2014-06-04 09:00:20

If a, b, and c are all unique prime numbers, which of the following CANNOT be true?

I. abc is even
II. abc is prime
III. abc is negative

(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III

The correct answer is D
Explanation: Check each of the Roman numeral choices. If there is one instance that works, then the choice can be eliminated, since the question is looking for something that must not be true in any case.

I. is incorrect. Because a, b, or c could be 2, abc could be even. Say a is 2, then b and c must both be odd. b x c is also going to be odd, as the product of two odd numbers is always odd. bc x a, then, would be even, since the product of an odd number and an even number is always even. This means abc can be even.

II. is correct. A prime number only has two factors: itself and 1. abc will be not be prime, even though a, b, and c are prime numbers. That is, abc will have more than two factors, as it will be divisible by 1, a, b, c, ab, ac, bc, and abc. This means abc cannot possibly be prime.

III. is correct. A prime number cannot be negative, as a prime number can only have two factors. Negative numbers are divisible by at least four numbers (for example, -3 is divisible by 1, 3, -1, and -3), so they are not prime. The product of three positive numbers will definitely be positive, so it cannot be true that abc is negative.

As II and III are both true, choice D is correct.