All 26 Quant questions from the CAT 2020 · Slot 3 paper, with the correct answer for each.
Two alcohol solutions, A and B, are mixed in the proportion 1:3 by volume. The volume of the mixture is then doubled by
adding solution A such that the resulting mixture has 72% alcohol. If solution A has 60% alcohol, then the percentage of
alcohol in solution B is
Correct answer: C · 92%
A batsman played n + 2 innings and got out on all occasions. His average score in these n + 2 innings was 29 runs and he
scored 38 and 15 runs in the last two innings. The batsman scored less than 38 runs in each of the first n innings. In these n
innings, his average score was 30 runs and lowest score was x runs. The smallest possible value of x is
Correct answer: C · 2
Let m and n be positive integers, If x2 + mx + 2n = 0 and x2 + 2nx + m = 0 have real roots, then the smallest possible value of
m + n is
Correct answer: B · 6
A contractor agreed to construct a 6 km road in 200 days. He employed 140 persons for the work. After 60 days, he realized
that only 1.5 km road has been completed. How many additional people would he need to employ in order to finish the work
exactly on time? (in numerical value)
Correct answer: 40
If x = -1 and x = x + (m + 1) for every positive integer m, then x equals
1 m m+1 100
Correct answer: A · -5050
If $\log_a 30 = A$, $\log_a\left(\frac{5}{3}\right) = -B$ and $\log_2 a = \frac{1}{3}$, then $\log_3 a$ equals
Correct answer: A · $\frac{2}{A+B-3}$
Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick's age is 1 year less than the average age of all three, then
Harry's age, in years, is (in numerical value)
Correct answer: 18
Vimla starts for office every day at 9 am and reaches exactly on time if she drives at her usual speed of 40 km/hr. She is late by
6 minutes if she drives at 35 km/hr. One day, she covers two-thirds of her distance to office in one-thirds of her usual time to
reach office, and then stops for 8 minutes. The speed, in km/hr, at which she should drive the remaining distance to reach office
exactly on time is
Correct answer: C · 28
Let m and n be natural numbers such that n is even and 0.2 < m/20, n/m, n/11 < 0.5. Then m − 2n equals
Correct answer: B · 1
How many integers in the set {100, 101, 102, ..., 999} have at least one digit repeated? (in numerical value)
Correct answer: 252
In the final examination, Bishnu scored 52% and Asha scored 64%. The marks obtained by Bishnu is 23 less, and that by Asha is
34 more than the marks obtained by Ramesh. The marks obtained by Geeta, who scored 84%, is
Correct answer: D · 399
If $a, b, c$ are non-zero and $14^a = 36^b = 84^c$, then $6b\left(\frac{1}{c} - \frac{1}{a}\right)$ is equal to (in numerical value)
Correct answer: 3
A person invested a certain amount of money at 10% annual interest, compounded half-yearly. After one and a half years, the
interest and principal together became Rs 18522. The amount, in rupees, that the person had invested is (in numerical value)
Correct answer: 16000
A man buys 35 kg of sugar and sets a marked price in order to make a 20% profit. He sells 5 kg at this price, and 15 kg at a 10%
discount. Accidentally, 3 kg of sugar is wasted. He sells the remaining sugar by raising the marked price by p percent so as to
make an overall profit of 15%. Then p is nearest to
Correct answer: C · 25
The points (2, 1) and (-3, -4) are opposite vertices of a parallelogram. If the other two vertices lie on the line x + 9y + c = 0, then
c is
Correct answer: D · 14
A and B are two railway stations 90 km apart. A train leaves A at 9:00 am, heading towards B at a speed of 40 km/hr. Another
train leaves B at 10:30 am, heading towards A at a speed of 20 km/hr. The trains meet each other at
Correct answer: C · 11 : 00 am
Let N, x and y be positive integers such that N = x + y, 2 < x < 10 and 14 < y < 23. If N > 25, then how many distinct values are
possible for N? (in numerical value)
Correct answer: 6
Let k be a constant. The equations kx + y = 3 and 4x + ky = 4 have a unique solution if and only if
Correct answer: A · |k| ≠ 2
How many of the integers 1, 2, ….., 120, are divisible by none of 2, 5 and 7?
Correct answer: B · 41
How many pairs $(a, b)$ of positive integers are there such that $a \le b$ and $ab = 4^{2017}$?
Correct answer: A · 2018
Anil, Sunil, and Ravi run along a circular path of length 3 km, starting from the same point at the same time, and going in the
clockwise direction. If they run at speeds of 15 km/hr, 10 km/hr, and 8 km/hr, respectively, how much distance in km will Ravi
have run when Anil and Sunil meet again for the first time at the starting point?
Correct answer: A · 4.8
In a trapezium ABCD, AB is parallel to DC, BC is perpendicular to DC and ∠BAD = 45°. If DC = 5 cm, BC = 4cm, the area of the
trapezium in sq cm is (in numerical value)
Correct answer: 28
The area, in sq. units, enclosed by the lines x = 2, y = |x - 2| + 4, the X-axis and the Y-axis is equal to
Correct answer: A · 10
If f(x + y) = f (x) f (y) and f(5) = 4, then f (10) - f (-10) is equal to
Correct answer: C · 15.9375
(2 × 4 × 8 × 16) / ((log₂4)² (log₄8)³ (log₈16)⁴) (in numerical value)
Correct answer: 24
The vertices of a triangle are (0, 0), and (4, 0) and (3, 9). The area of the circle passing through these three points is
Correct answer: D · 205π/9