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CAT 2023 Slot 03 QA (Quantitative Aptitude) | Complete Solutions with Video & Short Explanations

Preparing for CAT 2025 or CAT 2026? One of the smartest ways to boost your score in Quantitative Aptitude (QA) is by practicing previous year CAT papers with detailed solutions.


In this blog, we bring you all the questions of CAT 2023 Slot 03 QA (Quantitative Aptitude) along with:

✅ Full video explanations (step-by-step)

✅ Short explanations for quick revision (where possible)

✅ Smart solving tricks by Anshu Agarwal (99.97 %ile in CAT QA)


This blog is your one-stop preparation guide for mastering CAT Quant through real exam questions.

CAT 2023 Slot 03 QA
CAT 2023 Slot 03 Quantitative Aptitude

Why Solve CAT 2023 Slot 03 QA Questions?

  • Real CAT level exposure – No book can replicate actual exam quality.

  • Improves speed & accuracy – You’ll see the best methods to solve in limited time.

  • Concept clarity – From arithmetic to algebra, every chapter is covered.

  • Video + Short Solutions – Learn deeply, revise quickly.


1. If x is a positive real number such that x⁸ + (1/x)⁸ = 47, then the value of x⁹ + (1/x)⁹ is:

(a) 30√5

(b) 34√5

(c) 40√5

(d) 36√5


2. Let n and m be two positive integers such that there are exactly 41 integers greater than 8ᵐ and less than 8ⁿ, which can be expressed as powers of 2.

Then, the smallest possible value of n + m is:

(a) 42

(b) 44

(c) 16

(d) 14


3.

CAT 2023 Slot 03 QA

(a) log₄7

(b) log₄(23/2)

(c) log₄(3/2)

(d) log₄(7/2)

Short Explanation


4. For some real numbers a and b, the system of equations x + y = 4 and

(a + 5)x + (b² − 15)y = 8b

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

(a) 25

(b) 33

(c) 55

(d) 15


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

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6. A quadratic equation x²+bx+c=0 has two real roots. If the difference between the reciprocals of the roots is 1/3, and the sum of the reciprocals of the squares of the roots is 5/9, then the largest possible value of (b + c) is:


7. Let n be any natural number such that 5ⁿ⁻¹ < 3ⁿ⁺¹. Then, the least integer value of m that satisfies 3ⁿ⁺¹ < 2ⁿ⁺ᵐ for each such n is:

Short Explanation


8. The population of a town in 2020 was 100000. The population decreases 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:

(a) 75000

(b) 73000

(c) 74000

(d) 72000

Short Explanation


9. 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:

(a) 1

(b) 1.5

(c) 0.5

(d) 2


10. 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:

(a) 21

(b) 17

(c) 20

(d) 16

Short Explanation

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11. 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:

(a) 3(3- √5)

(b) 3( √5-1)

(c) 12(√5-2)

(d) 3(3+ √5)

Short Explanation


12. 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:

(a) 21

(b) 17

(c) 16

(d) 24

Short Explanation


13. A merchant purchases a cloth at a rate of ₹ 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 ₹ 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

(a) 16%

(b) 15.5%

(c) 4.2%

(d) 9.7%

Short Explanation


14. 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

Short Explanation


15. 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

Short Explanation

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16. 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:


17. 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:

(a) 1:1

(b) 2:1

(c) √5 ∶ 1

(d) √2 ∶ 1


18. Let ∆ABC 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 ∠AOB = 105°, then AD/BE equals:

(a) 2 sin 15°

(b) 2 cos 15°

(c) sin 15°

(d) cos 15°


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


20. The value of 1 + (1 + 1/3) × 1/4 + (1 + 1/3 + 1/9) × 1/16 + (1 + 1/3 + 1/9 + 1/27) × 1/64 + … is:

(a) 15/13

(b) 27/12

(c) 15/8

(d) 16/11

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21. Let aₙ = 46 + 8n and bₙ = 98 + 4n be two sequences for natural numbers n ≤ 100. Then, the sum of all terms common to both the sequences is:

(a) 14602

(b) 14798

(c) 15000

(d) 14900

Short Explanation


22. Suppose 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 xfor which f(x, 2x) = 27, is:

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