CAT 2024 QA Slot 2 Question Paper With Detailed PDF Solutions

Get the complete CAT 2024 paper with answers and explanations

Download PDF from Email

CAT 2024 QA Slot 2 Paper With Answers & Explanation

Q. 1 ABCD is a trapezium in which AB is parallel to CD. The sides AD and BC when extended, intersect at point E.

If AB = 2 cm, CD = 1 cm, and perimeter of ABCD is 6 cm, then the perimeter, in cm, of ΔAEB is

Correct Answer
and
Explanation
Correct Answer

3

Explanation

Q. 2 Amal and Vimal together can complete a task in 150 days, while Vimal and Sunil together can complete the same task in 100 days. Amal starts working on the task and works for 75 days, then Vimal takes over and works for 135 days. Finally, Sunil takes over and completes the remaining task in 45 days. If Amal had started the task alone and worked on all days, Vimal had worked on every second day, and Sunil had worked on every third day, then the number of days required to complete the task would have been

Correct Answer
and
Explanation
Correct Answer

139

Explanation

Q. 3 When Rajesh’s age was same as the present age of Garima, the ratio of their ages was 3 : 2. When Garima’s age becomes the same as the present age of Rajesh, the ratio of the ages of Rajesh and Garima will become

Correct Answer
and
Explanation
Correct Answer

4

Explanation

Q. 4 All the values of x satisfying the inequality 1/(x + 5) ≤ 1/(2x – 3) are

Correct Answer
and
Explanation
Correct Answer

4

Explanation

Q. 5 A bus starts at 9 am and follows a fixed route every day. One day, it traveled at a constant speed of 60 km per hour and reached its destination 3.5 hours later than its scheduled arrival time. Next day, it traveled two-thirds of its route in one-third of its total scheduled travel time, and the remaining part of the route at 40 km per hour to reach just on time. The scheduled arrival time of the bus is

Correct Answer
and
Explanation
Correct Answer

4

Explanation

Q. 6 A vessel contained a certain amount of a solution of acid and water. When 2 litres of water was added to it, the new solution had 50% acid concentration. When 15 litres of acid was further added to this new solution, the final solution had 80% acid concentration. The ratio of water and acid in the original solution was

Correct Answer
and
Explanation
Correct Answer

3

Explanation

Let the original solution had A and W litres of acid.
When 2 litres of water is added, then A = W + 2.
Similarly, when further 1 litres of acid is added, A + 15 = 4(W + 2).
Solve the two equations and get A = 5 and W = 3.
Hence, required ratio is 3 : 5.

Q. 7

Correct Answer
and
Explanation
Correct Answer

14

Explanation

Q. 8 If m and n are natural numbers such that n > 1, and mn = 225 × 340, then m – n equals

Correct Answer
and
Explanation
Correct Answer

3

Explanation

Q. 9 A company has 40 employees whose names are listed in a certain order. In the year 2022, the average bonus of the first 30 employees was Rs. 40,000, of the last 30 employees was Rs. 60,000, and of the first 10 and last 10 employees together was Rs. 50,000. Next year, the average bonus of the first 10 employees increased by 100%, of the last 10 employees increased by 200% and of the remaining employees was unchanged. Then, the average bonus, in rupees, of all the 40 employees together in the year 2023 was

Correct Answer
and
Explanation
Correct Answer

2

Explanation

Q. 10 The coordinates of the three vertices of a triangle are: (1, 2), (7, 2), and (1, 10). Then the radius of the in circle of the triangle is

Correct Answer
and
Explanation
Correct Answer

2

Explanation

Q. 11 If x and y are real numbers such that 4x2 + 4y2 – 4xy – 6y + 3 = 0, then the value of (4x + 5y) is

Correct Answer
and
Explanation
Correct Answer

7

Explanation

Q. 12 A function f maps the set of natural numbers to whole numbers, such that f(xy) = f(x)f(y) + f(x) + f(y) for all x, y and f(p) = 1 for every prime number p. Then, the value of f(160000) is

