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If n is an integer greater than 1, and n is not a prime number, then w [#permalink]
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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?
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Re: If n is an integer greater than 1, and n is not a prime number, then w [#permalink]
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Thanks for your reply, but I still struggle to justify.

The question already specified that n is not a prime number, so why would we hypothesize that n=2 and n cannot be 2 which is a prime number? likewise on n=3.

Thanks to clarify further!
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Re: If n is an integer greater than 1, and n is not a prime number, then w [#permalink]
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alsafaj wrote:
Thanks for your reply, but I still struggle to justify.

The question already specified that n is not a prime number, so why would we hypothesize that n=2 and n cannot be 2 which is a prime number? likewise on n=3.

Thanks to clarify further!

My bad. I somehow missed the "n is not a prime number" part.
I have edited my response above (using n = 4)

See what you think
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Re: If n is an integer greater than 1, and n is not a prime number, then w [#permalink]
GreenlightTestPrep wrote:
alsafaj wrote:
Thanks for your reply, but I still struggle to justify.

The question already specified that n is not a prime number, so why would we hypothesize that n=2 and n cannot be 2 which is a prime number? likewise on n=3.

Thanks to clarify further!

My bad. I somehow missed the "n is not a prime number" part.
I have edited my response above (using n = 4)

See what you think


It is clear now. Thank you.
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Re: If n is an integer greater than 1, and n is not a prime number, then w [#permalink]
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