CAT 2025QASlot 3 · Evening

CAT 2025 Slot 3 QA Question Paper with Solutions

40 Minutes44 QuestionsNov 30, 20253 marks correct · −1 wrong

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Q1CAT 2025 Slot 3 QA

Teams A, B, and C consist of five, eight, and ten members, respectively, such that every member within a team is equally productive. Working separately, teams A, B, and C can complete a certain job in 40 hours, 50 hours, and 4 hours, respectively. Two members from team A, three members from team B, and one member from team C together start the job, and the member from team C leaves after 23 hours. The number of additional member(s) from team B, that would be required to replace the member from team C, to finish the job in the next one hour, is

Q2CAT 2025 Slot 3 QA

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In September, the incomes of Kamal, Amal and Vimal are in the ratio 8 : 6 : 5. They rent a house together, and Kamal pays 15%, Amal pays 12% and Vimal pays 18% of their respective incomes to cover the total house rent in that month. In October, the house rent remains unchanged while their incomes increase by 10%, 12% and 15%, respectively. In October, the percentage of their total income that will be paid as house rent, is nearest to

Q3CAT 2025 Slot 3 QA

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(x^{2} + \dfrac{1}{x^{2}}) = 25

and

x > 0

, then the value of

(x^{7} + \dfrac{1}{x^{7}})

Q4CAT 2025 Slot 3 QA

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x

is a positive real number such that

4\log_{10} x + 4\log_{100} x + 8\log_{1000} x = 13

, then the greatest integer not exceeding

x

, is

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Q5CAT 2025 Slot 3 QA

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\triangle ABC

AB = AC = 12

cm and

D

is a point on side

BC

such that

AD = 8

cm. If

AD

is extended to a point

E

such that

\angle ACB = \angle AEB

, then the length, in cm, of

AE

Q6CAT 2025 Slot 3 QA

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For any natural number

n

, let

a_n

be the largest integer not exceeding

\sqrt{n}

. Then the value of

a_1 + a_2 + \cdots + a_{50}

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Q7CAT 2025 Slot 3 QA

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In a school with 1500 students, each student chooses any one of the streams out of science, arts, and commerce, by paying a fee of Rs 1100, Rs 1000, and Rs 800, respectively. The total fee paid by all the students is Rs 15,50,000. If the number of science students is not more than the number of arts students, then the maximum possible number of science students in the school is

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Q8CAT 2025 Slot 3 QA

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When

10^{100}

is divided by 7, the remainder is

Q9CAT 2025 Slot 3 QA

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12^{12x} \times 4^{24x + 12} \times 5^{2y} = 8^{4z} \times 20^{12x} \times 243^{3x - 6}

, where

x

y

and

z

are natural numbers, then

x + y + z

equals

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Q10CAT 2025 Slot 3 QA

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A glass is filled with milk. Two-thirds of its content is poured out and replaced with water. If this process of pouring out two-thirds the content and replacing with water is repeated three more times, then the final ratio of milk to water in the glass, is

Q11CAT 2025 Slot 3 QA

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In an arithmetic progression, if the sum of fourth, seventh and tenth terms is 99, and the sum of the first fourteen terms is 497, then the sum of first five terms is

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Q12CAT 2025 Slot 3 QA

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Let

x, y

and

z

be real numbers satisfying

4(x^2 + y^2 + z^2) = a

4(x - y - z) = 3 + a

Then

a

equals

Q13CAT 2025 Slot 3 QA

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Let

p

q

and

r

be three natural numbers such that their sum is 900, and

r

is a perfect square whose value lies between 150 and 500. If

p

is not less than

0.3q

and not more than

0.7q

, then the sum of the maximum and minimum possible values of

p

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Q14CAT 2025 Slot 3 QA

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The sum of all four-digit numbers that can be formed with the distinct non-zero digits

a, b, c

and

d

, with each digit appearing exactly once in every number, is

153310 + n

, where

n

is a single digit natural number. Then, the value of

a + b + c + d + n

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Q15CAT 2025 Slot 3 QA

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The ratio of the number of coins in boxes A and B was 17:7. After 108 coins were shifted from box A to box B, this ratio became 37:20. The number of coins that needs to be shifted further from A to B, to make this ratio 1:1, is

