If a and b are both prime numbers greater than 12, which of the following CANNOT be true?
I. ab is an even number.
II. The difference between a and b equals 117.
III. The sum of a and b is even.	Choices:  A) I only  B) I and III only  C) I and II only  D) II and III only  E) I, II and III
MANHATTAN GMATOFFICIAL SOLUTION:   Since a and b are both prime numbers greater than 10, they must both be odd. Therefore ab must be an odd number, so Statement I cannot be true. Similarly, if a and b are both odd, then a - b cannot equal 117 (an odd number). This difference must be even. Therefore, Statement II cannot be true. Finally, since a and b are both odd, a + b 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 (C).   Answer : I and II only
<result>C</result>
If a and b are both prime numbers greater than 12, which of the following CANNOT be true?
I. ab is an even number.
II. The difference between a and b equals 117.
III. The sum of a and b is even.