Then, the number of factors of the minimum possible value of N is

Answer: 6

Solution
The digits of \(N\) are non-zero, distinct, and not perfect squares (1, 4, 9). Thus, the available digits are \(\{2, 3, 5, 6, 7, 8\}\).
\(N\) contains exactly one prime digit (from 2, 3, 5, 7) and two non-prime digits. The only available non-prime digits are 6 and 8, so they must both be used.
To minimize the 3-digit number \(N\), the hundreds digit must be as small as possible. The smallest available prime is 2.
The digits are 2, 6, and 8, and the minimum possible value of \(N\) is 268.
The prime factorization of 268 is \(2^2 \times 67\).
The number of factors is \((2+1)(1+1) = 6\).

Question 4 · MCQ

Let \(3 \leq x \leq 6\) and \([x^2] = [x]^2\), where [x] is the greatest integer not exceeding x . If set S represents all feasible values of x, then a possible subset of S is
  1. A.
    \((3, \sqrt{10}) \cup [5, \sqrt{26}) \cup \{6\}\)
    ✓ Correct
  2. B.
    \([3, \sqrt{10}] \cup [5, \sqrt{26}]\)
  3. C.
    \([3, \sqrt{10}] \cup [4, \sqrt{17}] \cup \{6\}\)
  4. D.
    \([4, \sqrt{18}] \cup [5, \sqrt{27}] \cup \{6\}\)
Solution
Given \(3 \leq x \leq 6\), the possible values for \([x]\) are 3, 4, 5, and 6. We evaluate \([x^2] = [x]^2\) for each case:
\([x]\)\([x^2]\)Range of \(x^2\)Range of \(x\)
39\([9, 10)\)\([3, \sqrt{10})\)
416\([16, 17)\)\([4, \sqrt{17})\)
525\([25, 26)\)\([5, \sqrt{26})\)
636\(36\)\(\{6\}\)
The complete set of feasible values is \(S = [3, \sqrt{10}) \cup [4, \sqrt{17}) \cup [5, \sqrt{26}) \cup \{6\}\).
Option 1, \((3, \sqrt{10}) \cup [5, \sqrt{26}) \cup \{6\}\), is a valid subset of \(S\) because it uses valid intervals that fall entirely within \(S\).

Question 5 · MCQ

Stocks A, B and C are priced at rupees 120, 90 and 150 per share, respectively. A trader holds a portfolio consisting of 10 shares of stock A, and 20 shares of stocks B and C put together. If the total value of her portfolio is rupees 3300, then the number of shares of stock B that she holds, is
  1. A.
    10
  2. B.
    5
  3. C.
    15
    ✓ Correct
  4. D.
    12
Solution
Let the number of shares of stock B be \(b\) and stock C be \(c\).
Given \(b + c = 20\), so \(c = 20 - b\).
The total value of the portfolio is:
\(10(120) + 90b + 150c = 3300\)
\(1200 + 90b + 150(20 - b) = 3300\)
\(1200 + 90b + 3000 - 150b = 3300\)
\(4200 - 60b = 3300 \implies 60b = 900 \implies b = 15\).

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