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Q16CAT 2025 Slot 3 QA

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Consider two sets

A = \{2, 3, 5, 7, 11, 13\}

and

B = \{1, 8, 27\}

. Let

f

be a function from

A

B

such that for every element

b

B

there is at least one element

a

A

such that

f(a)=b

. Then, the total number of such functions

f

Q17CAT 2025 Slot 3 QA

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ABCD is a trapezium in which

AB

is parallel to

DC

AD

is perpendicular to

AB

, and

AB = 3DC

. If a circle inscribed in the trapezium touching all the sides has a radius of 3 cm, then the area, in sq. cm, of the trapezium is

Q18CAT 2025 Slot 3 QA

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Two places A and B are 45 kms apart and connected by a straight road. Anil goes from A to B while Sunil goes from B to A. Starting at the same time, they cross each other in exactly 1 hour 30 minutes. If Anil reaches B exactly 1 hour 15 minutes after Sunil reaches A, the speed of Anil, in km per hour, is

Q19CAT 2025 Slot 3 QA

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For a 4-digit number (greater than 1000), sum of the digits in the thousands, hundreds, and tens places is 15. Sum of the digits in the hundreds, tens, and units places is 16. Also, the digit in the tens place is 6 more than the digit in the units place. The difference between the largest and smallest possible value of the number is

Q20CAT 2025 Slot 3 QA

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If the equations

x^2 + mx + 9 = 0

x^2 + nx + 17 = 0

and

x^2 + (m+n)x + 35 = 0

have a common negative root, then the value of

2m + 3n

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Q21CAT 2025 Slot 3 QA

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For real values of

x

, the range of the function

f(x) = \dfrac{2x - 3}{2x^{2} + 4x - 6}

Q22CAT 2025 Slot 3 QA

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The surface area of a closed rectangular box, which is inscribed in a sphere, is 846 sq cm, and the sum of the lengths of all its edges is 144 cm. The volume, in cubic cm, of the sphere is

Q23CAT 2025 Slot 3 QA

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The sum of all possible real values of

x

for which

\log_{x-3}(x^2 - 9) = \log_{x-3}(x+1) + 2

, is

Q24CAT 2025 Slot 3 QA

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There are four numbers such that average of first two numbers is 1 more than the first number, average of first three numbers is 2 more than average of first two numbers, and average of first four numbers is 3 more than average of first three numbers. Then, the difference between the largest and the smallest numbers, is

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Q25CAT 2025 Slot 3 QA

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f(x) = (x^2 + 3x)(x^2 + 3x + 2)

, then the sum of all real roots of the equation

\sqrt{f(x)+1} = 9701

, is

Q26CAT 2025 Slot 3 QA

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A fruit seller has a total of 187 fruits consisting of apples, mangoes and oranges. The number of apples and mangoes are in the ratio 5 : 2. After she sells 75 apples, 26 mangoes and half of the oranges, the ratio of number of unsold apples to number of unsold oranges becomes 3 : 2. The total number of unsold fruits is

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Q27CAT 2025 Slot 3 QA

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In the

XY

-plane, the area, in sq. units, of the region defined by the inequalities

y \geq x + 4

and

-4 \leq x^2 + y^2 + 4(x-y) \leq 0

Q28CAT 2025 Slot 3 QA

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Ankita walks from A to C through B, and runs back through the same route at a speed that is 40% more than her walking speed. She takes exactly 3 hours 30 minutes to walk from B to C as well as to run from B to A. The total time, in minutes, she would take to walk from A to B and run from B to C, is

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Q29CAT 2025 Slot 3 QA

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In a class of 150 students, 75 students chose physics, 111 students chose mathematics and 40 students chose chemistry. All students chose at least one of the three subjects and at least one student chose all three subjects. The number of students who chose both physics and chemistry is equal to the number of students who chose both chemistry and mathematics, and this is half the number of students who chose both physics and mathematics. The maximum possible number of students who chose physics but not mathematics, is

Q30CAT 2025 Slot 3 QA

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An amount of Rs 10000 is deposited in bank A for a certain number of years at a simple interest of 5% per annum. On maturity, the total amount received is deposited in bank B for another 5 years at a simple interest of 6% per annum. If the interests received from bank A and bank B are in the ratio 10 : 13, then the investment period, in years, in bank A is

