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GMAT Data Insights

GMAT data sufficiency practice questions

Data sufficiency asks you whether the information is enough, not what the answer is. For every question, test each statement alone, then together if needed, and decide whether you can answer with certainty. In yes or no questions, a definite no is just as sufficient as a definite yes.

Key ideas

  • Evaluate statement 1 alone, cross out answers A and D if it fails, then evaluate statement 2.
  • For yes or no questions, a statement is sufficient if the answer is always yes or always no.
  • Try small test numbers, including 0, 1, negatives and fractions when the question allows them.
  • Use the combined statements only when neither works alone.

Common traps

  • Using statement 1 while judging statement 2.
  • Thinking that a "no" means the statement is insufficient.
  • Assuming a variable is positive or an integer when the stem does not say so.

Practice questions with solutions

Try each question first, then open the solution. Time yourself and note where you hesitate.

  1. If x and y are positive integers, what is the value of x? (1) x + y = 10 (2) x - y = 2

    • 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.
    Show answer and solution

    Answer: C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Statement 1 alone fits many pairs such as (1, 9) and (5, 5). Statement 2 alone fits many pairs such as (3, 1) and (4, 2). Together, adding the two equations gives 2x = 12, so x = 6. Both are needed.

  2. If x and y are positive integers, is x greater than y? (1) x = 2y (2) x + y = 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.
    • D EACH statement ALONE is sufficient.
    • E Statements (1) and (2) TOGETHER are NOT sufficient.
    Show answer and solution

    Answer: A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    Statement 1: if x = 2y and y is positive, then x is always greater than y, so the answer is always yes. Sufficient. Statement 2: (7, 5) gives yes but (5, 7) gives no. Not sufficient.

  3. If n is a positive integer, what is the value of n? (1) n² = 49 (2) n is a prime number greater than 5 and less than 10

    • 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.
    Show answer and solution

    Answer: D. EACH statement ALONE is sufficient.

    Statement 1: n² = 49 and n is positive, so n = 7. Sufficient. Statement 2: the primes between 5 and 10 are only 7. Sufficient. Each statement alone works.

  4. If k is an integer, is k even? (1) k² - k is even (2) k + 3 is odd

    • 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.
    Show answer and solution

    Answer: B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    Statement 1: k² - k = k(k - 1) is a product of consecutive integers, so it is always even for every integer k. It tells us nothing about k. Not sufficient. Statement 2: if k + 3 is odd then k is even. Sufficient.

  5. If x is a positive integer, what is the value of x? (1) x is a multiple of 3 (2) x is less than 10

    • 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.
    Show answer and solution

    Answer: E. Statements (1) and (2) TOGETHER are NOT sufficient.

    Together, x can be 3, 6 or 9, so the value is not determined. Neither statement alone is enough, and combining them still leaves three possibilities.

  6. If a, b and c are positive integers, what is the average (arithmetic mean) of a, b and c? (1) a = b (2) a + b + c = 30

    • 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.
    Show answer and solution

    Answer: B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    Average = (a + b + c) / 3. Statement 2 gives the sum directly, so the average is 10. Sufficient. Statement 1 says nothing about c or the sum. Not sufficient.

  7. A shop earned S from shirts and T from trousers, where S and T are positive integers. Did shirts account for more than half of the shop's total earnings? (1) S is more than T + 100 (2) S - T = 150

    • 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.
    Show answer and solution

    Answer: D. EACH statement ALONE is sufficient.

    Shirts account for more than half exactly when S > T. Statement 1 says S > T + 100, which means S > T. Sufficient. Statement 2 says S = T + 150, so S > T. Sufficient.

  8. If x and y are positive integers, what is the value of y/x? (1) x + y = 25 (2) x = 15

    • 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.
    Show answer and solution

    Answer: C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Statement 1 alone allows (1, 24), (5, 20) and many more pairs with different ratios. Statement 2 gives x but not y. Together x = 15, y = 10, and y/x = 2/3.

  9. If x is an integer, is x² greater than x? (1) x < 0 (2) x ≤ 1

    • 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.
    Show answer and solution

    Answer: A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    Statement 1: a negative number has a positive square, which is greater than the negative number. Always yes. Sufficient. Statement 2: x = 0 gives 0 > 0, which is no, but x = -1 gives 1 > -1, which is yes. Not sufficient.

  10. If n is an integer, what is the value of n? (1) n² < 20 (2) n > 0

    • 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.
    Show answer and solution

    Answer: E. Statements (1) and (2) TOGETHER are NOT sufficient.

    Statement 1 allows n from -4 to 4. Statement 2 allows every positive integer. Together n can be 1, 2, 3 or 4, so n is not determined.

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