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Math Expert V
Joined: 02 Sep 2009
Posts: 58402
If n is a positive integer, which of the following must be even? (n −  [#permalink]

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Difficulty:   15% (low)

Question Stats: 78% (01:23) correct 22% (01:18) wrong based on 170 sessions

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

A. (n − 1)( n + 1)
B. (n − 2)( n + 1)
C. (n − 2)( n + 4)
D. (n − 3)( n + 1)
E. (n − 3)( n + 5)

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Re: If n is a positive integer, which of the following must be even? (n −  [#permalink]

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4
A. (n − 1)( n + 1)
If n is even , n-1 and n+1 will both be odd.
If n = 2
(n − 1)( n + 1) = 1*3 = 3
Not even

B. (n − 2)( n + 1)
If n = 4 (Even)
2*5 = 10 is even
If n = 5 (Odd)
3*6 = 18 is even
If n = Odd , n+1 will be even and n-2 will be Odd . Product will be Even
If n = even , n+1 will be odd and n-2 will be Even . Product will be Even .

C. (n − 2)( n + 4)
If n is odd , n-2 and n+4 will both be odd .Product will be Odd .
D. (n − 3)( n + 1)
If n is even , n-3 will be odd and n+1 will also be odd.
Product will be Odd .
E. (n − 3)( n + 5)
If n is even , n-3 and n+5 will both be odd .
Product will be Odd .

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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If n is a positive integer, which of the following must be even? (n −  [#permalink]

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1
HI All,

This question can be solved by TESTing VALUES, using Number Properties, or a 'mix' of both (Skywalker18's solution properly shows how to use both approaches). When dealing with Quant questions that include the phrase "MUST be", it's important to be thorough with your work. In this prompt, we're told that N is a POSITIVE INTEGER, but we're NOT told whether it's ODD or EVEN. We're asked which of the answers MUST BE EVEN, which means "which of these answers is ALWAYS even no matter how many different examples we can come up with", so we have to consider BOTH odd values and even values. While this often requires a little more work than a typical question that can be solved by TESTing VALUES, the work is relatively easy and goes to prove how thorough your thinking is (which is something that Business Schools are interested in).

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Re: If n is a positive integer, which of the following must be even? (n −  [#permalink]

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Option B

n is a positive integer. Odd: O, Even: E & Fraction: F

n = Odd or Even = O or E

A. (n − 1)( n + 1) = (O − 1)( O + 1) or (E − 1)( E + 1) = E*E or O*O = E or O
B. (n − 2)( n + 1) = (O − 2)( O + 1) or (E − 2)( E + 1) = O*E or E*O = E
C. (n − 2)( n + 4) = (O − 2)( O + 4) or (E − 2)( E + 4) = O*O or E*E = O or E
D. (n − 3)( n + 1) = (O − 3)( O + 1) or (E − 3)( E + 1) = E*E or O*O = E or O
E. (n − 3)( n + 5) = (O − 3)( O + 5) or (E − 3)( E + 5) = E*E or O*O = E or O
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Re: If n is a positive integer, which of the following must be even? (n −  [#permalink]

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_________________ Re: If n is a positive integer, which of the following must be even? (n −   [#permalink] 02 Oct 2018, 17:56
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