If X is an integer, is Y an integer?

1. The average of X and Y is not an integer.

2. The average of X, Y, and X + 6, is Y.

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.

Answer

Since we can pick both integer and non-integer values for X that satisfy Statement 1, we can conclude that Statement 1 alone is insufficient to answer the question. For statement 2, remember that the average of a group of terms is equal to the sum of the terms divided by the number of terms. If X is an integer, X + 3 is also an integer; therefore, we can conclude that Y is an integer. Statement 2 alone is sufficient to answer the question.

Correct Answer - Choice B

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