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If n is an integer, then which one of the following expressions must b 05 Jul 2019, 04:31
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C
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15% (low)

Question Stats:

83% (00:56) correct 17% (00:56) wrong based on 76 sessions

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If n is an integer, then which one of the following expressions must be even?

(A) \(n^2 + 1\)

(B) \(n(n + 2)\)

(C) \(n(n + 1)\)

(D) \(n(n + 4)\)

(E) \((n + 1)(n + 3)\)

Source: Nova GMAT
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C
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If n is an integer, then which one of the following expressions must b 05 Jul 2019, 04:51
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Answer C is the product of two consecutive integers, so it's certainly always even.
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If n is an integer, then which one of the following expressions must b 05 Jul 2019, 04:56
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SajjadAhmad
If n is an integer, then which one of the following expressions must be even?

(A) \(n^2 + 1\)

(B) \(n(n + 2)\)

(C) \(n(n + 1)\)

(D) \(n(n + 4)\)

(E) \((n + 1)(n + 3)\)

Source: Nova GMAT
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n(n+1) is even since
if n = odd => n+1 = even
or if n = even => n+1 = odd
In both cases
n(n+1) = even * odd = even

IMO C
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If n is an integer, then which one of the following expressions must b 05 Jul 2019, 05:10
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SajjadAhmad
If n is an integer, then which one of the following expressions must be even?

(A) \(n^2 + 1\)

(B) \(n(n + 2)\)

(C) \(n(n + 1)\)

(D) \(n(n + 4)\)

(E) \((n + 1)(n + 3)\)

Source: Nova GMAT
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Another approach is to test (easy) values of n.

For example, if n = 0, we get:
(A) \(0^2 + 1 = 1\), which is ODD - ELIMINATE
(B) \(0(0 + 2)=0\), which is EVEN. KEEP.
(C) \(0(0 + 1) = 0\), which is EVEN. KEEP.
(D) \(0(0 + 4) = 0\), which is EVEN. KEEP.
(E) \((0 + 1)(0 + 3) = 3\), which is ODD - ELIMINATE

We're left with B, C and D
Next test n = 1 to get:
(B) \(1(1 + 2)=3\), which is ODD - ELIMINATE
(C) \(1(1 + 1) = 2\), which is EVEN. KEEP.
(D) \(1(1 + 4) = 5\), which is ODD - ELIMINATE

By the process of elimination, the correct answer is C

Cheers,
Brent
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If n is an integer, then which one of the following expressions must b 05 Jul 2019, 05:20
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SajjadAhmad
If n is an integer, then which one of the following expressions must be even?

(A) \(n^2 + 1\) Put n=odd answer= even, Put n=odd answer= even

(B) \(n(n + 2)\) Put n=odd answer= odd, Put n=even answer=even

(C) \(n(n + 1)\) Put n= odd answer= even, put n=even answer= even

(D) \(n(n + 4)\) Put n= odd answer= odd, Put n= even answe=even

(E) \((n + 1)(n + 3)\) Put n=odd answer=even,Put n= even answer=even/odd

Source: Nova GMAT
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If n is an integer, then which one of the following expressions must b 17 Feb 2021, 19:50
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