DI — Data Sufficiency

Data Sufficiency (DS) doesn't ask you to solve — it asks whether the given statements are enough to solve. You evaluate each statement's sufficiency, alone and together, and pick the standard option. It rewards judgement over calculation and is a recurring CAT/other-MBA-test format.

The five standard options

Option	Meaning
A	Statement 1 ALONE is sufficient, 2 alone is not
B	Statement 2 ALONE is sufficient, 1 alone is not
C	BOTH together sufficient, neither alone
D	EACH alone is sufficient
E	Even together, NOT sufficient

The golden rule: don't solve, just test sufficiency

A statement is sufficient if it forces a unique answer (or a definite yes/no). You never need the actual number — only whether it is determined.

Method

1. Read the question; note exactly what must be determined.
2. Test Statement 1 alone (cover statement 2). Sufficient?
3. Test Statement 2 alone (cover statement 1). Sufficient?
4. If neither alone works, test both together. Then map to A/B/C/D/E.

Exam Tricks & Tips

• 🎯 Never carry over. When testing statement 2 alone, forget everything statement 1 said — the commonest DS error.
• 🎯 Sufficient = unique answer. Two possible values (e.g. x² = 16 → x = ±4) means NOT sufficient unless a constraint kills one.
• 🎯 A yes/no question is "sufficient" even if the answer is NO — a definite no is still a determination.
• 🎯 Use the "AD/BCE" split. If statement 1 is sufficient, the answer is A or D; if not, it's B, C, or E — this halves the work.
• 🎯 Don't compute the value. As soon as you know it's determined, stop — DS penalises over-solving with lost time.
• ❌ Common mistake: picking C (both together) out of caution when one statement alone already suffices — always test each alone first.

Expected exam pattern

DS appears as a question style (in CAT-adjacent tests and occasionally CAT DILR/QA). Two statements, five fixed options. No arithmetic reward — pure sufficiency logic. Traps: hidden non-uniqueness, and needlessly combining statements.

Quick recap

Judge, don't solve. Test each statement alone (wiping memory between them), where sufficient = a unique/definite answer, then together only if needed. Use the AD/BCE split, accept a definite "no" as sufficient, and stop the moment the answer is determined.

Cover the answer, recall, then check. 12 cards on data sufficiency.

Q1. What does a DS question ask?
A1. Whether the statements are ENOUGH to solve — not the actual answer.

Q2. What does option D mean?
A2. Each statement ALONE is sufficient.

Q3. What does option C mean?
A3. Both together are sufficient, but neither alone.

Q4. What does option E mean?
A4. Even together, the statements are not sufficient.

Q5. Define "sufficient".
A5. The statement forces a unique value (or a definite yes/no).

Q6. The #1 DS error?
A6. Carrying statement 1's info while testing statement 2 alone — always wipe memory between them.

Q7. Is x² = 16 sufficient to find x?
A7. No — x = +4 or −4, two values, unless another constraint removes one.

Q8. Is a definite "NO" answer to a yes/no question sufficient?
A8. Yes — a definite determination either way is sufficient.

Q9. What is the AD/BCE split?
A9. If statement 1 alone works, answer is A or D; if not, it's B, C, or E — halves the work.

Q10. Should you compute the final value?
A10. No — stop as soon as you know it's determined; over-solving wastes time.

Q11. Why not default to C?
A11. Picking "both together" out of caution is wrong when one statement alone already suffices — test each alone first.

Q12. First step in any DS question?
A12. Note exactly what must be determined.

Data Sufficiency (DS) flips DI on its head: you're not asked to find the answer, only to judge whether the given information is enough to find it. The classic format gives a question plus two statements, and you decide if statement 1 alone, statement 2 alone, both together, or neither, suffice. The number-cruncher's instinct — solve it fully — is exactly the wrong reflex here and the main way students burn time.

What this tests

Sufficiency judgment — determining whether data pins down a unique answer, without actually computing it, and evaluating each statement independently before combining.

The method

Beginner — the five-option framework

Standard DS answer choices:

• (A) Statement 1 alone is sufficient, 2 alone is not.
• (B) Statement 2 alone is sufficient, 1 alone is not.
• (C) Both together are sufficient, neither alone is.
• (D) Each alone is sufficient.
• (E) Both together are still not sufficient.

Your job is to slot the problem into one of these — a yes/no about enough-ness, not a numeric answer.

