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Free practice questions/GMAT Focus Edition

GMAT Focus Edition — Data Sufficiency

6 free practice questions with full explanations.

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Question 1

Is the integer n divisible by 6? (1) n is divisible by 3. (2) n is divisible by 4.

  • 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.
Show answer & explanation

Correct answer: C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Divisibility by 6 requires divisibility by both 2 and 3. Statement (1) alone gives divisibility by 3 but not necessarily 2 (e.g., n=9). Statement (2) alone gives divisibility by 4, hence by 2, but not necessarily 3 (e.g., n=4). Together, n divisible by both 3 and 4 means n is divisible by 12, which guarantees divisibility by 6 -- so together they are sufficient, though neither is alone.

Question 2

Is x an even integer? (1) x/2 is an integer. (2) x^2 is an even integer.

  • 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.
Show answer & explanation

Correct answer: D) EACH statement ALONE is sufficient.

Statement (1) alone: if x/2 is an integer, x must be even -- sufficient. Statement (2) alone: an odd number squared is always odd, so if x^2 is even, x itself must be even too -- also sufficient. Each statement alone establishes that x is even.

Question 3

If x and y are integers, what is the value of x? (1) x + y = 10 (2) x - y = 4

  • 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.
Show answer & explanation

Correct answer: C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Neither equation alone determines both x and y (infinitely many solutions each). Adding the two equations: 2x = 14, so x = 7. Both together are sufficient, but neither alone determines x uniquely.

Question 4

What is the area of rectangle R? (1) The perimeter of R is 20. (2) The length of R is 6.

  • 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.
Show answer & explanation

Correct answer: C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Statement (1) alone: perimeter 20 gives length+width=10, but many (length,width) pairs satisfy this, so area is not determined. Statement (2) alone: length=6 alone does not give width or area. Together: length=6, and 6+width=10 so width=4, giving area=24. Both together are sufficient, neither alone is.

Question 5

Is triangle ABC a right triangle? (1) The sides of triangle ABC have lengths 3, 4, and 5. (2) Angle B measures 90 degrees.

  • 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.
Show answer & explanation

Correct answer: D) EACH statement ALONE is sufficient.

Statement (1) alone: sides 3,4,5 satisfy the Pythagorean theorem (3^2+4^2=5^2), so it must be a right triangle -- sufficient alone. Statement (2) alone: a 90-degree angle directly means it is a right triangle -- sufficient alone. Each statement alone answers the question.

Question 6

What is the value of x? (1) x^2 = 49 (2) x > 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.
Show answer & explanation

Correct answer: C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Statement (1) alone gives x = 7 or x = -7, not sufficient alone. Statement (2) alone only tells us x is positive, not its value. Together, x must be positive and satisfy x^2=49, so x = 7. Both together are sufficient, but neither alone is.

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