CAT 2024 QA Slot 3 Question Paper With Detailed PDF Solutions

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CAT 2024 QA Slot 3 Paper With Answers & Explanation

Q. 1 The number of all positive integers up to 500 with non-repeating digits is

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and
Explanation
Correct Answer

378

Explanation

One digit numbers from 1 to 9 = 9
Two digit numbers from 10 to 99 = 9 × 9 = 81
(tens digit can take values 1 to 9, units digit can take remaining 8 values as well as 0)
Three digit numbers from 100 to 500 = 4 × 9 × 8 = 288
(hundreds digit can take values 1 to 4, tens digit can take 9 values and units digit can take any one of the remaining 8 values)
All positive integers up to 500 with non repeating digits = 9 + 81 + 288 = 378.

Q. 2 If (a + b√3)2 = 52 + 30√3, where a and b are natural numbers, then a + b equals

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Explanation
Correct Answer

2

Explanation

Q. 3 After two successive increments, Gopal’s salary became 187.5% of his initial salary. If the percentage of salary increase in the second increment was twice of that in the first increment, then the percentage of salary increase in the first increment was

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Explanation
Correct Answer

1

Explanation

Q. 4 A regular octagon ABCDEFGH has sides of length 6 cm each. Then the area, in sq. cm, of the square ACEG is

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Explanation
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1

Explanation

Q. 5 If 3a = 4, 4b = 5, 5c = 6, 6d = 7, 7e = 8 and 8f = 9, then the value of the product abcdef is

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Explanation
Correct Answer

2

Explanation

Q. 6 Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayna in the same job. They undertake a job with an arrangement where Sam and Mohit work together on the first day, Sam and Ayna on the second day, Mohit and Ayna on the third day, and this three-day pattern is repeated till the work gets completed. Then, the fraction of total work done by Sam is

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and
Explanation
Correct Answer

1

Explanation

Q. 7 The number of distinct real values of x, satisfying the equation max{x, 2} – min{x, 2} = Ix + 2| – Ix – 2|, is

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Explanation
Correct Answer

2

Explanation

Q. 8 A train travelled a certain distance at a uniform speed. Had the speed been 6 km per hour more, it would have needed 4 hours less. Had the speed been 6 km per hour less, it would have needed 6 hours more. The distance, in km, travelled by the train is

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Explanation
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4

Explanation

Q. 9

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Explanation
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1

Explanation

Q. 10 The number of distinct integer solutions (x, y) of the equation Ix + yl + Ix – yl = 2, is

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Explanation
Correct Answer

8

Explanation

Q. 11 In a group of 250 students, the percentage of girls was at least 44% and at most 60%.
The rest of the students were boys. Each student opted for either swimming or running or both. If 50% of the boys and 80% of the girls opted for swimming while 70% of the boys and 60% of the girls opted for running, then the minimum and maximum possible number of students who opted for both swimming and running, are

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Explanation
Correct Answer

2

Explanation

Q. 12 The average of three distinct real numbers is 28. If the smallest number is increased by 7 and the largest number is reduced by 10, the order of the numbers remains unchanged, and the new arithmetic mean becomes 2 more than the middle number, while the difference between the largest and the smallest numbers becomes 64. Then, the largest number in the original set of three numbers is

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Explanation
Correct Answer

70

Explanation

Q. 13 Gopi marks a price on a product in order to make 20% profit. Ravi gets 10% discount on this marked price, and thus saves Rs 15. Then, the profit, in rupees, made by Gopi by selling the product to Ravi, is

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and
Explanation
Correct Answer

1

Explanation

Q. 14 For some constant real numbers p, k and a, consider the following system of linear equations in x and y:
px – 4y = 2
3x + ky = a
A necessary condition for the system to have no solution for (x, y), is

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and
Explanation
Correct Answer

3

Explanation

Q. 15 The midpoints of sides AB, BC, and AC in ΔABC are M, N, and P, respectively. The medians drawn from A, B, and C intersect the line segments MP, MN and NP at X, Y, and Z, respectively. If the area of ΔABC is 1440 sq cm, then the area, in sq cm, of ΔXYZ is

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Explanation
Correct Answer

90

Explanation

Q. 16 A certain amount of water was poured into a 300 litre container and the remaining portion of the container was filled with milk. Then an amount of this solution was taken out from the container which was twice the volume of water that was earlier poured into it, and water was poured to refill the container again. If the resulting solution contains 72% milk, then the amount of water, in litres, that was initially poured into the container was

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Explanation
Correct Answer

30

Explanation

Q. 17 Rajesh and Vimal own 20 hectares and 30 hectares of agricultural land, respectively, which are entirely covered by wheat and mustard crops. The cultivation area of wheat and mustard in the land owned by Vimal are in the ratio of 5 : 3. If the total cultivation area of wheat and mustard are in the ratio 11 : 9, then the ratio of cultivation area of wheat and mustard in the land owned by Rajesh is

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and
Explanation
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3

Explanation

Q. 18

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Explanation
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3

Explanation

Q. 19 If 1068 is divided by 13, the remainder is

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Explanation
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2

Explanation

Q. 20

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Explanation
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4

Explanation

Q. 21 Aman invests Rs 4000 in a bank at a certain rate of interest, compounded annually. If the ratio of the value of the investment after 3 years to the value of the investment after 5 years is 25 : 36, then the minimum number of years required for the value of the investment to exceed Rs 20000 is

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Explanation
Correct Answer

9

Explanation

Q. 22 A circular plot of land is divided into two regions by a chord of length 10√3 meters such that the chord subtends an angle of 120° at the center. Then, the area, in square meters, of the smaller region is

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Explanation
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2

Explanation