Reasoning

Data Sufficiency: Practice Questions with Answers

11 practice questions on Data Sufficiency, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.

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1. Q.1

   Question: Is x greater than y? Statement I: x = y + 3. Statement II: y is a positive number.

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   Answer: Statement I alone is sufficient, but Statement II alone is not

   Solution:

   1. Statement I alone: x = y + 3 means x exceeds y by exactly 3, for ANY value of y — a definite "yes" regardless of what y actually is — sufficient alone.
   2. Statement II alone: knowing only that y is positive says nothing about x at all — not sufficient.

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2. Q.2

   Question: What is the area of a rectangular field? Statement I: The length of the field is 20 metres. Statement II: The perimeter of the field is 60 metres.

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   Answer: Both statements together are needed

   Solution:

   1. Statement I alone: only gives length, not width — can’t find area — not sufficient.
   2. Statement II alone: only gives perimeter, which alone doesn’t pin down a unique length and width combination — not sufficient.
   3. Both together: 2(20 + width) = 60 gives width = 10, so area = 20 × 10 = 200 — a single definite value — sufficient together.

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3. Q.3

   Question: Is x an even number? Statement I: x is divisible by 4. Statement II: x is divisible by 6.

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   Answer: Either statement alone is sufficient

   Solution:

   1. Statement I alone: any multiple of 4 is automatically even, so this gives a definite "yes" — sufficient alone.
   2. Statement II alone: any multiple of 6 is also automatically even, so this too gives a definite "yes" — sufficient alone.

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4. Q.4

   Question: What is the value of x? Statement I: x + 5 = 12. Statement II: x is a positive integer.

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   Answer: Statement I alone is sufficient, but Statement II alone is not

   Solution:

   1. Statement I alone: x + 5 = 12 gives exactly one value, x = 7 — sufficient alone.
   2. Statement II alone: "a positive integer" allows many values (1, 2, 3, …) — not sufficient alone.

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5. Q.5

   Question: What is the value of x? Statement I: x is a prime number less than 10. Statement II: x is an odd number.

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   Answer: Even both statements together are not sufficient

   Solution:

   1. Statement I alone: primes less than 10 are 2, 3, 5, 7 — multiple values, not sufficient.
   2. Statement II alone: infinitely many odd numbers — not sufficient.
   3. Both together: an odd prime less than 10 could be 3, 5, or 7 — still multiple values, not narrowed to one.

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6. Q.6

   Question: What is the two-digit number N? Statement I: The sum of the digits of N is 9. Statement II: N is a multiple of 9 and is less than 20.

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   Answer: Statement II alone is sufficient, but Statement I alone is not

   Solution:

   1. Statement I alone: many two-digit numbers have a digit sum of 9 (18, 27, 36, … 90) — not sufficient.
   2. Statement II alone: two-digit multiples of 9 below 20 — only 18 qualifies (9 itself is single-digit, and 27 already exceeds 20) — exactly one value — sufficient alone.

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7. Q.7

   Question: What is the value of n? Statement I: n is a multiple of 5. Statement II: n is a two-digit number that is both a multiple of 5 and a perfect square.

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   Answer: Statement II alone is sufficient, but Statement I alone is not (the only two-digit perfect square that’s a multiple of 5 is 25)

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8. Q.8

   Question: What is Rahul’s age? Statement I: Rahul is 5 years younger than his brother. Statement II: Rahul’s brother is 20 years old.

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   Answer: Both statements together are needed (Rahul = 20 − 5 = 15)

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9. Q.9

   Question: How many sons does Mr. Verma have? Statement I: Mr. Verma has exactly 2 children, both of whom are sons. Statement II: Mr. Verma has more than 1 child.

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   Answer: Statement I alone is sufficient, but Statement II alone is not

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10. Q.10

    Question: What is the speed of a train? Statement I: The train covers a certain distance in 4 hours. Statement II: The distance covered by the train is 240 km.

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    Answer: Both statements together are needed

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11. Q.11

    Question: Is the number Z divisible by 6? Statement I: Z is divisible by 2. Statement II: Z is divisible by 3.

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    Answer: Both statements together are needed (divisible by both 2 and 3 guarantees divisible by 6)

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