Here's a question type with a delightful twist: you're often not asked to solve the problem at all. Instead, you're asked whether you could solve it with the information given. It's like being handed two clues to a mystery and asked, "Is this enough to name the culprit?" — without ever having to name them. Data-sufficiency questions test a subtler, more valuable skill than raw calculation: knowing when you have enough information to decide. This chapter teaches you to judge sufficiency quickly and avoid the traps that catch most examinees.
Data-sufficiency questions present a question followed by two statements, and ask whether the information is enough to answer — not what the numeric answer is. You determine: does Statement 1 alone suffice? Statement 2 alone? Both together? Or is it unanswerable even with both?
On the Civil Service Exam, data-sufficiency items appear in Analytical Reasoning (and sometimes Numerical). They reward disciplined evaluation over computation, and the format repeats with the same five answer choices every time — so learning the structure is a durable advantage.
The difficulty is intermediate to advanced, mostly because the format is unfamiliar. The keys are to evaluate each statement alone first (without letting one leak into the other), understand that "sufficient" means "narrows to exactly one answer" (even a yes/no), and know the five standard outcomes. This lesson builds each.
After completing this lesson you will be able to:
You should be comfortable with:
A quick refresher on the core idea: a statement is sufficient if it narrows the answer to exactly one possibility. For "What is x?", sufficiency means x can be only one value. For a yes/no question like "Is x positive?", sufficiency means the answer is always yes or always no — you don't need x's exact value, just a definite verdict. Hold this "narrows to one definite answer" meaning of sufficiency in mind; it's the crux of the whole topic.
Judging whether you have enough information is a genuinely useful skill:
The exam tests data sufficiency because knowing the limits of your information is as important as computing with it.
Let's build the evaluation method and the five outcomes.
You are not solving for a final number. You're judging whether the given information is enough to answer the question definitely. Often you can decide sufficiency without computing the actual answer at all.
Analogy: It's like a detective asking, "With these two clues, can I identify the thief — yes or no?" The detective doesn't have to name the thief to answer that meta-question; they just judge whether the clues pin down exactly one suspect.
Almost every data-sufficiency question maps to one of these:
Learn these five; the answer to every item is one of them.
Check Statement 1 completely on its own — does it, by itself, give exactly one answer? Then separately check Statement 2 alone, deliberately ignoring Statement 1. Only after both solo checks do you consider them together.
"What is the value of x?" Statement 1: "x is a positive integer less than 3." (Alone: x could be 1 or 2 — not sufficient.) Statement 2: "x is even." (Alone: many even numbers — not sufficient.) Together: positive even integer less than 3 → x = 2 — sufficient together. This is outcome 3.
"Is n even?" Statement 1: "n is divisible by 4." (Any multiple of 4 is even — sufficient, answer "yes".) Statement 2: "n is divisible by 6." (Any multiple of 6 is even — sufficient, answer "yes".) Each alone settles it → outcome 4.
"Is x greater than y?" Statement 1: "x + y = 10." (Many splits — not sufficient.) Statement 2: "x and y are positive." (Doesn't compare them — not sufficient.) Together: x + y = 10 with both positive still allows x > y (6, 4), x < y (4, 6), or x = y (5, 5) — still not sufficient → outcome 5.
A statement is sufficient if it narrows to exactly one valid answer — even if that answer is "yes" or "no." "Is x positive?" is sufficiently answered by "always yes" or "always no," without pinning x's exact value. Don't dismiss a statement as insufficient just because it doesn't yield a specific number.
The most common error is letting Statement 1's information "carry over" when judging Statement 2 alone. Each statement must be judged strictly on its own first. Mentally erase Statement 1 before evaluating Statement 2; otherwise you'll wrongly rate Statement 2 as sufficient.
With the method built, let's picture, tabulate, and drill.
Data sufficiency uses the outcome framework:
| Outcome | Meaning |
|---|---|
| 1 | Statement 1 alone sufficient; 2 alone not |
| 2 | Statement 2 alone sufficient; 1 alone not |
| 3 | Both together sufficient; neither alone |
| 4 | Either alone sufficient |
| 5 | Not sufficient even together |
| Sufficient | narrows to exactly one answer (incl. yes/no) |
| Evaluate | each statement alone first, then combine |
| When a statement… | It's… |
|---|---|
| pins the value to exactly one | sufficient |
| leaves multiple possible values | not sufficient |
| gives a definite yes/no (even without the number) | sufficient |
| needs the other statement to pin it down | sufficient only "together" |
| each independently settles it | "either alone" (outcome 4) |
| even combined leaves options open | outcome 5 |
Step 1 — Read the question precisely (a value? a yes/no?). ↓ Step 2 — Evaluate Statement 1 alone: does it narrow to exactly one answer? ↓ Step 3 — Evaluate Statement 2 alone, ignoring Statement 1 entirely. ↓ Step 4 — If neither alone suffices, combine them and re-check. ↓ Step 5 — Match to one of the five outcomes, remembering yes/no answers count as sufficient.
Why Step 3's independence matters: the carry-over trap — importing Statement 1 into Statement 2's evaluation — is the defining error. Judge each strictly alone before ever combining.
For each: which of the five outcomes applies?
