Data Sufficiency
Data Sufficiency is a game, not a math test. You don't solve for the answer — you decide whether you *could* solve for it given the information provided. The five-answer framework is mechanical: test each statement alone, then together if needed, and pick the letter that matches the sufficiency pattern. Master the AD/BCE decision tree, learn to rephrase the question before testing statements, and you'll finish every DS question in under 2 minutes without ever doing unnecessary arithmetic.
The five-answer framework and the AD/BCE decision tree
Data Sufficiency looks different from every other question type on the GMAT. You're given a question and two statements, and asked whether the statements (individually or together) are sufficient to answer the question. You never have to compute the final answer — you only decide whether you could.
Mental model. Data Sufficiency isn't a math problem — it's a classification problem. Each statement either pins down a unique answer or it doesn't, full stop. The AD/BCE grid (statement 1 sufficient? statement 2 sufficient? together?) covers all five answer choices mechanically. Once you stop trying to compute the answer and start asking can the answer be computed, DS becomes a different game.
The five answers (always the same, in the same order):
- A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
- B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
- C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- D) EACH statement ALONE is sufficient.
- E) Statements (1) and (2) TOGETHER are NOT sufficient.
Memorize these. Every DS question uses this exact list.
The AD/BCE decision tree — the single most important tool in DS.
Test Statement (1) alone first. Two outcomes:
- (1) is sufficient → answer is either A or D.
- (1) is NOT sufficient → answer is either B, C, or E.
Then test Statement (2) alone. Combined results:
| (1) alone | (2) alone | Answer |
|---|---|---|
| Sufficient | Sufficient | D |
| Sufficient | Not sufficient | A |
| Not sufficient | Sufficient | B |
| Not sufficient | Not sufficient | C (if together work) or E (if they don't) |
This grid eliminates guessing. Every DS answer falls out of two binary tests.
Example. "What is the value of x? (1) 3x + 7 = 22. (2) x is a positive integer less than 10."
Test (1): 3x = 15 → x = 5. Unique value → sufficient.
Test (2): x could be 1, 2, 3, ..., 9. Multiple values → not sufficient.
(1) sufficient + (2) not sufficient = A. Answer: A.
The definition of "sufficient" — the single most misunderstood concept in DS.
A statement is sufficient if it uniquely determines the answer to the question. That's it.
- For value questions ("What is x?"): sufficient = yields exactly one value of x.
- For yes/no questions ("Is x > 5?"): sufficient = the answer is always yes, OR the answer is always no. A definite answer — even if it's "no" — counts as sufficient.
The most common DS mistake: students think "sufficient" means "I know the value now." It doesn't. Sufficient on a yes/no question means "the question has a definite answer" — which can be yes or no.
The "don't solve" principle. You do not need to find x, y, or the final answer on DS. You only need to know whether you could. This saves massive time. A system of two independent linear equations in two unknowns is always solvable — you don't need to actually solve it on test day. The word "independent" is the key; see the C-trap section.
The order matters. Always test statement (1) first, then (2), then together only if both are individually insufficient. Skipping to "together" too quickly is the biggest source of wrong D vs. C answers.
Recall check. Close your eyes. Recite the five answer choices (A through E) in order. Now — without peeking — state the four outcomes of the AD/BCE grid. (If (1) sufficient and (2) sufficient, answer is D. If (1) sufficient and (2) not sufficient, answer is A. If (1) not sufficient and (2) sufficient, answer is B. If both not sufficient individually, answer is C or E depending on whether they work together.) Forced retrieval of this grid is what converts DS from "which letter?" guessing into a mechanical evaluation. Redo this until it's automatic.
Trap to watch. "Not sufficient" doesn't mean "gives no information" — it means "doesn't uniquely determine the answer." A statement that rules out 5 of 10 possible values is informative but insufficient. The standard is uniqueness, not usefulness.
Rephrasing the question — the highest-leverage DS habit
The single highest-leverage DS habit: before testing any statement, simplify the question.
A question like "Is x² + 4x + 4 > 0?" looks different from "Is (x + 2)² > 0?" even though they're the same. The second form makes the answer obvious: (x + 2)² is always ≥ 0, and equals 0 only when x = -2. So the question really asks "Is x ≠ -2?" A clean rephrasing turns a complex statement test into a trivial one.
The rephrasing workflow.
- Read the question.
- Simplify algebraically if possible: factor, combine like terms, solve for the unknown.
- Ask: "What do I actually need to know?" — write that down as a new, simpler question.
- Then test the statements against the simpler question.
Example. "Is 4x + 2y = 10?"
Rephrase: divide by 2. "Is 2x + y = 5?" Same question, cleaner form. Now when you see Statement (1) "x + y/2 = 5/2," you multiply by 2 to get "2x + y = 5" — immediately sufficient.
Example (yes/no rephrase). "If n is a positive integer, is n² odd?"
A number's square is odd if and only if the number itself is odd. Rephrase: "Is n odd?" Now a statement like "n is divisible by 4" tells you n is even → n² is even → definite "no" — still sufficient (with answer "no").
The "unknown elimination" rephrase. When the question involves multiple unknowns, ask yourself: which unknowns do I actually need? If the question asks for x + y and you have x and y both unknown, you don't need to solve for x and y individually — you just need x + y. A statement giving you "x = 2y + 5" may or may not get you to x + y.
Example. "What is x + y?" Statement: "x - y = 4 and xy = 5."
From statement: (x + y)² = (x - y)² + 4xy = 16 + 20 = 36, so x + y = ±6. That's two possible values → not sufficient. But notice you didn't have to solve for x and y individually — you used the algebraic identity to get to x + y directly.
Rephrasing geometry questions. "Is triangle ABC isosceles?" Rephrase to "Does triangle ABC have at least two equal sides, OR equivalently, at least two equal angles?" The "or equivalently" form often lets you use statements about angles instead of sides (or vice versa).
Rephrasing inequality questions. "Is x > y?" often rephrases to "Is x - y > 0?" — now statements that give you info about "x - y" (like "x² > y²" or "x + y > 0") become relevant.
The "what does sufficient require?" rephrase. Before testing statements, explicitly write: "Statement (1) will be sufficient if it tells me _______." Filling in the blank forces you to know exactly what you're looking for.
Example. "What is the value of xyz?" A statement is sufficient if it uniquely determines xyz — it doesn't have to determine x, y, or z individually.
Self-explanation prompt. Why does rephrasing save so much time? If you can say "because the question as written often obscures what you actually need; the rephrase strips away noise and makes it obvious which statements help," you've internalized the core DS discipline. Rephrasing is where experts gain 20+ seconds per question over novices.
4 more reading sections, two pre-test questions, and 45 graded practice questions across three difficulty tiers — all included with the platform.
What you just read is one chapter of seventeen
The full curriculum is 17 chapters like this one.
Plus the diagnostic, the adaptive study plan, the error log with six-tag taxonomy, the spaced review queue, and the full question bank tagged by topic and difficulty. Seven days of full access on the trial — no card required.