GMAT Data Sufficiency: Arithmetic
Last updated: May 2, 2026
Data Sufficiency: Arithmetic 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
Data sufficiency arithmetic problems test whether the information given is enough to answer a definite numerical or yes/no question — not what the answer actually is. You succeed by isolating each statement, asking whether it pins the answer down to a single value (or single yes/no verdict), and refusing to mash the statements together until each has failed alone. Because arithmetic topics — divisibility, evens and odds, signs, fractions, percents, ratios — admit clean test cases, the fastest path is usually picking the smallest legal integers that satisfy a statement and checking whether the verdict flips.
Elements breakdown
Decode the Stem
Identify exactly what the question asks before you read either statement.
- Classify as value question or yes/no question
- Note pre-given constraints (positive, integer, nonzero)
- Restate the question in your own words
- Translate the question into an algebraic target
Common examples:
- 'Is $n$ divisible by 12?' is yes/no, $n$ is a positive integer.
- 'What is $x$?' is value-based and demands a single number.
Test Statement (1) Alone
Evaluate Statement (1) in complete isolation from Statement (2).
- Cover Statement (2) with your hand
- Pick small legal values satisfying Statement (1)
- Check whether the verdict locks or varies
- Try a boundary case (zero, negative, one)
- Conclude sufficient or insufficient before moving on
Test Statement (2) Alone
Reset and evaluate Statement (2) without any Statement (1) memory.
- Forget what you just learned from Statement (1)
- Pick small legal values satisfying Statement (2)
- Check whether the verdict locks or varies
- Try the same boundary cases for symmetry
- Conclude before considering combining
Combine Only If Both Failed
Combine the statements only when neither was sufficient alone.
- Find values satisfying both statements simultaneously
- Check whether the verdict still varies
- Decide C (locked together) versus E (still varies)
Map to the Fixed Choices
Translate your conclusions into the rigid A-E schema.
- (1) yes, (2) no $\to$ A
- (1) no, (2) yes $\to$ B
- Each alone yes $\to$ D
- Both fail alone, together yes $\to$ C
- Even together no $\to$ E
Common patterns and traps
C-Trap (Overcombining)
The two statements are constructed so that, taken together, they obviously fix the answer — and most students stop there and pick C. But one of the statements, often the algebraically richer one, is already sufficient by itself once you push it past easy cases. The trap rewards the student who tests each statement alone with edge cases instead of jumping to the combination.
Statement (1) is a clean equation that, once you account for the integer constraint, forces a unique answer; Statement (2) is a tidy fact that helps but is redundant. Picking C feels safe; the actual answer is A.
Yes/No Verdict Flip
In a yes/no DS question, a statement is sufficient only if the verdict is the same for every legal input that satisfies it. Students often find one value that gives 'yes', stop, and call it sufficient. The trap is hiding a single counterexample — usually at zero, one, or a negative — that flips the verdict to 'no'.
Statement looks like a clean inequality or product condition; the bulk of values give one verdict, but a small edge case gives the opposite. The student who only tests the obvious case mis-rules the statement sufficient.
Hidden Integer Constraint
Many DS arithmetic stems quietly say 'positive integer' or 'nonzero' in the prompt. Students who skim the stem then test fractions or zero, mis-classifying a statement as insufficient when in fact the integer constraint locks the verdict. The reverse also happens — students assume integers when none were specified and miss a fractional counterexample.
The stem says 'If $m$ and $n$ are positive integers...' and Statement (1) is something like '$\frac{m}{n}$ is an integer.' A student who tries $m = 1.5$ wrongly believes the statement permits non-integer values.
Missing the LCM/GCF Combine
When both statements supply divisibility information about the same variable, the combined statement is governed by the lcm of the two divisors. Students who don't recognize this often pick E, thinking the divisibility facts can't be merged. Conversely, when the question asks about a divisor that the lcm does not cover, students sometimes assume combining must work and pick C.
Statement (1): $n$ is a multiple of $a$. Statement (2): $n$ is a multiple of $b$. Question: is $n$ a multiple of some $d$? The verdict hinges on whether $d \mid \text{lcm}(a, b)$ — a step many students skip.
Premature Sufficiency
After one or two supportive test cases, students declare a statement sufficient without sweeping the boundary cases that arithmetic loves: zero, one, negatives, and equality cases. This pattern most often shows up in sign and parity questions, where students confirm with one positive integer and never check what happens at the edges.
Statement (1) is something like '$x^2 > x$.' A student tests $x = 2$ (true, positive) and stops, missing that $x = -1$ also satisfies the statement and would flip a sign-based verdict.
How it works
Suppose a question asks 'Is positive integer $k$ a multiple of 6?' Statement (1) says $k$ is a multiple of 2. Test $k = 2$: not a multiple of 6, verdict no. Test $k = 12$: verdict yes. Same statement, two verdicts, so (1) alone is insufficient. Statement (2) says $k$ is a multiple of 3. Try $k = 3$: no. Try $k = 6$: yes. Insufficient. Combining, $k$ is a multiple of $\text{lcm}(2, 3) = 6$, which guarantees yes — sufficient. Answer C. Notice you never had to compute a single final number; you only had to ask whether each pool of legal $k$-values produced one verdict. That is the entire game in DS arithmetic — controlling the verdict, not crunching the value.
Worked examples
Is $n$ divisible by 12?
- 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: Statement (1) alone: $n = 6$ is not divisible by 12 (no), but $n = 12$ is (yes) — verdict flips, insufficient. Statement (2) alone: $n = 8$ is no, $n = 24$ is yes — insufficient. Together, $n$ is a multiple of $\text{lcm}(6, 8) = 24$, and $24$ is a multiple of $12$, so every legal $n$ is divisible by $12$. Sufficient together but not alone, so the answer is C.
