Practice GMAT Data Sufficiency Question
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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
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.
 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.
 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  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.
 Statement (1) alone is SUFFICIENT.

Evaluate Statement (2) alone.
 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.
 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  Statement (2) alone is NOT SUFFICIENT.
 Since Statement (1) alone is SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, answer A is correct.
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