CAT 2021 · Slot 1 — Quantitative Ability

All 22 Quant questions from the CAT 2021 · Slot 1 paper, with the correct answer for each.

Question 1

Two trains cross each other in 14 seconds when running in opposite directions along parallel tracks. The faster train is 160 m
long and crosses a lamp post in 12 seconds. If the speed of the other train is 6 km/hr less than the faster one, its length, in m,
is

  1. 184
  2. 192
  3. 190
  4. 180

Correct answer: C · 190

Question 2

If the area of a regular hexagon equals the area of an equilateral triangle of side 12 cm, then the length, in cm, of each side of the hexagon is

  1. $4\sqrt{6}$
  2. $6\sqrt{6}$
  3. $\sqrt{6}$
  4. $2\sqrt{6}$

Correct answer: D · $2\sqrt{6}$

Question 3

Suppose the length of each side of a regular hexagon ABCDEF is 2 cm. If T is the midpoint of CD, then the length of AT, in cm, is

  1. $\sqrt{13}$
  2. $\sqrt{14}$
  3. $\sqrt{12}$
  4. $\sqrt{15}$

Correct answer: A · $\sqrt{13}$

Question 4

Anu, Vinu and Manu can complete a work alone in 15 days, 12 days and 20 days, respectively. Vinu works everyday. Anu works only on alternate days
starting from the first day while Manu works only on alternate days starting from the second day. Then, the number of days needed to complete the work
is

  1. 5
  2. 8
  3. 6
  4. 7

Correct answer: D · 7

Question 5

The amount Neeta and Geeta together earn in a day equals what Sita alone earns in 6days. The amount Sita and Neeta
together earn in a day equals what Geeta alone earns in 2 days. The ratio of the daily earnings of the one who earns the most
to that of the one who earns the least is

  1. 3 : 2
  2. 11 : 7
  3. 11 : 3
  4. 7 : 3

Correct answer: C · 11 : 3

Question 6

Onion is sold for 5 consecutive months at the rate of Rs 10, 20, 25, 25, and 50 per kg, respectively. A family spends a fixed
amount of money on onion for each of the first three months, and then spends half that amount on onion for each of the next
two months. The average expense for onion, in rupees per kg, for the family over these 5months is closest to

  1. 26
  2. 18
  3. 16
  4. 20

Correct answer: B · 18

Question 7

The number of groups of three or more distinct numbers that can be chosen from 1,2, 3, 4, 5, 6, 7 and 8 so that the groups
always include 3 and 5, while 7 and 8 are never included together is

Correct answer: 47

Question 8

Amal purchases some pens at ₹ 8 each. To sell these, he hires an employee at a fixed wage. He sells 100 of these pens at ₹ 12
each. If the remaining pens are sold at₹ 11 each, then he makes a net profit of ₹ 300, while he makes a net loss of ₹ 300 if the
remaining pens are sold at ₹ 9 each. The wage of the employee, in INR, is

Correct answer: 1000

Question 9

A basket of 2 apples, 4 oranges and 6 mangoes costs the same as a basket of 1 apple,4 oranges and 8 mangoes, or a basket of
8 oranges and 7 mangoes. Then the number of mangoes in a basket of mangoes that has the same cost as the other baskets is

  1. 11
  2. 13
  3. 10
  4. 12

Correct answer: B · 13

Question 10

The number of integers n that satisfy the inequalities |n -60| < |n-100| <| n-20| is

  1. 21
  2. 19
  3. 18
  4. 20

Correct answer: B · 19

Question 11

How many three-digit numbers greater than 100 increase by 198 when their three digits are reversed? (numerical value)

Correct answer: 70

Question 12

Anil invests some money at a fixed rate of interest, compounded annually. If the interests accrued during the second and third
year are ₹ 806.25 and ₹ 866.72, respectively, the interest accrued, in INR, during the fourth year is nearest to

  1. 929.48
  2. 934.65
  3. 931.72
  4. 926.84

Correct answer: C · 931.72

Question 13

Hospital A admitted 21 fewer Covid patients than hospital B (all recovered). The total recovery days were 200 for A and 152 for B. If A's average recovery time was 3 days more than B's, the number admitted in hospital A was (numerical value)

Correct answer: 35

Question 14

The number of integers n satisfying |n − 60| < |n − 100| < |n − 20| is

Correct answer: 120

Question 15

f(x) = (x² + 2x − 15)/(x² − 7x − 18) is negative if and only if x lies in

  1. −5 < x < −2 or 3 < x < 9
  2. x < −5 or −2 < x < 3
  3. −2 < x < 3 or x > 9
  4. x < −5 or 3 < x < 9

Correct answer: A · −5 < x < −2 or 3 < x < 9

Question 16

If $5 - \log_{10}\sqrt{1+x} + 4\log_{10}\sqrt{1-x} = \log_{10}\left(\frac{1}{\sqrt{1-x^2}}\right)$, then $100x$ equals (numerical value)

Correct answer: 99

Question 17

Amar, Akbar and Anthony: Amar+Akbar finish in 1 year, Akbar+Anthony in 16 months, Anthony+Amar in 2 years. The one who is neither fastest nor slowest, working alone, takes (months, numerical value)

Correct answer: 32

Question 18

If x₀ = 1, x₁ = 2 and xₙ₊₂ = (1 + xₙ₊₁)/xₙ for n = 0,1,2,…, then x₂₀₂₁ equals

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

Correct answer: D · 2

Question 19

Two 800 cc bottles hold indigo solutions of strengths 33% and 17%. Part of the first bottle's solution is thrown away and replaced by an equal volume from the second bottle; the first bottle's strength becomes 21%. The volume (cc) left in the second bottle is (numerical value)

Correct answer: 200

Question 20

Identical chocolate pieces are sold in boxes of two sizes, small and large. The large box is sold for twice the price of the small
box. If the selling price per gram of chocolate in the large box is 12% less than that in the small box, then the percentage by
which the weight of chocolate in the large box exceeds that in the small box is nearest to

  1. 144
  2. 127
  3. 135
  4. 124

Correct answer: B · 127

Question 21

The natural numbers are divided into groups as (1), (2, 3, 4), (5, 6, 7, 8, 9), ….. and so on. Then, the sum of the numbers in the
15th group is equal to

  1. 6119
  2. 6090
  3. 4941
  4. 7471

Correct answer: A · 6119

Question 22

If r a constant such that |x2 - 4x - 13| = r has exactly three distinct real roots, then the value of r is

  1. 17
  2. 21
  3. 15
  4. 18

Correct answer: A · 17