Why each wrong choice fails:
- A: Statement (1) alone allows both $n = 6$ (not divisible by $12$) and $n = 12$ (divisible by $12$), so the verdict varies and (1) alone cannot be sufficient. (Yes/No Verdict Flip)
- B: Statement (2) alone allows $n = 8$ (no) and $n = 24$ (yes), so the verdict is not locked and (2) alone is insufficient. (Yes/No Verdict Flip)
- D: D would require each statement to be sufficient on its own; both produce verdict flips, so neither is sufficient alone. (Premature Sufficiency)
- E: Combining the statements forces $n$ to be a multiple of $\text{lcm}(6, 8) = 24$, and every multiple of $24$ is a multiple of $12$, so the verdict locks to yes. (Missing the LCM/GCF Combine)
Is $k$ positive?
- 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: Rewrite Statement (1) as $k(k-1)(k+1) > 0$. Plug integer values: $k = -3, -2, -1, 0, 1$ all give $0$ or a negative product; $k = 2$ gives $6 > 0$ and every integer $k \ge 2$ keeps the product positive. So Statement (1) forces $k \ge 2$, which is always positive — sufficient. Statement (2) gives $|k| > 1$, satisfied by $k = 2$ (positive) and $k = -2$ (negative), so the verdict flips — insufficient. Only (1) alone works, so the answer is A.
Why each wrong choice fails:
- B: Statement (2) is satisfied by both $k = 2$ and $k = -2$, giving opposite verdicts on whether $k$ is positive, so (2) alone cannot be sufficient. (Yes/No Verdict Flip)
- C: Choosing C ignores that Statement (1) alone already pins $k \ge 2$; you do not need (2) to lock the verdict. (C-Trap (Overcombining))
- D: D requires each statement to be sufficient alone, but Statement (2) is satisfied by both $k = 2$ and $k = -2$ and so does not lock the verdict. (Premature Sufficiency)
- E: E claims even both statements together fail, but Statement (1) alone is already sufficient, so the combined information is also sufficient.
Is $mn$ even?
- 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: Statement (1): if $m + n$ is odd, exactly one of $m, n$ is odd and the other is even, so the product $mn$ is even — verdict locks to yes, sufficient. Statement (2): factor $m^2 - n^2 = (m - n)(m + n)$. The product of two integers is odd only when both factors are odd, so both $m - n$ and $m + n$ are odd, which forces $m$ and $n$ to have opposite parity — again $mn$ is even, verdict locks to yes, sufficient. Each statement alone is sufficient, so the answer is D.
Why each wrong choice fails:
- A: A would require Statement (2) to fail, but $m^2 - n^2$ odd forces $m$ and $n$ to differ in parity, which guarantees $mn$ is even, so (2) is also sufficient. (Premature Sufficiency)
- B: B requires Statement (1) to fail, but $m + n$ odd already forces one of $m, n$ to be even, locking $mn$ even, so (1) is sufficient. (Premature Sufficiency)
- C: C insists that you need both statements, but each one independently forces opposite parities and therefore an even product. (C-Trap (Overcombining))
- E: E claims even the combined information is insufficient, but each piece alone already locks $mn$ as even, so the combination certainly does.
Memory aid
AD-or-BCE. After Statement (1) is sufficient, your answer is A or D; if not, your answer lives in {B, C, E}. After Statement (2), if it's also sufficient you are at D; if only (2) is sufficient you are at B; otherwise you combine and choose between C and E. This split prevents the single most common DS mistake — peeking at Statement (2) while you should still be judging Statement (1).
Key distinction
Data sufficiency does not ask 'what is the answer' — it asks 'do you have enough information to lock the answer.' For yes/no questions, both 'always yes' and 'always no' are sufficient; only 'sometimes yes, sometimes no' is insufficient. Treat the verdict, not the value, as the target.
Summary
Test each statement in isolation against the smallest legal cases, combine only after each fails alone, and judge sufficiency by whether the verdict locks, not by whether you can compute a number.
Practice data sufficiency: arithmetic adaptively
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Start your free 7-day trialFrequently asked questions
What is data sufficiency: arithmetic on the GMAT?
Data sufficiency arithmetic problems test whether the information given is enough to answer a definite numerical or yes/no question — not what the answer actually is. You succeed by isolating each statement, asking whether it pins the answer down to a single value (or single yes/no verdict), and refusing to mash the statements together until each has failed alone. Because arithmetic topics — divisibility, evens and odds, signs, fractions, percents, ratios — admit clean test cases, the fastest path is usually picking the smallest legal integers that satisfy a statement and checking whether the verdict flips.
How do I practice data sufficiency: arithmetic questions?
The fastest way to improve on data sufficiency: arithmetic 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: arithmetic?
Data sufficiency does not ask 'what is the answer' — it asks 'do you have enough information to lock the answer.' For yes/no questions, both 'always yes' and 'always no' are sufficient; only 'sometimes yes, sometimes no' is insufficient. Treat the verdict, not the value, as the target.
Is there a memory aid for data sufficiency: arithmetic questions?
AD-or-BCE. After Statement (1) is sufficient, your answer is A or D; if not, your answer lives in {B, C, E}. After Statement (2), if it's also sufficient you are at D; if only (2) is sufficient you are at B; otherwise you combine and choose between C and E. This split prevents the single most common DS mistake — peeking at Statement (2) while you should still be judging Statement (1).
What's a common trap on data sufficiency: arithmetic questions?
Combining statements before testing each alone
What's a common trap on data sufficiency: arithmetic questions?
Stopping after one supportive case without checking a flip
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