CAT 2025QASlot 1 · Morning

CAT 2025 Slot 1 QA Question Paper with Solutions

40 Minutes22 QuestionsNov 30, 20253 marks correct · −1 wrong

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Q1CAT 2025 Slot 1 QA

The

(x, y)

coordinates of vertices P, Q and R of a parallelogram PQRS are

(-3, -2)

(1, -5)

and

(9, 1)

, respectively. If the diagonal SQ intersects the

x

-axis at

(a, 0)

, then the value of

a

Q2CAT 2025 Slot 1 QA

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A container holds 200 litres of a solution of acid and water, having 30% acid by volume. Atul replaces 20% of this solution with water, then replaces 10% of the resulting solution with acid, and finally replaces 15% of the solution thus obtained, with water. The percentage of acid by volume in the final solution obtained after these three replacements, is nearest to

Q3CAT 2025 Slot 1 QA

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In a class, there were more than 10 boys and a certain number of girls. After 40% of the girls and 60% of the boys left the class, the remaining number of girls was 8 more than the remaining number of boys. Then, the minimum possible number of students initially in the class was

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Q4CAT 2025 Slot 1 QA

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The number of distinct pairs of integers

(x, y)

satisfying the inequalities

x > y \geq 3

and

x + y < 14

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Q5CAT 2025 Slot 1 QA

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If the length of a side of a rhombus is 36 cm and the area of the rhombus is 396 sq. cm, then the absolute value of the difference between the lengths, in cm, of the diagonals of the rhombus is

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Q6CAT 2025 Slot 1 QA

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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

Q7CAT 2025 Slot 1 QA

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The number of non-negative integer values of

k

for which the quadratic equation

x^{2} - 5x + k = 0

has only integer roots, is

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Q8CAT 2025 Slot 1 QA

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In the set of consecutive odd numbers

\{1, 3, 5, \ldots, 57\}

, there is a number

k

such that the sum of all the elements less than

k

is equal to the sum of all the elements greater than

k

. Then,

k

equals

Q9CAT 2025 Slot 1 QA

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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

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Q10CAT 2025 Slot 1 QA

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A shopkeeper offers a discount of 22% on the marked price of each chair, and gives 13 chairs to a customer for the discounted price of 12 chairs to earn a profit of 26% on the transaction. If the cost price of each chair is Rs 100, then the marked price, in rupees, of each chair is

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Q11CAT 2025 Slot 1 QA

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Kamala divided her investment of Rs 100000 between stocks, bonds, and gold. Her investment in bonds was 25% of her investment in gold. With annual returns of 10%, 6%, 8% on stocks, bonds, and gold, respectively, she gained a total amount of Rs 8200 in one year. The amount, in rupees, that she gained from the bonds, was

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Q12CAT 2025 Slot 1 QA

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Arun, Varun and Tarun, if working alone, can complete a task in 24, 21, and 15 days, respectively. They charge Rs 2160, Rs 2400, and Rs 2160 per day, respectively, even if they are employed for a partial day. On any given day, any of the workers may or may not be employed to work. If the task needs to be completed in 10 days or less, then the minimum possible amount, in rupees, required to be paid for the entire task is

Q13CAT 2025 Slot 1 QA

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At a certain simple rate of interest, a given sum amounts to Rs 13920 in 3 years, and to Rs 18960 in 6 years and 6 months. If the same given sum had been invested for 2 years at the same rate as before but with interest compounded every 6 months, then the total interest earned, in rupees, would have been nearest to

Q14CAT 2025 Slot 1 QA

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A cafeteria offers 5 types of sandwiches. Moreover, for each type of sandwich, a customer can choose one of 4 breads and opt for either small or large sized sandwich. Optionally, the customer may also add up to 2 out of 6 available sauces. The number of different ways in which an order can be placed for a sandwich, is

Q15CAT 2025 Slot 1 QA

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For any natural number

k

, let

a_{k} = 3^{k}

. The smallest natural number

m

for which

\{(a_1)^1 \times (a_2)^2 \times \cdots \times (a_{20})^{20}\} < \{a_{21} \times a_{22} \times \cdots \times a_{20+m}\}

Q16CAT 2025 Slot 1 QA

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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

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Q17CAT 2025 Slot 1 QA

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The number of distinct integers

n

for which

\log_{\frac{1}{4}}(n^2 - 7n + 11) > 0

, is

Q18CAT 2025 Slot 1 QA

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In a circle with center C and radius

6\sqrt{2}

cm, PQ and SR are two parallel chords separated by one of the diameters. If

\angle PQC = 45^\circ

, and the ratio of the perpendicular distance of PQ and SR from C is

3:2

, then the area, in sq. cm, of the quadrilateral PQRS is

Q19CAT 2025 Slot 1 QA

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The ratio of the number of students in the morning shift and afternoon shift of a school was 13 : 9. After 21 students moved from the morning shift to the afternoon shift, this ratio became 19 : 14. Next, some new students joined the morning and afternoon shifts in the ratio 3 : 8 and then the ratio of the number of students in the morning shift and the afternoon shift became 5 : 4. The number of new students who joined is

Q20CAT 2025 Slot 1 QA

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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

Q21CAT 2025 Slot 1 QA

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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

Q22CAT 2025 Slot 1 QA

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a - 6b + 6c = 4

and

6a + 3b - 3c = 50

, where

a

b

and

c

are real numbers, the value of

2a + 3b - 3c

About CAT 2025 Slot 1 QA

The QA section of CAT 2025 Slot 1 was conducted on November 30, 2025, the last Sunday of November — consistent with IIM's scheduling across all recent years. The section contains 24 questions to be answered in 40 minutes, carrying 72 marks in total. There is no sectional time limit within the overall exam, but students choosing to switch sections mid-paper lose the ability to return — making pacing within QA critical.

Passage Topics in CAT 2025 Slot 1 QA

CAT 2025 Slot 1 QA featured four reading comprehension passages and a standalone Verbal Ability block. The RC passages spanned complexity theory and global systems, the aesthetics of electronic music, the economics of income inequality, and the legal history of criminal responsibility — a typical CAT spread across the sciences, humanities, and social sciences. The VA section included Para Jumbles, Para Summary, and Odd Sentence Out questions, consistent with the pattern since CAT 2019.

CAT 2025 QA Marking Scheme

Correct answer (MCQ): +3 marks
Wrong answer (MCQ): −1 mark
Unattempted (MCQ): 0 marks
TITA questions (if any): +3 correct, no negative marking

How to Use This Question Paper

Click any answer option to immediately check your answer. The correct option is highlighted in green; if you selected the wrong option, it is shown in red and the correct answer is revealed. A detailed explanation appears below each question after you answer it, along with statistics showing what percentage of students answered correctly in the actual exam.

The question navigator at the top of the page updates in real time — green bubbles indicate correct answers and red indicate wrong. Use this to spot weak areas at a glance. To practice under timed conditions, use the Take Full Mock button to attempt the complete CAT 2025 Slot 1 paper with a live timer and percentile benchmarking.

Tips for CAT QA Preparation

Reading Comprehension accounts for roughly two-thirds of the QA section. The passages in CAT are dense and argumentative — they reward close reading of the author's position rather than skimming for facts. Practising on past papers is the most reliable way to calibrate your reading speed, improve inference accuracy, and recognise the types of questions IIM setters favour. Use the answer statistics on this page to benchmark yourself; questions where more than 50% of test-takers answered correctly are ones you should aim to get right every time.