Intermediate — evaluate each statement in isolation, then combine

Test statement 1 alone (cover statement 2 completely — a top error is letting statement 2's info leak in). Ask: does it force a unique answer? Then test statement 2 alone the same way. Only if neither alone works do you combine them. "Sufficient" means the data determines one and only one value (or a definite yes/no) — if two different scenarios satisfy the statement but give different answers, it's insufficient.

Advanced — the FAST CAT approach: seek a counter-example, don't solve

• To prove insufficiency, find two cases that both fit the statement but yield different answers — one counter-example is enough, and far faster than solving.
• To prove sufficiency, confirm the data locks a unique value — you don't need to compute it, just verify it's determined (e.g., "one equation, one unknown → determined; stop").
• Watch the C-trap: don't jump to "both together" out of caution. If a single statement already suffices, the answer is A/B/D, not C. And don't assume "both together" works without checking — sometimes the answer is E.
• For yes/no questions, "always yes" and "always no" are both sufficient; only a "sometimes yes, sometimes no" is insufficient.

Worked example

Question: Is the integer n even?
Statement 1: n is divisible by 3. → n could be 6 (even) or 9 (odd). Two cases, different answers → insufficient.
Statement 2: n is divisible by 4. → any multiple of 4 (4, 8, 12…) is always even → always yes → sufficient alone.
So statement 2 alone suffices, statement 1 alone does not → answer (B). Notice we never found the value of n — we only judged sufficiency, and used a counter-example (6 vs 9) to kill statement 1 in seconds.

CAT relevance

Data Sufficiency appears in DILR (and the logic transfers to QA). It's a time-saver's format — mastering "judge, don't solve" lets you clear DS questions in under a minute and reinvest time in calculation-heavy sets. The counter-example habit also sharpens your general problem-solving rigour.

Speed tricks & shortcuts

• Memorise the five options cold so you're classifying, not solving.
• One statement at a time — physically cover the other to stop info leaking.
• Insufficiency = one counter-example (two valid cases, different answers).
• Sufficiency = unique determination — you needn't compute the value.
• Mnemonic — "Judge, don't solve; one at a time; then combine."
• Avoid the C-trap — check each alone before defaulting to "both".

Key formulas

• Decide whether each statement alone, or both together, fixes a unique answer.
• Standard options: (A) I alone, (B) II alone, (C) both together, (D) either alone, (E) neither.
• A statement is sufficient if it yields exactly one value/answer.
• Do NOT actually compute the final number — only test sufficiency.
• Watch for statements that look useful but leave multiple possibilities.

Usage: ask "does this pin down one answer?" for each statement independently first.

Worked Example

Problem: Question: What is the value of x?
Statement (1): x + y = 10.
Statement (2): 2x − y = 5.
Using the standard data-sufficiency options, decide sufficiency:
(A) statement 1 alone sufficient; (B) statement 2 alone sufficient; (C) both together sufficient but neither alone; (D) each alone sufficient; (E) even both together insufficient.

Solution:
Data sufficiency asks NOT for the value but whether the statements pin it down to a unique value. Evaluate each statement alone, then together — and never carry information from one statement into the other while testing them individually.

Statement (1) alone: x + y = 10. This is one equation in two unknowns; x can be anything (if y = 4, x = 6; if y = 0, x = 10). No unique x → statement 1 alone is NOT sufficient. Eliminate options A and D.

Statement (2) alone: 2x − y = 5. Again one equation, two unknowns; x is not fixed (if y = 1, 2x = 6, x = 3; if y = 3, 2x = 8, x = 4). Not sufficient alone. Eliminate B (and D already gone).

Both together: two independent linear equations in two unknowns:
x + y = 10 … (1)
2x − y = 5 … (2)
Add (1) and (2): 3x = 15 → x = 5 (and y = 5). A unique solution exists, so together they ARE sufficient → the answer is (C): both needed, neither alone.

Key discipline: in data sufficiency you determine sufficiency, not the number — though here solving confirms uniqueness. Two distinct (non-parallel) linear equations in two variables always give a unique solution, which is why (1)+(2) suffice while each alone (one equation, two unknowns) does not.

Answer: (C). Each statement alone is one equation in two unknowns (x not fixed), so neither is sufficient; together they form two independent equations giving the unique x = 5. The task was to judge sufficiency, and both statements are required.