Correct Answer
and
Explanation
Correct Answer

1

Explanation

f(xy) = f(x)f(y) + f(x) + f(y) = (f(x) + 1)(f(y) + 1) – 1
f(160000) = f(400 × 400) = (f(400) + 1)(f(400) + 1) – 1
Now, f(400) = f(20 × 20) = (f(20) + 1)(f(20) + 1) – 1
Now, f(20) = f(4 × 5) = (f(4) + 1)(f(5) + 1) – 1
Now, f(4) = f(2 × 2) = (f(2) + 1)(f(2) + 1) – 1
Since f(p) = 1 where p is a prime number, so
f(4) = (1 + 1)(1 + 1) – 1 = 3
f(20) = (3 + 1)(1 + 1) – 1 = 7
f(400) = (7 + 1)(7 + 1) – 1 = 63
f(160000) = (63 + 1)(63 + 1) – 1 = 4095.

Q. 13 Three circles of equal radii touch (but not cross) each other externally. Two other circles X and Y, are drawn such that both touch (but not cross) each of the three previous circles. If the radius of X is more than that of Y, the ratio of the radii of X and Y is

Correct Answer
and
Explanation
Correct Answer

4

Explanation

Q. 14 If x and y satisfy the equations |x| + x + y = 15 and x + |y| – y = 20, then (x – y) equals

Correct Answer
and
Explanation
Correct Answer

1

Explanation

First quadrant: Both x and y are positive. This would change the equation to 2x + y = 15 and x = 20, giving a negative value of y; hence, this is not the case.
Second quadrant: x is negative, but y is positive. This would change the equations to y = 15 and x = 20, giving a positive value of x, which hence cannot be the case.
Third quadrant: Both x and y are negative. This would change the equation to y = 15 and x – 2y = 20; this gives a positive value of y and hence cannot be the case.
Fourth quadrant: x is positive, but y is negative. This would change the equations to 2x + y = 15 and x – 2y = 20; this gives the value of x as 10 and y as –5, which would lie in the fourth quadrant. The value of (x – y) would be 10 – (–5) = 15.

Q. 15 P, Q, R and S are four towns. One can travel between P and Q along 3 direct paths, between Q and S along 4 direct paths, and between P and R along 4 direct paths. There is no direct path between P and S, while there are few direct paths between Q and R, and between R and S. One can travel from P to S either via Q, or via R, or via Q followed by R, respectively, in exactly 62 possible ways. One can also travel from Q to R either directly, or via P, or via S, in exactly 27 possible ways. Then, the number of direct paths between Q and R is

Correct Answer
and
Explanation
Correct Answer

7

Explanation

Q. 16

Correct Answer
and
Explanation
Correct Answer

3

Explanation

Q. 17 Bina incurs 19% loss when she sells a product at Rs. 4,860 to Shyam, who in turn sells this product to Hari. If Bina would have sold this product to Shyam at the purchase price of Hari, she would have obtained 17% profit. Then, the profit, in rupees, made by Shyam is

Correct Answer
and
Explanation
Correct Answer

2160

Explanation

Let the cost price of the item be P.
We are given that Bina sells this at 19% loss or at 0.81 × P at 4860.
This gives us the value of P as Rs. 6,000.
If Bina had sold this at 17% profit, the selling price would have been 1.17 × 6,000 = Rs. 7,020.
So, Shyam bought the product at Rs. 4,860 and sold it to Hari at Rs. 7,020, thus making a profit of 7,020 – 4,860 = Rs. 2,160.

Q. 18 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

Correct Answer
and
Explanation
Correct Answer

340

Explanation

Q. 19

Correct Answer
and
Explanation
Correct Answer

11

Explanation

Q. 20 When 3333 is divided by 11, the remainder is

Correct Answer
and
Explanation
Correct Answer

3

Explanation

Q. 21

Correct Answer
and
Explanation
Correct Answer

2

Explanation

Q. 22 Anil invests Rs 22000 for 6 years in a scheme with 4% interest per annum, compounded half-yearly. Separately, Sunil invests a certain amount in the same scheme for 5 years, and then reinvests the entire amount he receives at the end of 5 years, for one year at 10% simple interest. If the amounts received by both at the end of 6 years are equal, then the initial investment, in rupees, made by Sunil is

Correct Answer
and
Explanation
Correct Answer

2

Explanation