boomgoesthegmat wrote:If n is an integer, which of the following must be even?

A) n + 1
B) n + 2
C) 2n
D) 2n + 1
E) n^2

The definition of an even number is that it can be written as the product of 2 and some integer.
So the correct answer is C

Alternatively, we can show that A, B, D and E need not be even numbers.

A) If n = 2, then n+1 is NOT even. ELIMINATE.
B) If n = 1, then n+2 is NOT even. ELIMINATE.
C) If n = 1, then 2n+1 is NOT even. ELIMINATE.
D) If n = 1, then n^2 is NOT even. ELIMINATE.

Cheers,
Brent

Hi All,

We're told that N is an INTEGER. We're asked which of the following MUST be even (which really means "which of the following is ALWAYS EVEN no matter how many different examples we can come up with?"). This question can be solved in a couple of different ways. There are a number of different Number Property rules involved in this prompt, so we can do a quick review of all of them and find the correct answer that way.

Answer A: N+1.... adding 1 to an EVEN leads to an ODD, adding 1 to an ODD leads to an EVEN. Eliminate Answer A.
Answer B: N+2.... adding 2 to an EVEN leads to an EVEN, adding 2 to an ODD leads to an ODD. Eliminate Answer B.
Answer C: 2N.... multiplying ANY integer by 2 leads to an EVEN. This is ALWAYS EVEN.
Answer D: 2N+1.... multiplying ANY integer by 2 leads to an EVEN and then adding 1 leads to an ODD.
Answer E: N^2.... squaring an EVEN leads to an EVEN, squaring an ODD leads to an ODD.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich