If a and b are both prime numbers greater than 10, which of the following CANNOT be true?
I. ab is an even number.
II. a-b = 117.
III. ( a + B) is even.  Choose the correct answer:
A) I, II and III  B) I only  C) I and III only  D) II and III only  E) I and II only
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 (E).   Answer : I and II only
<result>E</result>
If a and b are both prime numbers greater than 10, which of the following CANNOT be true?
I. ab is an even number.
II. a-b = 117.
III. ( a + B) is even.