Data Sufficiency (Quant) — Practice

Question 1

Find the two-digit number. (I) The sum of its digits is 9. (II) It is divisible by 9 and lies between 40 and 50. Sufficiency?
(a) I alone  (b) II alone  (c) Either  (d) Both together

Accepted Answer

(I) many numbers (18,27,45…). (II) divisible by 9 in 40–50 ⇒ 45, unique.

Answer: (b) II alone.

Question 2

Find x and y. (I) x + y = 12. (II) x − y = 4. Sufficiency?
(a) I alone  (b) II alone  (c) Both together  (d) Either

Accepted Answer

Each alone: 1 equation, 2 unknowns. Together: 2 independent equations ⇒ x=8, y=4.

Answer: (c) Both together.

Question 3

Find x and y. (I) 2x + 3y = 13. (II) 4x + 6y = 26. Sufficiency?
(a) Both together  (b) I alone  (c) Either  (d) Even both together are not sufficient

Accepted Answer

(II) = 2×(I) — the same equation. Together still one relation for two unknowns.

Answer: (d) Even both together not sufficient.

Question 4

Find x. (I) x² = 49. (II) x is a positive integer. Sufficiency?
(a) I alone  (b) Both together  (c) Either  (d) Neither

Accepted Answer

(I) gives ±7. (II) alone gives nothing. Together: x = +7 (positive) — unique.

Answer: (b) Both together.

Question 5

Is x an even number? (I) x is a multiple of 4. Sufficiency of I?
(a) Sufficient  (b) Not sufficient  (c) Only with more data  (d) Cannot say

Accepted Answer

Every multiple of 4 is even ⇒ definite 'yes'. A definite answer is sufficient.

Answer: (a) Sufficient.

Question 6

Find A's present age. (I) A:B = 3:4. (II) B is 24 years old. Sufficiency?
(a) I alone  (b) II alone  (c) Both together  (d) Neither

Accepted Answer

(I) a ratio only, no absolute. (II) B alone. Together: A = 24×3/4 = 18.

Answer: (c) Both together.

Practice — Data Sufficiency (Quant)

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