Data Sufficiency — Decisions

In Data Sufficiency questions you are given a question and two statements (Statement 1 and Statement 2). You do NOT solve for the actual answer — you only decide whether the given data is enough to answer the question uniquely.

The five standard answer choices are:

• A — Statement 1 alone is sufficient; Statement 2 alone is not.
• B — Statement 2 alone is sufficient; Statement 1 alone is not.
• C — Both statements together are sufficient; neither alone is.
• D — Each statement alone is sufficient.
• E — Even both statements together are not sufficient.

1. Read the question carefully — identify exactly what you need to find (a unique value, yes/no, etc.).
2. Test Statement 1 alone — ignore Statement 2 completely. Can you answer the question? If yes, eliminate B, C, E.
3. Test Statement 2 alone — ignore Statement 1 completely. Can you answer the question? If yes, eliminate A, C, E.
4. Combine both only if neither alone was sufficient.
5. Choose A / B / C / D / E based on your findings.

Example 1: Is integer n even?

• S1: n + 3 is odd.
• S2: n² is even.

Test S1 alone: n + 3 is odd → n must be even. Sufficient. ✓ Test S2 alone: n² is even → n is even. Sufficient. ✓ Both work independently → Answer: D

Example 2: What is the value of x?

• S1: 2x + y = 10
• S2: x − y = 2

Test S1 alone: two unknowns, one equation — not sufficient. ✗ Test S2 alone: two unknowns, one equation — not sufficient. ✗ Together: solve the system → x = 4, y = 2. Unique answer. ✓ Answer: C

• Solving for the value instead of checking sufficiency — you only need to know whether you can solve, not the actual answer.
• Carrying information from S1 into the S2-alone test — test each statement in complete isolation.
• Confusing "sufficient" with "useful" — a statement can give extra information yet still not pin down a unique answer.

1. Is x > 0? S1: x² = 9. S2: x + 5 > 0. Which answer choice is correct?
2. What is the area of a rectangle? S1: perimeter = 20. S2: length = 6. Which answer choice?

(Answers: 1 → E [S1 gives x = ±3, S2 gives x > −5; together still x = 3 or −3 both satisfy S2, so E]; 2 → C)