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If n is a positive integer, which of the following must be an even int

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Bunuel
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If n is a positive integer, which of the following must be an even int [#permalink] New post  14 Oct 2019, 07:35
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If n is a positive integer, which of the following must be an even integer?

(A) n + 1
(B) n + 2
(C) n^2 + 2
(D) n^2 + n
(E) n^2 + 2n
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BrentGMATPrepNow
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Re: If n is a positive integer, which of the following must be an even int [#permalink] New post  14 Oct 2019, 07:45
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Bunuel wrote:
If n is a positive integer, which of the following must be an even integer?

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


Scan the answers....

D) n² + n
Factor to get: n(n+1)
Since n and (n+1) are CONSECUTIVE INTEGERS, we know that one number is ODD and the other must be EVEN
As such, the product n(n+1) must be EVEN

Answer: D

Cheers,
Brent
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Abhishek009
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Re: If n is a positive integer, which of the following must be an even int [#permalink] New post  14 Oct 2019, 11:14
Bunuel wrote:
If n is a positive integer, which of the following must be an even integer?

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


Negation of Options -

(A) Not possible when n = Even
(B) Not possible when n = Odd
(C) Not possible when n = Odd
(D) Possible whether n = Odd/Even
(E) Not possible when n = Odd

If in doubt plug in some number such as 1 or 3 and reconfirm the Answer, Correct Answer must be (D)
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Re: If n is a positive integer, which of the following must be an even int [#permalink]
14 Oct 2019, 11:14
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