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Is the product of two positive integers x and y divisible by the sum of x and y ?

1. x = y

2. x = 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. Statements (1) and (2) TOGETHER are NOT sufficient.


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答案:
C
="font-size: 14px;">Arithmetic Properties of Numbers

1. Given that x = y, then xy could be divisible by x + y (for example, if x = y = 2, then xy = 4 is divisible by x + y = 4) and xy could fail to be divisible by x + y (for example, if x = y = 3, then xy = 9 is not divisible by x + y = 6); NOT sufficient.

2. Given that x = 2, then xy could be divisible by x + y (for example, if x = y = 2, then xy = 4 is divisible by x + y = 4) and xy could fail to be divisible by x + y (for example, if x = 2 and y = 3, then xy = 6 is not divisible by x + y = 5); NOT sufficient.

 

Taking (1) and (2) together, it follows that x = y = 2, and so xy = 4 is divisible by x + y = 4.

 

The correct answer is C;

both statements together are sufficient.


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