CAT 2023QASlot 3 · Evening

CAT 2023 Slot 3 QA Question Paper with Solutions

40 Minutes22 QuestionsNov 26, 20233 marks correct · −1 wrong

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Q1CAT 2023 Slot 3 QA

For some real numbers a and b, the system of equations

x + y = 4

and

(a + 5)x + (b^2 - 15)y = 8b

has infinitely many solutions for x and y. Then, the maximum possible value of ab is

Q2CAT 2023 Slot 3 QA

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If x is a positive real number such that

x^8 + \left(\dfrac{1}{x}\right)^8 = 47

, then the value of

x^9 + \left(\dfrac{1}{x}\right)^9

Q3CAT 2023 Slot 3 QA

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For a real number x, if

\dfrac{1}{2}

\dfrac{\log_3(2^x - 9)}{\log_3 4}

, and

\dfrac{\log_5\left(2^x + \dfrac{17}{2}\right)}{\log_5 4}

are in an arithmetic progression, then the common difference is

Q4CAT 2023 Slot 3 QA

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Let n and m be two positive integers such that there are exactly 41 integers greater than

8^m

and less than

8^n

, which can be expressed as powers of 2. Then, the smallest possible value of

n + m

Q5CAT 2023 Slot 3 QA

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A quadratic equation

x^2 + bx + c = 0

has two real roots. If the difference between the reciprocals of the roots is

\dfrac{1}{3}

, and the sum of the reciprocals of the squares of the roots is

\dfrac{5}{9}

, then the largest possible value of

(b + c)

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Q6CAT 2023 Slot 3 QA

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The sum of the first two natural numbers, each having 15 factors (including 1 and the number itself), is

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Q7CAT 2023 Slot 3 QA

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Let n be any natural number such that

5^{n - 1} < 3^{n + 1}

. Then, the least integer value of m that satisfies

3^{n + 1} < 2^{n + m}

for each such n, is

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Q8CAT 2023 Slot 3 QA

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A merchant purchases a cloth at a rate of Rs.100 per meter and receives 5 cm length of cloth free for every 100 cm length of cloth purchased by him. He sells the same cloth at a rate of Rs.110 per meter but cheats his customers by giving 95 cm length of cloth for every 100 cm length of cloth purchased by the customers. If the merchant provides a 5% discount, the resulting profit earned by him is

Q9CAT 2023 Slot 3 QA

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Anil mixes cocoa with sugar in the ratio 3 : 2 to prepare mixture A, and coffee with sugar in the ratio 7 : 3 to prepare mixture B. He combines mixtures A and B in the ratio 2 : 3 to make a new mixture C. If he mixes C with an equal amount of milk to make a drink, then the percentage of sugar in this drink will be

Q10CAT 2023 Slot 3 QA

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There are three persons A, B and C in a room. If a person D joins the room, the average weight of the persons in the room reduces by x kg. Instead of D, if person E joins the room, the average weight of the persons in the room increases by

2x

kg. If the weight of E is 12 kg more than that of D, then the value of x is

Q11CAT 2023 Slot 3 QA

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The population of a town in 2020 was 100000. The population decreased by y% from the year 2020 to 2021, and increased by x% from the year 2021 to 2022, where x and y are two natural numbers. If population in 2022 was greater than the population in 2020 and the difference between x and y is 10, then the lowest possible population of the town in 2021 was

Q12CAT 2023 Slot 3 QA

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Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number of days she would have taken to finish the job, cannot be

Q13CAT 2023 Slot 3 QA

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A boat takes 2 hours to travel downstream a river from port A to port B, and 3 hours to return to port A. Another boat takes a total of 6 hours to travel from port B to port A and return to port B. If the speeds of the boats and the river are constant, then the time, in hours, taken by the slower boat to travel from port A to port B is

Q14CAT 2023 Slot 3 QA

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A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At the beginning of a day, the number of mangoes make up 40% of his stock. That day, he sells half of the mangoes, 96 bananas and 40% of the apples. At the end of the day, he ends up selling 50% of the fruits. The smallest possible total number of fruits in the stock at the beginning of the day is

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Q15CAT 2023 Slot 3 QA

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The number of coins collected per week by two coin-collectors A and B are in the ratio 3 : 4. If the total number of coins collected by A in 5 weeks is a multiple of 7, and the total number of coins collected by B in 3 weeks is a multiple of 24, then the minimum possible number of coins collected by A in one week is

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Q16CAT 2023 Slot 3 QA

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Gautam and Suhani, working together, can finish a job in 20 days. If Gautam does only 60% of his usual work on a day, Suhani must do 150% of her usual work on that day to exactly make up for it. Then, the number of days required by the faster worker to complete the job working alone is

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Q17CAT 2023 Slot 3 QA

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A rectangle with the largest possible area is drawn inside a semicircle of radius 2 cm. Then, the ratio of the lengths of the largest to the smallest side of this rectangle is

Q18CAT 2023 Slot 3 QA

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Let ΔABC be an isosceles triangle such that AB and AC are of equal length. AD is the altitude from A on BC and BE is the altitude from B on AC. If AD and BE intersect at O such that

\angle AOB = 105^\circ

, then

\dfrac{AD}{BE}

equals

Q19CAT 2023 Slot 3 QA

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n a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is

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Q20CAT 2023 Slot 3 QA

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The value of

1 + \left(1 + \dfrac{1}{3}\right)\dfrac{1}{4} + \left(1 + \dfrac{1}{3} + \dfrac{1}{9}\right)\dfrac{1}{16} + \left(1 + \dfrac{1}{3} + \dfrac{1}{9} + \dfrac{1}{27}\right)\dfrac{1}{64} + \cdots

, is

Q21CAT 2023 Slot 3 QA

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Let

a_n = 46 + 8n

and

b_n = 98 + 4n

be two sequences for natural numbers

n \leq 100

. Then, the sum of all terms common to both the sequences is

Q22CAT 2023 Slot 3 QA

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uppose

f(x,y)

is a real-valued function such that

f(3x + 2y, 2x - 5y) = 19x

, for all real numbers x and y. The value of x for which

f(x, 2x) = 27

, is

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About CAT 2023 Slot 3 QA

The QA section of CAT 2023 Slot 3 was conducted on November 30, 2023, 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 2023 Slot 3 QA

CAT 2023 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 2023 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 2023 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.