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# If x is a positive integer, which of the following must be odd?

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Math Expert
Joined: 02 Sep 2009
Posts: 58434
If x is a positive integer, which of the following must be odd?  [#permalink]

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28 Feb 2016, 10:03
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If x is a positive integer, which of the following must be odd?

A. x+1
B. x^2+x
C. x^2+x+1
D. x^2−1
E. 3x^2−3

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Joined: 25 Dec 2012
Posts: 116
Re: If x is a positive integer, which of the following must be odd?  [#permalink]

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28 Feb 2016, 10:12
Bunuel wrote:
If x is a positive integer, which of the following must be odd?

A. x+1
B. x^2+x
C. x^2+x+1
D. x^2−1
E. 3x^2−3

A. X+1 = can be odd or even. Since O + O =E or E + O = O

B. X^2 + X = X(X+1). Since from the above derivation we already know the term X+1 can be Odd or Even, directly substitute here. X(ODD) = Even (When X is Even) or X(EVEN) = EVEN [When X is ODD]

C. Here's the answer. Since we know the term x^2 + X can always take a EVEN number, EVEN + 1 = ODD

Hence C.
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Joined: 12 Sep 2015
Posts: 4015
Re: If x is a positive integer, which of the following must be odd?  [#permalink]

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28 Feb 2016, 10:19
1
Bunuel wrote:
If x is a positive integer, which of the following must be odd?

A. x+1
B. x^2+x
C. x^2+x+1
D. x^2−1
E. 3x^2−3

Let's test some values.
Try x = 1

A. 1 + 1 = 2 EVEN - ELIMINATE A
B. 1^2 + 1 = 2 EVEN - ELIMINATE B
C. 1^2 + 1 + 1 = 3 ODD - KEEP C
D. 1^2 − 1 = 0 EVEN - ELIMINATE D
E. 3(1^2) − 3 = 0 EVEN - ELIMINATE E

Cheers,
Brent
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Re: If x is a positive integer, which of the following must be odd?  [#permalink]

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27 Mar 2016, 14:09
try 2 numbers one even and the other odd for various options to get the correct answer
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Joined: 18 Oct 2016
Posts: 130
Location: India
WE: Engineering (Energy and Utilities)
Re: If x is a positive integer, which of the following must be odd?  [#permalink]

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13 Apr 2017, 02:12
Option C

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

x = Even or Odd = E or O

A. x + 1 = E + 1 or O + 1 = O or E
B. x^2 + x = E^2 + E or O^2 + O = E or E
C. x^2 + x + 1 = E^2 + E + 1 or O^2 + O + 1 = E + 1 or E + 1 = O or O
D. x^2 − 1 = E^2 - 1 or O^2 - 1 = E - 1 or O - 1 = O or E
E. 3x^2 − 3 = 3*E^3 - 3 or 3*O^2 - 3 = E - 3 or O - 3 = O or E
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Re: If x is a positive integer, which of the following must be odd?   [#permalink] 13 Apr 2017, 02:12
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# If x is a positive integer, which of the following must be odd?

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