Q31CAT 2025 Slot 3 QA

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Rahul starts on his journey at 5 pm at a constant speed so that he reaches his destination at 11 pm the same day. However, on his way, he stops for 20 minutes, and after that, increases his speed by 3 km per hour to reach on time. If he had stopped for 10 minutes more, he would have had to increase his speed by 5 km per hour to reach on time. His initial speed, in km per hour, was

Q32CAT 2025 Slot 3 QA

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ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. Then, the length, in cm, of radius of incircle of

\triangle ADE

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Q33CAT 2025 Slot 3 QA

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The sum of all the digits of the number

(10^{50} + 10^{25} - 123)

, is

Q34CAT 2025 Slot 3 QA

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The sum of all real values of

k

for which

\left(\dfrac{1}{8}\right)^k \times \left(\dfrac{1}{32768}\right)^{1/3} = \left(\dfrac{1}{8}\right) \times \left(\dfrac{1}{32768}\right)^{1/k}

is,

Q35CAT 2025 Slot 3 QA

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Vessels A and B contain 60 litres of alcohol and 60 litres of water, respectively. A certain volume is taken out from A and poured into B. After stirring, the same volume is taken out from B and poured into A. If the resultant ratio of alcohol and water in A is 15 : 4, then the volume, in litres, initially taken out from A is

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Q36CAT 2025 Slot 3 QA

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a + b\sqrt{n}

is a positive square root of

29 - 12\sqrt{5}

, where

a

and

b

are integers, and

n

is a natural number, the maximum possible value of

a + b + n

Q37CAT 2025 Slot 3 QA

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The rate of water flow through three pipes A, B and C are in the ratio 4 : 9 : 36. An empty tank can be filled up completely by pipe A in 15 hours. If all the three pipes are used simultaneously to fill up this empty tank, the time, in minutes, required to fill up the entire tank completely is nearest to

Q38CAT 2025 Slot 3 QA

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A shop wants to sell a certain quantity (in kg) of grains. It sells half the quantity and an additional 3 kg of these grains to the first customer. Then, it sells half of the remaining quantity and an additional 3 kg of these grains to the second customer. Finally, when the shop sells half of the remaining quantity and an additional 3 kg of these grains to the third customer, there are no grains left. The initial quantity, in kg, of grains is

Q39CAT 2025 Slot 3 QA

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The average salary of 5 managers and 25 engineers in a company is 60000 rupees. If each of the managers received 20% salary increase while the salary of the engineers remained unchanged, the average salary of all 30 employees would have increased by 5%. The average salary, in rupees, of the engineers is

Q40CAT 2025 Slot 3 QA

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Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema would take 8 days working 5 hours per day to complete the same task. They decide to work together to complete this task. Seema agrees to work for double the number of hours per day as Renu, while Renu agrees to work for double the number of days as Seema. If Renu works 2 hours per day, then the number of days Seema will work, is

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Q41CAT 2025 Slot 3 QA

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A triangle ABC is formed with

AB = AC = 50

cm and

BC = 80

cm. Then, the sum of the lengths, in cm, of all three altitudes of the triangle ABC is

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Q42CAT 2025 Slot 3 QA

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Suppose

x_1, x_2, x_3, \ldots, x_{100}

are in arithmetic progression such that

x_5 = -4

and

2x_6 + 2x_9 = x_{11} + x_{13}

. Then,

x_{100}

equals

Q43CAT 2025 Slot 3 QA

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The monthly sales of a product from January to April were 120, 135, 150 and 165 units, respectively. The cost price of the product was Rs. 240 per unit, and a fixed marked price was used for the product in all the four months. Discounts of 20%, 10% and 5% were given on the marked price per unit in January, February and March, respectively, while no discounts were given in April. If the total profit from January to April was Rs. 138825, then the marked price per unit, in rupees, was

Q44CAT 2025 Slot 3 QA

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The selling price of a product is fixed to ensure 40% profit. If the product had cost 40% less and had been sold for 5 rupees less, then the resulting profit would have been 50%. The original selling price, in rupees, of the product is

About CAT 2025 Slot 3 QA

The QA section of CAT 2025 Slot 3 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 3 QA

CAT 2025 Slot 3 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 3 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.