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GMAT Practice Question (One of Hundreds)

If x is a positive integer, is x > 15?

x > 10
x < 14

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: B

Try plugging in different values for x and seeing whether the inequality definitively answers the question.

In order for a statement to be sufficient, it must definitively answer the question (i.e., it must definitively indicate whether x > 15?) For sufficiency to exist, the information in the statement must allow you to answer the question with the same answer every time (either "yes" or "no). The key is not whether the answer is "yes" or "no", but whether the information allows you to answer the same way each time.
Statement (1) indicates that x > 10. So, x could be 11, 12, 13, 14, 15, 16, 17...
Since x could be 11, in which case it would not be greater than 15 and the answer to the origial question would be "no", or x could be 17, in which case it would be greater than 15 and the answer to the original question would be "yes", Statement (1) is NOT SUFFICIENT.
Statement (2) indicates that x < 14. So, x could be 13, 12, 11, 10, 9... Since all the possible values of x permissible by Statement (2) allow you to answer "no" to the question, Statement (2) is SUFFICIENT.

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