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Re: If n is an integer, which of the following must be even? [#permalink]

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18 Sep 2012, 06:18

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Bunuel 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

Since n is an integer, it can be EVEN or ODD. But any integer when multiplied by 2 is even. For example, 3 * 2 = 6 (even) The rule is: EVEN * ODD = EVEN EVEN * EVEN = EVEN ODD * ODD = ODD

A) we cant say as it depends if n is odd or even B) same as A) C) Even as n is multiplied by 2 D) It is ODD as EVEN+1 = ODD E) depends if n is even or odd.

Re: If n is an integer, which of the following must be even? [#permalink]

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24 May 2014, 01:34

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I thought that an integer could be 0. If that is the case, then 2*(0), would equal 0, which is not equal an even number. Thus, it does not answer the question. Can someone please clarify? Thanks.

Re: If n is an integer, which of the following must be even? [#permalink]

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24 May 2014, 03:13

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Can you please clarify. My understanding is that 0 is an integer. If that the case you cant say any integer multiplied by an even number equals an even number. Because 0 multiplied by an even number equals 0, which is not an even number.

Im wondering if this question is erroneous. Shouldnt the question state any "if n is a positive or negative integer..."?

Re: If n is an integer, which of the following must be even? [#permalink]

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24 May 2014, 03:17

Expert's post

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momentofzen wrote:

Can you please clarify. My understanding is that 0 is an integer. If that the case you cant say any integer multiplied by an even number equals an even number. Because 0 multiplied by an even number equals 0, which is not an even number.

Im wondering if this question is erroneous. Shouldnt the question state any "if n is a positive or negative integer..."?

Zero is an even integer. Zero is nether positive nor negative, but zero is definitely an even number.

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even (in fact zero is divisible by every integer except zero itself).

Re: If n is an integer, which of the following must be even? [#permalink]

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22 Dec 2015, 19:29

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Re: If n is an integer, which of the following must be even? [#permalink]

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27 May 2016, 07:24

Bunuel 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

To solve this question, we need to consider a few odd/even rules.

1) (even + even) or (odd + odd) = even

2) even + odd = odd

3) (even x even) or (even x odd) = even (Note that an even integer times any integer, whether even or odd, will yield an even answer for the product.)

4) odd x odd = odd

Doing a quick scan of our answer choices allows us to select C as the correct option. Regardless whether n is even or odd, 2 (which is even) times any integer will always be even.

The answer is C. _________________

Jeffrey Miller Jeffrey Miller Head of GMAT Instruction

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