Practice GMAT Data Sufficiency Question

Return to the list of practice GMAT data sufficiency questions.

If X is a positive integer, is X divisible by 4?

X has at least two 2s in its prime factorization
X is divisible by 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)	Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Correct Answer: A

A number is divisible by any of its prime factors or any combination of its prime factors. For a number to be divisible by four, it must have two 2s in its prime factorization since 2*2 = 4 and, if 4 is a factor of X, X will be divisible by 4.
Evaluate Statement (1) alone.
1. Since X has two 2s in its prime factorization, 4 must be a factor of X and, consequently, X must be divisible by 4. Statement (1) is SUFFICIENT.
2. If this seems too abstract, consider the following examples which show that whenever X has at least two 2s in its prime factorization (which it must as per Statement (1)), X is divisible by 4:
  X = 4: has two 2s in its prime factorization and, as a result, is divisible by 4
  X = 6: has only one 2 in its prime factorization and, as a result, is not divisible by 4
  X = 8: has at least two 2s in its prime factorization and, as a result, is divisible by 4
  X = 10: has only one 2 in its prime factorization and, as a result, is not divisible by 4
3. Since X cannot be 6, 10, etc. as these values do not have at least two 2s as prime factors (as is required by Statement (1)), X can only be 4, 8, etc. and will always be divisible by 4.
4. Statement (1) alone is SUFFICIENT.
Evaluate Statement (2) alone.
1. If X is divisible by 2, you know that X must have at least one 2 in its prime factorization. However, you do not know that X has two 2s in its prime factorization and, as a result, you cannot be sure that X is divisible by 4.
2. If this seems too abstract, consider the following examples, all of which are divisible by 2 in keeping with the requirements of Statement (2):
  X = 4: has two 2s in its prime factorization and, as a result, is divisible by 4
  X = 6: has only one 2 in its prime factorization and, as a result, is not divisible by 4
  X = 8: has at least two 2s in its prime factorization and, as a result, is divisible by 4
  X = 10: has only one 2 in its prime factorization and, as a result, is not divisible by 4
3. Statement (2) alone is NOT SUFFICIENT.
Since Statement (1) alone is SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, answer A is correct.

Return to the list of practice GMAT data sufficiency questions.