CAT 2023 · Slot 2 — Quantitative Ability

All 22 Quant questions from the CAT 2023 · Slot 2 paper, with the correct answer for each.

Question 1

Let a, b, m and n be natural numbers such that a > 1 and b > 1. If am bn = 144145, then the largest possible value of n – m is

  1. 580
  2. 290
  3. 289
  4. 579

Correct answer: D · 579

Question 2

Any non-zero real numbers x, y such that y != 3 and x/y < (x+3)/(y-3), will satisfy the condition

  1. x/y < y/x
  2. If y < 0, then -x < y
  3. If y > 10, then -x > y
  4. If x < 0, then -x < y

Correct answer: B · If y < 0, then -x < y

Question 3

For any natural numbers m, n, and k, such that k divides both m + 2n and 3m + 4n, k must be a common divisor of

  1. m and n
  2. 2m and 3n
  3. m and 2n
  4. 2m and n

Correct answer: C · m and 2n

Question 4

The sum of all possible values of $x$ satisfying the equation $2^{4x^2} - 2^{2x^2+x+16} + 2^{2x+30} = 0$, is

  1. 3
  2. 3/2
  3. 5/2
  4. 1/2

Correct answer: D · 1/2

Question 5

The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is (type in numerical)

Correct answer: 15

Question 6

For some positive real number $x$, if $\log_{\sqrt{3}}(x) + \frac{\log_x(25)}{\log_x(0.008)} = 16/3$, then the value of $\log_3(3x^2)$ is

Correct answer: 7

Question 7

Let k be the largest integer such that the equation (x – 1)2 + 2kx + 11 = 0 has no real roots. If y is a positive real number, then
the least possible value of k/4y + 9y is (type in numerical)

Correct answer: 6

Question 8

Pipes A and C are fill pipes while Pipe B is a drain pipe of a tank. Pipe B empties the full tank in one hour less than the time
taken by Pipe A to fill the empty tank. When pipes A, B and C are turned on together, the empty tank is filled in two hours. If
pipes B and C are turned on together when the tank is empty and Pipe B is turned off after one hour, then Pipe C takes another
one hour and 15 minutes to fill the remaining tank. If Pipe A can fill the empty tank in less than five hours, then the time taken,
in minutes, by Pipe C to fill the empty tank is

  1. 90
  2. 120
  3. 75
  4. 60

Correct answer: A · 90

Question 9

Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. He repays Rs 10320 at the end of the first
year and closes the loan by paying the outstanding amount at the end of the third year. Then, the total interest, in rupees, paid
over the three years is nearest to

  1. 45311
  2. 51311
  3. 33130
  4. 40991

Correct answer: B · 51311

Question 10

Ravi is driving at a speed of 40 km/h on a road. Vijay is 54 meters behind Ravi and driving in the same direction as Ravi. Ashok
is driving along the same road from the opposite direction at a speed of 50 km/h and is 225 meters away from Ravi. The speed,
in km/h, at which Vijay should drive so that all the three cross each other at the same time, is

  1. 58.8
  2. 67.2
  3. 61.6
  4. 64.4

Correct answer: C · 61.6

Question 11

Minu purchases a pair of sunglasses at Rs.1000 and sells to Kanu at 20% profit. Then, Kanu sells it back to Minu at 20% loss.
Finally, Minu sells the same pair of sunglasses to Tanu. If the total profit made by Minu from all her transactions is Rs. 500, then
Actual CAT 2023 Slot II
the percentage of profit made by Minu when she sold the pair of sunglasses to Tanu is

  1. 35.42%
  2. 52%
  3. 31.25%
  4. 26%

Correct answer: C · 31.25%

Question 12

The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If
she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and
lowest possible values of the total price of the four pieces will be 288000. Then, the price of the original precious stone is

  1. 1944000
  2. 972000
  3. 1620000
  4. 1296000

Correct answer: D · 1296000

Question 13

In a company, 20% of the employees work in the manufacturing department. If the total salary obtained by all the
manufacturing employees is one-sixth of the total salary obtained by all the employees in the company, then the ratio of the
average salary obtained by the manufacturing employees to the average salary obtained by the non-manufacturing employees
is

  1. 6 : 5
  2. 4 : 5
  3. 5 : 4
  4. 5 : 6

Correct answer: B · 4 : 5

Question 14

If certain amount of money is divided equally among n person, each one receives Rs 352. However, if two persons receive Rs
506 each and the remaining amount is divided equally among the other persons, each of them received less than or equal to Rs
330. Then, the maximum possible value of n is (type in numerical)

Correct answer: 16

Question 15

Jayant bought a certain number of white shirts at the rate of Rs 1000 per piece and a certain number of blue shirts at the rate of
Rs 1125 per piece. For each shirt, he then set a fixed market price which was 25% higher than the average cost of all the shirts.
He sold all the shirts at a discount of 10% and made a total profit of Rs 51000. If he bought both colors of shirts, then the
maximum possible total number of shirts that he could have bought is (type in numerical)

Correct answer: 407

Question 16

A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process
of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number
of times of doing this process, after which the volume of milk in the container becomes less than that of water, is (type in
numerical)

Correct answer: 7

Question 17

A triangle is drawn with its vertices on the circle $C$ such that one of its sides is a diameter of $C$ and the other two sides have their lengths in the ratio $a:b$. If the radius of the circle is $r$, then the area of the triangle is

  1. $\frac{abr^2}{2(a^2+b^2)}$
  2. $\frac{2abr^2}{a^2+b^2}$
  3. $\frac{4abr^2}{a^2+b^2}$
  4. $\frac{abr^2}{a^2+b^2}$

Correct answer: B · $\frac{2abr^2}{a^2+b^2}$

Question 18

In a rectangle ABCD, AB = 9 cm and BC = 6 cm. P and Q are two points on BC such that the areas of the figures ABP, APQ, and
AQCD are in geometric progression. If the area of the figure AQCD is four times the area of triangle ABP, then BP : PQ : QC is

  1. 1 : 2 : 4
  2. 1 : 2 : 1
  3. 2 : 4 : 1
  4. 1 : 1 : 2

Correct answer: C · 2 : 4 : 1

Question 19

The area of the quadrilateral bounded by the Y-axis, the line x = 5, and the lines |x – y| - |x – 5| = 2, is (type in numerical)

Correct answer: 45

Question 20

Let both the series a , a , a , ….. and b , b , b … be in arithmetic progression such that the common differences of both the
1 2 3 1 2 3
series are prime numbers. If a = b , a = b and b = 0, then a equals
5 9 19 19 2 11

  1. 86
  2. 79
  3. 83
  4. 84

Correct answer: B · 79

Question 21

If p2 + q2 – 29 = 2pq – 20 = 52 – 2pq, then the difference between the maximum and minimum possible value of (p3 – q3) is

  1. 243
  2. 486
  3. 378
  4. 189

Correct answer: C · 378

Question 22

Let a and b be two sequences such that a = 13 + 6 (n – 1) and b = 15 + 7 (n – 1) for all natural numbers n. Then, the largest
n n n n
three digit integer that is common to both these sequences, is (type in numerical)

Correct answer: 967