alsafaj wrote:
GreenlightTestPrep wrote:
Carcass wrote:
If n is an integer greater than 1, and n is not a prime number, then which of the following must be true?
(A) n is the sum of three prime numbers
(B) n is the difference between 2 even numbers
(C) n is the difference between one even number and one odd number
(D) n is the product of one even number and one odd number
(E) n is the product of prime numbers
Key Property #1: If n is an integer greater than 1, then EITHER n is a prime number, OR n is a composite number.
Key Property #2: All composite integers can be expressed as the product of prime numbers. Since we're told integer n is NOT a prime number, we know that n must be a composite number, which means
n can be expressed as the product of prime number.
Answer: E
Why is (A) and (D) are incorrect?
The key words in this question are "must be true."
So, for example, if we can show that an answer choice is not necessarily true, then we can eliminate that answer choice.
For example, if n = 4, n cannot be the sum of three prime numbers. Eliminate A.
Similarly, if n = 4, and cannot be the product of one even number and one odd number. Eliminate D.
Does that help?