If x and y are both prime numbers greater than 10, which of the following CANNOT be true?
I. xy is an even number.
II. The difference between x and y equals 117.
III. The sum of x and y is even.
Choose the correct choice from the following answers.
A) I only B) II and III only C) I and III only D) I and II only E) I, II and III
MANHATTAN GMATOFFICIAL SOLUTION:   Since x and y are both prime numbers greater than 10, they must both be odd. Therefore xy must be an odd number, so Statement I cannot be true. Similarly, if x and y are both odd, then x - y cannot equal 117 (an odd number). This difference must be even. Therefore, Statement II cannot be true. Finally, since x and y are both odd, x + y must be even, so Statement III will always be true. Since Statements I and II CANNOT be true, but Statement III IS true,the correct answer is (D).   Answer : I and II only
<result>D</result>
If x and y are both prime numbers greater than 10, which of the following CANNOT be true?
I. xy is an even number.
II. The difference between x and y equals 117.
III. The sum of x and y is even.