Example 1. What is x? (1) x = 5. (2) x is odd. Thinking: (1) pins x = 5 (sufficient). (2) many odd numbers (not sufficient). Solution: Outcome 1 (Statement 1 alone). Difficulty: ★☆☆☆☆
Example 2. Is n even? (1) n = 8. (2) n is a multiple of 10. Thinking: (1) 8 is even (sufficient). (2) multiples of 10 are even (sufficient). Solution: Outcome 4 (either alone). Difficulty: ★★☆☆☆
Example 3 (together). What is x? (1) x is a positive integer less than 4. (2) x is a multiple of 3. Thinking: (1) x = 1, 2, or 3 (not sufficient). (2) many multiples of 3 (not sufficient). Together: positive integer < 4 and a multiple of 3 → x = 3 (sufficient). Solution: Outcome 3 (both together). Difficulty: ★★★☆☆
Example 4 (neither, even together). Is x > y? (1) x + y = 12. (2) both are positive integers. Thinking: Together: x + y = 12 with positives still allows 7,5 or 5,7 — not sufficient. Solution: Outcome 5. Difficulty: ★★★☆☆
Example 5 (yes/no sufficiency). Is x positive? (1) x² = 9. (2) x = 3. Thinking: (1) x = 3 or −3 — can't tell the sign (not sufficient). (2) x = 3, positive (sufficient). Solution: Outcome 2 (Statement 2 alone). Difficulty: ★★★☆☆
Example 6 (carry-over trap). What is the age of A? (1) A is 5 years older than B. (2) B is 20. Thinking: (1) alone: A = B + 5, but B unknown (not sufficient). (2) alone: B = 20 says nothing about A (not sufficient). Together: A = 25 (sufficient). Beware rating (1) as sufficient by sneaking in (2)'s B = 20. Solution: Outcome 3 (both together). Difficulty: ★★★★☆
Example 7 (each alone). Is the number divisible by 6? (1) It is divisible by 12. (2) It is divisible by 18. Thinking: (1) 12 is a multiple of 6, so any multiple of 12 is divisible by 6 (sufficient). (2) 18 is a multiple of 6, same logic (sufficient). Solution: Outcome 4 (either alone). Difficulty: ★★★★☆
Example 8 (sign question). Is x negative? (1) x < 5. (2) x³ < 0. Thinking: (1) x < 5 includes positives and negatives (not sufficient). (2) x³ < 0 means x is negative (sufficient). Solution: Outcome 2. Difficulty: ★★★★☆
Example 9 (together needed). What is the two-digit number? (1) Its tens digit is 4. (2) Its units digit is twice its tens digit. Thinking: (1) 40–49 (not sufficient). (2) units = 2 × tens, but tens unknown alone (not sufficient). Together: tens 4, units 8 → 48 (sufficient). Solution: Outcome 3. Difficulty: ★★★★☆
Example 10 (insufficient together). Is quadrilateral ABCD a square? (1) All sides are equal. (2) It has a right angle. Thinking: (1) alone: could be a rhombus. (2) alone: many shapes. Together: equal sides + one right angle → actually forces a square (a rhombus with a right angle is a square). So together is sufficient. Solution: Outcome 3 (both together) — a reminder to reason carefully, not assume outcome 5. Difficulty: ★★★★★
Example 11 (either alone, value). What is x? (1) 2x = 10. (2) x + 3 = 8. Thinking: (1) x = 5 (sufficient). (2) x = 5 (sufficient). Each alone pins x = 5. Solution: Outcome 4. Difficulty: ★★★☆☆
Example 12 (yes/no, not sufficient). Is x an integer? (1) x = √y. (2) y = 16. Thinking: (1) alone: √y unknown (not sufficient). (2) alone: says nothing about x (not sufficient). Together: x = √16 = 4, an integer (sufficient). Solution: Outcome 3. (Note: if y weren't a perfect square, x wouldn't be an integer — but with y = 16 it is, a definite "yes".) Difficulty: ★★★★★
Which of the five outcomes applies?
Data-sufficiency questions ask whether the information is enough to answer — not what the answer is. Evaluate each statement alone first, deliberately ignoring the other (the carry-over trap is the top error), then combine only if needed. A statement is sufficient if it narrows to exactly one answer — and a definite yes or no counts, even without a specific number. Match every item to one of the five outcomes (1 alone, 2 alone, both together, either alone, or not even together). Reason carefully before declaring "not sufficient," since two weak statements can combine to force a unique answer. Judge sufficiency, check each alone, remember yes/no counts — and this unfamiliar format becomes dependable, quick points.
| Item | Key point |
|---|---|
| Task | judge sufficiency, not the answer |
| Order | each statement alone, then both |
| Sufficient | narrows to one answer (incl. yes/no) |
| Outcome 1 / 2 | one statement alone suffices |
| Outcome 3 | both together (neither alone) |
| Outcome 4 | either alone |
| Outcome 5 | not sufficient even together |
| Trap | no carry-over between statements |
Do I have to solve the problem? No. You only judge whether the given information determines a unique answer. Often you can decide sufficiency without computing the actual value.
What does "sufficient" mean? A statement is sufficient if it narrows the answer to exactly one possibility. For a yes/no question, a guaranteed "yes" or "no" is sufficient — you don't need the exact number.
What's the carry-over trap? Letting information from Statement 1 influence your evaluation of Statement 2 alone. Each statement must be judged in isolation first; mentally erase Statement 1 when checking Statement 2.
How is "either alone" different from "both together"? "Either alone" (outcome 4) means each statement independently settles the question. "Both together" (outcome 3) means neither works alone, but combined they do. Verify which by testing each alone.
Can two insufficient statements become sufficient together? Yes — that's outcome 3, and it's common. But don't assume the reverse: sometimes even combined they still leave multiple answers (outcome 5). Reason it through rather than guessing.
Tick them all and data-sufficiency questions become quick, dependable points — and you'll sharpen the real-world skill of knowing when you have enough information to decide.
Put it to the test with 1,638 practice questions on this topic.