CAT 2024QASlot 1 · Morning

CAT 2024 Slot 1 QA Question Paper with Solutions

40 Minutes22 QuestionsNov 24, 20243 marks correct · −1 wrong

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Q1CAT 2024 Slot 1 QA

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

Q2CAT 2024 Slot 1 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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Q3CAT 2024 Slot 1 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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Q4CAT 2024 Slot 1 QA

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When

10^{100}

is divided by 7, the remainder is

Q5CAT 2024 Slot 1 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

Q6CAT 2024 Slot 1 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

Q7CAT 2024 Slot 1 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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Q8CAT 2024 Slot 1 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

Q9CAT 2024 Slot 1 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

Q10CAT 2024 Slot 1 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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Q11CAT 2024 Slot 1 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

Q12CAT 2024 Slot 1 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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Q13CAT 2024 Slot 1 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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Q14CAT 2024 Slot 1 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

Q15CAT 2024 Slot 1 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

Q16CAT 2024 Slot 1 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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Q17CAT 2024 Slot 1 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,

Q18CAT 2024 Slot 1 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

Q19CAT 2024 Slot 1 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

Q20CAT 2024 Slot 1 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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Q21CAT 2024 Slot 1 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

Q22CAT 2024 Slot 1 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 2024 Slot 1 QA

The QA section of CAT 2024 Slot 1 was conducted on November 30, 2024, 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 2024 Slot 1 QA

CAT 2024 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 2024 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 2024 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.