Official CAT 2025 Exam Slot 1• Official Answer Keys

CAT 2025 Slot 1 Official Question Paper

Complete 66-Question Unabridged Official Exam Paper (VARC + DILR + QA) with Verified Answer Keys & Step-by-Step Solutions

68 Total Questions

MCQ: 45 (+3 / -1)

TITA: 23 (0 Negative Penalty)

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Official Exam Questions & Explanations (25 of 68)

Sorted in official convenor sequence

Question 1 of 68

CAT 2025 Slot 1QAArithmetic • Ratio, Proportion & VariationModerate

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 :

The number of new students who joined is

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Question 2 of 68

CAT 2025 Slot 1QAGeometry • CirclesHard

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

3:2

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

PQRS

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Question 3 of 68

CAT 2025 Slot 1QAAlgebra • FunctionsHard

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

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Question 4 of 68

CAT 2025 Slot 1QANumber Systems • Integral SolutionsModerate

The number of distinct pairs of integers

(x, y)

satisfying the inequalities

x > y \geq 3

and

x + y < 14

TITA Answer:

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Question 5 of 68

CAT 2025 Slot 1QAAlgebra • PolynomialsEasy

The number of non-negative integer values of

k

for which the quadratic equation

x^2 - 5x + k = 0

has only integer roots, is

TITA Answer:

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Question 6 of 68

CAT 2025 Slot 1QAGeometry • Straight LinesModerate

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

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Question 7 of 68

CAT 2025 Slot 1QANumber Systems • FactorisationModerate

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

TITA Answer:

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Question 8 of 68

CAT 2025 Slot 1QAModern Math • Permutation & CombinationModerate

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

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Question 9 of 68

CAT 2025 Slot 1QAAlgebra • Progression & SeriesModerate

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

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Question 10 of 68

CAT 2025 Slot 1QAAlgebra • Minima & MaximaModerate

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

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Question 11 of 68

CAT 2025 Slot 1QAArithmetic • Simple & Compound InterestHard

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

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Question 12 of 68

CAT 2025 Slot 1QAGeometry • QuadrilateralsModerate

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

TITA Answer:

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Question 13 of 68

CAT 2025 Slot 1QAAlgebra • Progression & SeriesHard

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 \ldots \times (a_{20})^{20}\} < \{a_{21} \times a_{22} \times \ldots \times a_{(20+m)}\}

, is

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Question 14 of 68

CAT 2025 Slot 1QAArithmetic • Time, Speed & DistanceHard

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

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Question 15 of 68

CAT 2025 Slot 1QAArithmetic • Mixture & AlligationModerate

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

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Question 16 of 68

CAT 2025 Slot 1QAArithmetic • Time & WorkHard

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

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Question 17 of 68

CAT 2025 Slot 1QAAlgebra • Linear EquationModerate

a - 6b + 6c = 4

and

6a + 3b - 3c = 50

, where

a

b

and

c

are real numbers, the value of

2a + 3b - 3c

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Question 18 of 68

CAT 2025 Slot 1QAArithmetic • PercentagesModerate

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

TITA Answer:

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Question 19 of 68

CAT 2025 Slot 1QAArithmetic • PercentagesModerate

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

TITA Answer:

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Question 20 of 68

CAT 2025 Slot 1QAAlgebra • Linear EquationEasy

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

TITA Answer:

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Question 21 of 68

CAT 2025 Slot 1QAModern Math • LogarithmsHard

The number of distinct integers

n

for which

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

, is

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Question 22 of 68

CAT 2025 Slot 1QAArithmetic • Profit & LossModerate

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

TITA Answer:

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Question 23 of 68

CAT 2025 Slot 1DILRData Interpretation • Other ChartsModerate

Caselet / Problem Set Context•~173 words

Five countries engage in trade with each other. Each country levies import tariffs on the other countries. The import tariff levied by Country X on Country Y is calculated by multiplying the corresponding tariff percentage with the total imports of Country X from Country Y. The radar chart below depicts different import tariff percentages charged by each of the five countries on the others. For example, US (the blue line in the chart) charges 20%, 40%, 30%, and 30% import tariff percentages on imports from France, India, Japan, and UK, respectively. The bar chart depicts the import tariffs levied by each county on other countries. For example, US charged import tariff of 3 billion USD on UK.

Assume that imports from one country to another equals the exports from the latter to the former. The trade surplus of Country X with Country Y is defined as follows. Trade surplus = Exports from Country X to Country Y – Imports to Country X from Country Y. A negative trade surplus is called trade deficit.3a

How much is Japan's export to India worth?

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Question 24 of 68

CAT 2025 Slot 1DILRData Interpretation • Other ChartsModerate

Caselet / Problem Set Context•~173 words

Which among the following is the highest?

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Question 25 of 68

CAT 2025 Slot 1DILRData Interpretation • Other ChartsModerate

Caselet / Problem Set Context•~173 words

What is the trade surplus/trade deficit of India with UK?

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Frequently Asked Questions about CAT 2025 Slot 1 Official Question Paper

What was the total score and question pattern in CAT 2025 Slot 1?

CAT 2025 Slot 1 featured 66 questions across three sections: VARC, DILR, and Quantitative Aptitude. Marking scheme was +3 marks for every correct answer and -1 for every incorrect MCQ (0 for TITA).

How can I practice CAT 2025 Slot 1 under real timed conditions?

You can launch the free ThinkCAT TCS iON CBT Mock Simulator on this page. It replicates the official 20-minute/40-minute sectional timers, virtual calculator, and 5-state question palette.

Are these official answer keys verified by IIM convenors?

Yes, all 100% of answer keys on ThinkCAT match the official released candidate response sheet answer keys from the conducting IIM convenor.

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CAT 2025 Slot 1 Official Question Paper

Attempt under official TCS iON 40-Min countdown timer

Official Exam Questions & Explanations (25 of 68)

+ 43 More Official Questions in this Bank

Join 2,400+ CAT Aspirants WhatsApp Study Circle

Unlock 27 Full-Length CAT CBT Mocks & AI Percentile Engine

Frequently Asked Questions about CAT 2025 Slot 1 Official Question Paper

What was the total score and question pattern in CAT 2025 Slot 1?

How can I practice CAT 2025 Slot 1 under real timed conditions?

Are these official answer keys verified by IIM convenors?

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