CAT 2022 · Slot 3 — Quantitative Ability

All 22 Quant questions from the CAT 2022 · Slot 3 paper, with the correct answer for each.

Question 1

If C = 16x/y + 49y/x for nonzero reals x,y, then C cannot take the value

  1. 60
  2. -50
  3. -70
  4. -60

Correct answer: B · -50

Question 2

$k$ is an integer with $2x^2 + kx + 5 = 0$ having NO real roots and $x^2 + (k-5)x + 1 = 0$ having two DISTINCT real roots. The number of possible values of $k$ is

  1. 9
  2. 7
  3. 8
  4. 13

Correct answer: A · 9

Question 3

If $\left(\sqrt{7/5}\right)^{3x-y} = 875/2401$ and $\left(\frac{4a}{b}\right)^{6x-y} = \left(\frac{2a}{b}\right)^{y-6x}$ for all nonzero $a, b$, then $x+y$ is

Correct answer: 14

Question 4

Six distinct natural numbers: the average of the two smallest is 14 and of the two largest is 28. The maximum possible average of the six is

  1. 23
  2. 24
  3. 23.5
  4. 22.5

Correct answer: D · 22.5

Question 5

Medians BD and CE of triangle ABC meet at centroid O. If area of ABC = 108, the area of triangle EOD (in sq cm) is

Correct answer: 9

Question 6

If $(3 + 2\sqrt{2})$ is a root of $ax^2 + bx + c = 0$ and $(4 + 2\sqrt{3})$ is a root of $ay^2 + my + n = 0$ ($a, b, c, m, n$ integers), then $\left(\frac{b}{m} + \frac{c-2b}{n}\right)$ is

  1. 0
  2. 1
  3. 3
  4. 4

Correct answer: D · 4

Question 7

A group of N people finished 35% of a project by working 7 hours a day for 10 days. Then 10 people left and the rest finished the remaining 65% in 14 days at 10 hours a day. The value of N is

  1. 150
  2. 23
  3. 36
  4. 140

Correct answer: D · 140

Question 8

Glass 500cc milk, cup 500cc water. 150cc milk moved to cup (mixed), then 150cc of the mixture moved back. Ratio of water in glass to milk in cup is

  1. 1 : 1
  2. 10 : 13
  3. 3 : 10
  4. 10 : 3

Correct answer: A · 1 : 1

Question 9

Nitu invests Rs.20000: Rs.8000 at 5.5% (A), Rs.5000 at 5.6% (B), the rest at x% (C), all simple interest. Total annual interest = 5% of 20000 = Rs.1000. If she put the whole Rs.20000 in bank C, her annual interest would be

  1. 700
  2. 800
  3. 900
  4. 1000

Correct answer: B · 800

Question 10

Two cars from different locations at constant speeds meet in 1.5 h travelling towards each other, 10.5 h travelling in the same direction. Slower car speed 60 km/h. Distance travelled by the slower car when they meet travelling towards each other is

  1. 100
  2. 90
  3. 120
  4. 150

Correct answer: B · 90

Question 11

The arithmetic mean of all the distinct numbers obtained by rearranging the digits of 1421 (including itself) is

  1. 2222
  2. 2442
  3. 2592
  4. 3333

Correct answer: A · 2222

Question 12

The four sides of a quadrilateral are integers. Three sides are 1, 2 and 4 cm. The number of possible integer lengths of the fourth side is

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

Correct answer: D · 5

Question 13

The average of all 3-digit terms in the arithmetic progression 38, 55, 72, ... is

Correct answer: 548

Question 14

Average marks in sections A and B are 32 and 60; A has 10 fewer students than B. If the combined average is an integer, the difference between the max and min possible number of students in A is

Correct answer: 63

Question 15

Let f(x) = 2x - r if x >= r, and f(x) = r if x < r. The equation f(x) = f(f(x)) holds for all x where

  1. x > r
  2. x <= r
  3. x != r
  4. x >= r

Correct answer: B · x <= r

Question 16

In triangle ABC, AB=AC=8 cm. A circle with BC as diameter passes through A; another circle centred at A passes through B and C. The area (sq cm) of the overlapping region is

  1. 16π
  2. 16(π - 1)
  3. 32(π - 1)
  4. 32π

Correct answer: C · 32(π - 1)

Question 17

A school has <5000 students. Divided into teams of 9/10/12/25, exactly 4 are left out each time; divided into teams of 11, none left out. The maximum number of teams of 12 that can be formed is

Correct answer: 150

Question 18

The minimum possible value of $\frac{x^2 - 6x + 10}{3 - x}$, for $x < 3$, is

  1. -1/2
  2. 2
  3. 1/2
  4. -2

Correct answer: B · 2

Question 19

A donation box holds only Rs.100, Rs.250 and Rs.500 cheques. It contains exactly 100 cheques totalling Rs.15250. The maximum possible number of Rs.500 cheques is

Correct answer: 12

Question 20

Moody takes 30 s to ride an escalator walking at normal speed (same direction), 20 s at twice normal speed. If he stands still, the time (seconds) to finish riding is

Correct answer: 60

Question 21

Two ships approach a port along straight routes at constant speeds; initially the two ships and the port form an equilateral triangle of side 24 km. When the slower ship travelled 8 km, the triangle became right-angled. When the faster ship reaches the port, the distance (km) between the other ship and the port is

  1. 4
  2. 12
  3. 8
  4. 6

Correct answer: B · 12

Question 22

Bob finishes a job in 40 days. Alex is twice as fast as Bob and thrice as fast as Cole. Alex+Bob (day 1), Bob+Cole (day 2), Cole+Alex (day 3), repeat. Total days Alex worked when the job finishes is

Correct answer: 11