GMAT Data Sufficiency: Word Problems

Last updated: May 2, 2026

Data Sufficiency: Word Problems questions are one of the highest-leverage areas to study for the GMAT. This guide breaks down the rule, the elements you need to recognize, the named traps that catch most students, and a memory aid that scales to test day. Read it once, then practice the same sub-topic adaptively in the app.

The rule

A Data Sufficiency word problem asks whether the given information lets you answer the question — not whether you can grind out a number. Translate the prose into variables and an equation before you read either statement, restate exactly what the question is asking, and then test each statement alone for whether it forces a single answer. Combine statements only if neither suffices on its own. Your job is to verify uniqueness of the answer, not to compute it.

Elements breakdown

Translate the Question

Turn the word setup into clean algebra before you touch the statements.

  • Define variables for every unknown
  • Write equations from the prompt only
  • Note hidden constraints (integer, positive, nonzero)
  • Restate the question algebraically
  • Identify whether question is value or yes/no

Common examples:

  • If '3 apples and 2 pears cost $8', write $3a + 2p = 8$ before reading the statements.

Test Statement (1) Alone

Ignore Statement (2) entirely and ask whether (1) plus the prompt forces a unique answer.

  • Cover Statement (2) with your hand
  • Combine (1) with the prompt's equations
  • Check for unique solution
  • Look for multiple cases that fit
  • Mark sufficient or not sufficient

Test Statement (2) Alone

Reset and ask whether (2) plus the prompt forces a unique answer, ignoring (1).

  • Reset — forget what (1) said
  • Combine (2) with the prompt only
  • Check for unique solution
  • Search for counterexamples
  • Mark sufficient or not sufficient

Combine Only If Forced

If and only if both statements failed alone, test them together.

  • Skip this step if either was sufficient
  • Stack equations from (1) and (2)
  • Check that combined system is determined
  • Beware redundant statements (same equation)
  • Decide between C and E

Pick the Verdict

Map your sufficiency findings to one of the five fixed answer letters.

  • (1) yes, (2) no → A
  • (1) no, (2) yes → B
  • Both no, together yes → C
  • Each alone yes → D
  • Together still no → E

Common patterns and traps

The C-Trap

The setup feels like it 'obviously' needs both pieces of information, so students reflexively pick C without testing each statement alone. In reality one statement (often the algebraically richer one, like a rate, ratio, or harmonic relationship) already pins the answer down, while the other supplies a redundant or unnecessary fact such as a distance, total, or time. Always force yourself to evaluate each statement in isolation before combining.

A round-trip average-speed question where Statement (1) gives both leg speeds and Statement (2) gives the one-way distance — students grab C, but (1) alone is enough.

The Phantom Variable

A statement looks like it adds an equation, but the equation introduces a brand-new unknown the prompt never restricted, leaving the system underdetermined. Mixture, revenue, and inventory problems are the usual hiding places: a percent or per-unit price slips in and you cannot solve without the second statement. Count variables and equations before declaring sufficiency.

A mixture statement that says 'the final solution is 35% acid' when the prompt has not fixed how many liters of each component were used — three unknowns, two equations, not sufficient.

The Hidden Constraint

The word problem implicitly requires integers, positive values, or whole units (people, books, vehicles) and that constraint, plus a single Diophantine equation, may already narrow the answer to one case — flipping a 'looks insufficient' statement into a sufficient one. Conversely, ignoring the constraint can fool you into thinking infinitely many answers exist when integrality forces a unique one. Always ask: what counts as a legal solution given the story?

A statement giving $4c + 3m = 17$ alongside 'how many cupcakes were sold?' — only nonnegative integer solutions are legal, and there is exactly one.

Same Equation Repackaged

Both statements encode the same underlying relationship in different prose. Combined, they look like a 2×2 system but are algebraically a single equation — the matrix is singular. The verdict is E, not C, because together they still leave the unknown free. Reduce each statement to its algebraic core and check whether one is a scalar multiple of the other.

Statement (1): 'The ratio of apples to pears is 3 to 2.' Statement (2): 'There are 1.5 apples for every pear.' Both say $a = 1.5p$ — combining contributes no new constraint.

Don't Solve, Just Determine

Many DS word problems are designed so that fully computing the value takes minutes but proving uniqueness takes seconds. The trap is sinking time into arithmetic when a structural argument — count of equations vs. unknowns, monotonicity, or symmetry — settles sufficiency immediately. Train yourself to stop at the moment a unique answer is guaranteed.

A statement combined with the prompt yields a clearly determined linear system in two variables; you mark sufficient and move on without computing the actual values.

How it works

Suppose a problem says: 'A box holds $a$ apples and $p$ pears; 3 apples and 2 pears together cost $\$8$. What is the price of an apple?' First, translate: let $a$ and $p$ be the prices, write $3a + 2p = 8$, and note the question wants the value of $a$. Now imagine Statement (1) says 'pears cost $\$1$ each.' Substitute $p=1$ into the prompt equation: $3a = 6$, so $a = 2$. Unique value — Statement (1) is sufficient. Reset. Imagine Statement (2) says 'apples cost twice as much as pears,' i.e. $a = 2p$. Substitute into $3a + 2p = 8$: $3(2p) + 2p = 8p = 8$, so $p = 1$ and $a = 2$. Unique again — Statement (2) is also sufficient. Each works alone, so the answer is D. Notice that you never compared the two statements to each other, and you stopped the moment uniqueness was confirmed.

Worked examples

Worked Example 1

How old is Diego, in years, right now?

  • 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. ✓ Correct
  • E Statements (1) and (2) TOGETHER are NOT sufficient.

