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Data Sufficiency

What a data-sufficiency question asks and the standard five options; the discipline of deciding sufficiency without computing the answer; testing each statement alone before testing them together; when a statement gives a unique answer and when it leaves two; sufficiency in arithmetic, ranking, blood relations, directions and coding questions; the traps — a statement that repeats the question, and two statements that are individually enough — with fully worked examples.

📑 Contents (5 sections)

Last reviewed 22 Sept 2026 · 5 min read

The question and the options

You are given a question and two (sometimes three) statements, and asked whether the statements are enough to answer it — not what the answer is.

The usual option set:

Option Meaning
(a) Statement I alone is sufficient, II alone is not
(b) Statement II alone is sufficient, I alone is not
(c) Each statement alone is sufficient
(d) Both together are not sufficient
(e) Both together are sufficient, but neither alone

Read the paper's own option list once — some papers order (d) and (e) the other way round.

The method

FormulaFour steps, in this order
  1. Read the question and decide exactly what would settle it (a single value, a yes/no, a name).
  2. Test Statement I alone, covering II with your hand.
  3. Test Statement II alone, forgetting I completely.
  4. Only if both fail individually, test them together.

Never compute more than you must. Sufficiency is reached the moment the answer is pinned to one possibility.

Exam TipA yes/no question is settled by a definite "no" too

If the question is "Is x greater than 5?", a statement forcing is sufficient — it answers the question, even though the answer is no. Sufficiency is about certainty, not about a positive answer.

Where candidates lose marks

  • Carrying I into II. Once step 2 is done, statement I must be forgotten entirely.
  • Computing the answer. It wastes the time this question type is designed to save.
  • Accepting two possibilities. "" gives or — not sufficient for the value of , though sufficient for .
  • Assuming the obvious. A statement that ages are whole numbers, or that a person is male, must be given, not supposed.

Worked examples

Worked ExampleExample 1 — one statement enough

What is the value of ? I. II. is a positive integer less than 10.

Solution. I gives → sufficient. II allows 1 to 9 → not sufficient. Option (a).

Worked ExampleExample 2 — each alone

How old is Ravi? I. Ravi is twice as old as his sister, who is 12. II. Ravi was born in 2002 and it is now 2026.

Solution. I gives 24; II gives 24 → each alone is sufficient, option (c).

Worked ExampleExample 3 — both needed

What is the two-digit number? I. The sum of its digits is 9. II. The number is divisible by 5 and greater than 40.

Solution. I alone: 18, 27, 36, 45, 54, 63, 72, 81, 90. II alone: 45, 50, 55, … Together: 45 and 90 both fit → not sufficient even together, option (d).

Worked ExampleExample 4 — both together suffice

Who sits at the extreme left of a row of five? I. A sits third from the right. II. B sits to the immediate left of A, and C sits to the immediate left of B.

Solution. I places A at seat 3. II then places B at 2 and C at 1 → together they settle it; neither alone does → option (e).

Worked ExampleExample 5 — a yes/no question

Is an even number? I. is divisible by 6. II. is a prime number greater than 2.

Solution. I forces even → sufficient. II forces odd → also sufficient (the answer is "no", which is still an answer) → each alone, option (c).

Worked ExampleExample 6 — two possibilities

What is the value of ? I. . II. is negative.

Solution. I gives → insufficient. II alone gives nothing. Together, → option (e).

Worked ExampleExample 7 — a relationship

How is P related to Q? I. P is the son of Q's brother. II. Q has only one brother.

Solution. I alone makes P Q's nephew — the brother's son, whether or not Q has other brothers → statement I alone is sufficient, option (a). II adds nothing.

Worked ExampleExample 8 — a statement that repeats the question

In which direction is X from Y? I. Y is to the north of X. II. X and Y are 5 km apart.

Solution. I answers it directly (X is south of Y) → sufficient. II gives distance only → option (a).

Worked ExampleExample 9 — coding

What is the code for "book"? I. In that code, "book my ticket" is written "sa ka na". II. In the same code, "my new ticket" is written "ka da na".

Solution. Together, the words common to both sentences are my and ticket, with common codes ka and na; so book is sa → sufficient together, neither alone → option (e).

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