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# If x is a positive integer, then which of the following is always true

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Senior Manager
Joined: 18 Feb 2019
Posts: 280
Location: India
GMAT 1: 490 Q47 V13
GPA: 3.6
If x is a positive integer, then which of the following is always true  [#permalink]

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20 Mar 2019, 09:42
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25% (medium)

Question Stats:

80% (02:25) correct 20% (01:43) wrong based on 20 sessions

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If x is a positive integer, then which of the following is always true for n=x^(x+1)+(x+1)^x?

A. n is even for all values of x
B. n is even for even values of x
C. n is multiple of 3 when x is even
D. n is a prime number
E. n is odd for all values of x
Director
Joined: 18 Jul 2018
Posts: 825
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: If x is a positive integer, then which of the following is always true  [#permalink]

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20 Mar 2019, 09:55
As x is positive number. Let us take x as 1 or 2.
When x = 1.
$$n = x^{x+1}+(x+1)^x$$
n = 1+2 = 3 = odd.
When x = 2.
$$n = x^{x+1}+(x+1)^x$$
n = 8+9 = 17 = odd.

So, for any value of x, x is always an odd integer.

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Re: If x is a positive integer, then which of the following is always true   [#permalink] 20 Mar 2019, 09:55
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