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Data Sufficiency Questions with Solutions

Data Sufficiency doesn’t ask you to solve the problem — it asks whether the given information is enough to solve it, in principle, without you ever finishing the arithmetic. Here’s the approach, four fully worked examples covering all the standard answer patterns, and a few to try yourself.

The approach, quickly

  • These questions give a question plus two numbered Statements, and ask whether the statements provide ENOUGH information to answer it — you’re judging sufficiency, not computing the final answer.
  • Standard answer choices: Statement I alone is sufficient (but not II); Statement II alone is sufficient (but not I); both together are needed (neither alone works); either statement alone is sufficient; or even both together are not sufficient.
  • Evaluate each statement completely independently first, as if the other didn’t exist — mixing information from both before checking each one alone is the most common mistake here.
  • "Sufficient" means you could, in principle, pin down a single definite answer — it doesn’t mean you have to finish the arithmetic. If a statement sets up a valid equation or relationship with exactly one solution, it’s sufficient even without computing the final number.

Worked examples

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

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.

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

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

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.

Answer: Either statement alone is sufficient

3. 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.

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.

Answer: Both statements together are needed

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

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.

Answer: Even both statements together are not sufficient

Try these yourself

Evaluate each statement alone first, then check against the answer.

1. 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.

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

2. 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.

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)

3. 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.

Answer: Both statements together are needed

Where this comes up

Data Sufficiency is a regular topic in the Reasoning/General Intelligence section of every exam Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk — and is especially common in banking exams.

Practice more Data Sufficiency questions

This page covers the approach and a handful of worked examples. Pariksha Saathi has full topic-wise practice sets for Data Sufficiency (and every other Reasoning/Quant/English topic) with instant scoring and explanations — free, no account required.

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