Why D is correct: Translate the prompt as $M = 3D$. Statement (1) gives $M + 8 = 2(D + 8)$; substituting yields $3D + 8 = 2D + 16$, so $D = 8$ — unique, sufficient. Statement (2) gives $M + D = 32$; substituting yields $3D + D = 32$, so $D = 8$ — unique, sufficient. Each statement alone forces a single value of $D$, so the answer is D.

Why each wrong choice fails:

  • A: This requires Statement (2) alone to be insufficient, but $M + D = 32$ together with $M = 3D$ uniquely gives $D = 8$. (Don't Solve, Just Determine)
  • B: This requires Statement (1) alone to be insufficient, but the future-age relation combined with $M = 3D$ uniquely gives $D = 8$. (Don't Solve, Just Determine)
  • C: Choosing C says neither statement alone works, but each one independently nails down $D = 8$ when paired with the prompt's $M = 3D$. (The C-Trap)
  • E: If each statement alone is sufficient, then certainly together they are too — E contradicts both individual sufficiencies.
Worked Example 2

What is the percent of acid by volume in Solution Y?

  • 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. ✓ Correct
  • D EACH statement ALONE is sufficient.
  • E Statements (1) and (2) TOGETHER are NOT sufficient.

Why C is correct: Let $p$ be the percent acid in Y, written as a decimal. The prompt gives $x + y = 40$. Statement (1) adds $0.20x + p \cdot y = 0.35 \times 40 = 14$, but $x$, $y$, and $p$ remain underdetermined — three unknowns, two equations. Statement (2) fixes $x = 16$, hence $y = 24$, but says nothing about $p$. Together, $0.20(16) + 24p = 14$ gives $24p = 10.8$, so $p = 0.45 = 45\%$ — unique, sufficient.

Why each wrong choice fails:

  • A: Statement (1) alone leaves three unknowns ($x$, $y$, $p$) constrained by only two equations, so $p$ is not pinned down. (The Phantom Variable)
  • B: Statement (2) fixes the volumes of X and Y but never constrains the acid percentage of Y, so $p$ can still be anything. (The Phantom Variable)
  • D: D requires each statement alone to determine $p$, but neither does — the percentage in Y can vary in both single-statement scenarios. (The Phantom Variable)
  • E: Together the statements give $x = 16$, $y = 24$, and $0.20(16) + 24p = 14$, which solves uniquely for $p = 45\%$.
Worked Example 3

What was the van's average speed, in miles per hour, for the entire round trip?

  • A Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient. ✓ Correct
  • 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.

Why A is correct: For a round trip over equal one-way distances at speeds $v_1$ and $v_2$, the average speed is the harmonic mean $\frac{2 v_1 v_2}{v_1 + v_2}$, which does not depend on the distance. Statement (1) gives $\frac{2(60)(40)}{60 + 40} = \frac{4800}{100} = 48$ mph — unique, sufficient. Statement (2) supplies only a distance with no speed information, so the average speed could be any positive value — insufficient. Therefore (1) alone suffices and (2) does not.

Why each wrong choice fails:

  • B: Statement (2) gives only the one-way distance and provides no information about how fast the van traveled in either direction, so no average speed is determined. (The Phantom Variable)
  • C: C is the classic distance-feels-necessary trap. The harmonic-mean formula in Statement (1) cancels the distance entirely, so adding Statement (2) is redundant. (The C-Trap)
  • D: D would require Statement (2) alone to be sufficient, but a distance with no speeds cannot determine an average speed.
  • E: If Statement (1) alone is sufficient, the two together are certainly sufficient as well, contradicting E.

Memory aid

TWO-T: Translate first, then Test (1) alone, Test (2) alone, then Together only if you must. The moment a unique answer is forced, stop computing.

Key distinction

Sufficiency is about uniqueness, not calculability. A statement is sufficient when every scenario consistent with the prompt plus that statement gives the same answer to the question — not when you happen to find a pleasant number. A statement is insufficient if even one alternative scenario produces a different answer.

Summary

Translate the words into algebra, then test each statement's power to pin down a single answer — don't solve, just verify.

Practice data sufficiency: word problems adaptively

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Frequently asked questions

What is data sufficiency: word problems on the GMAT?

A Data Sufficiency word problem asks whether the given information lets you answer the question — not whether you can grind out a number. Translate the prose into variables and an equation before you read either statement, restate exactly what the question is asking, and then test each statement alone for whether it forces a single answer. Combine statements only if neither suffices on its own. Your job is to verify uniqueness of the answer, not to compute it.

How do I practice data sufficiency: word problems questions?

The fastest way to improve on data sufficiency: word problems is targeted, adaptive practice — working questions that focus on your specific weak spots within this sub-topic, getting immediate feedback, and revisiting items you missed on a spaced-repetition schedule. Neureto's adaptive engine does this automatically across the GMAT; start a free 7-day trial to see your sub-topic mastery climb in real time.

What's the most important distinction to remember for data sufficiency: word problems?

Sufficiency is about uniqueness, not calculability. A statement is sufficient when every scenario consistent with the prompt plus that statement gives the same answer to the question — not when you happen to find a pleasant number. A statement is insufficient if even one alternative scenario produces a different answer.

Is there a memory aid for data sufficiency: word problems questions?

TWO-T: Translate first, then Test (1) alone, Test (2) alone, then Together only if you must. The moment a unique answer is forced, stop computing.

What's a common trap on data sufficiency: word problems questions?

Combining statements out of habit

What's a common trap on data sufficiency: word problems questions?

Solving instead of just verifying sufficiency

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