Two-Statement Data Sufficiency

The classic data sufficiency format gives you a question plus two statements. You choose from five answer codes that describe which combination of statements is sufficient to answer the question.

1. Read the question — determine what "answering" means (unique value, yes/no, ranking, etc.).
2. Test S1 alone (cover S2 with your hand). Sufficient? Note S or NS.
3. Test S2 alone (cover S1 with your hand). Sufficient? Note S or NS.
4. Combine both only if both were NS in steps 2–3.
5. Map to a code using the table above.

Memory aid — AD / BCE split: if S1 alone works, the answer is A or D. If S2 alone works, the answer is B or D. If neither alone works, the answer is C or E.

Example 1: What is the value of a + b?

• S1: a = 7
• S2: b = 3

S1 alone: a = 7 but b unknown → NS. S2 alone: b = 3 but a unknown → NS. Together: a + b = 7 + 3 = 10. Unique. ✓ Answer: C

Example 2: Is quadrilateral PQRS a rectangle?

• S1: All four angles of PQRS are 90°.
• S2: Opposite sides of PQRS are equal.

S1 alone: four right angles → must be a rectangle. Sufficient. ✓ S2 alone: opposite sides equal → could be parallelogram or rectangle; not certain. NS. Answer: A

• Forgetting to test statements independently — the most common error; always cover the other statement first.
• Choosing C when D is correct — if each statement works alone, the answer is D (not C).
• Yes/No trap — for yes/no questions, sufficiency requires the same answer in every case, not just one possible case.

1. How old is Kiran? S1: Kiran is twice as old as Sana. S2: Sana is 9 years old. Which code?
2. Is p divisible by 4? S1: p is divisible by 8. S2: p = 12. Which code?

(Answers: 1 → C; 2 → D)