Data Sufficiency — Decide If You Can Answer, Without Solving

A data sufficiency (DS) question gives a question and two statements. You don't find the answer — you decide whether the statements give enough information to find it.

1. The method

The five standard options (the wording varies):

1. I alone is sufficient, II alone is not.
2. II alone is sufficient, I alone is not.
3. Either I alone or II alone is sufficient.
4. Both together are needed (neither alone works).
5. Not sufficient even together.

When you test statement II alone, forget everything statement I told you. This is the most common mistake.

2. Solved examples

Example 1

What is the value of x? I. 2x + 3 = 11 II. x² = 16

• I alone: x = 4 ✓ (one value)
• II alone: x = 4 or −4 ✗ (two values)
• Answer: I alone.

Example 2

Is A taller than B? I. A is taller than C. II. C is taller than B.

• I alone: nothing about B ✗. II alone: nothing about A ✗.
• Together: A > C > B → yes ✓.
• Answer: Both together.

Example 3

What is Ravi's age? I. Ravi is 5 years older than Sunil. II. The sum of their ages is 45.

• Each alone ✗. Together: R − S = 5, R + S = 45 → R = 25 ✓.
• Answer: Both together.

Example 4

How many students are in the class? I. Riya is 10th from the top and 21st from the bottom. II. There are 18 boys and the girls are 12.

• I alone: 10 + 21 − 1 = 30 ✓.
• II alone: 18 + 12 = 30 ✓.
• Answer: Either statement alone.

Example 5 — a yes/no question

Is n an even number? I. n is divisible by 4. II. n is a multiple of 3.

• I: every multiple of 4 is even → definitely yes ✓.
• II: 6 is even, 9 is odd → could be either ✗.
• Answer: I alone.

For yes/no questions, a statement is sufficient if it gives a definite yes or a definite no. "Definitely no" also counts as sufficient!

Traps

• Don't solve fully. Once you know there's exactly one answer, stop.
• Two values are not sufficient (like x² = 16).
• Don't assume things that aren't stated (e.g. that x is positive or a whole number).

Quick recap

• Test I alone, II alone (forget I), then both.
• Map the result to one of the five options.
• A definite "no" is sufficient.
• Watch for hidden second values and unstated assumptions.