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This problem trains for: SAT-I, GMAT.

If x and y are distinct prime numbers and:

is an odd number, then which of the following statements can be true?

Since:

is odd, then both factors are odd. A sum or a difference of integers is odd only if one of the operands is even and the other is odd.

Since there is only one even prime, one of x and y must be equal to 2.

Then, the product xy is always even (cannot be odd).

Since the sum is odd, the average cannot be integer.

The sum can be a multiple of 5. It is sufficient to think of one example for the statement to have at least one possibility of being true: