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# If X is a positive integer, is X even?

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Math Expert
Joined: 02 Sep 2009
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If X is a positive integer, is X even?  [#permalink]

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24 Jun 2016, 03:12
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Difficulty:

5% (low)

Question Stats:

86% (01:20) correct 14% (01:29) wrong based on 115 sessions

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If X is a positive integer, is X even?

(1) 9X^2 is divisible by 4.
(2) 3X + 2 is divisible by 8.

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Re: If X is a positive integer, is X even?  [#permalink]

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24 Jun 2016, 05:28
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Statement 1: 9X^2 mod 4 = 0. We know square of even is even and square of odd is odd. So, X has to be even if 9X^2 mod 4 = 0.
So, Statement 1 is sufficient.

Statement 2: 3X+2 mod 8 = 0. Hence, X has to be even for it to be true.
So, Statement 2 is also sufficient.

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Re: If X is a positive integer, is X even?  [#permalink]

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27 Mar 2018, 06:35
Bunuel wrote:
If X is a positive integer, is X even?

(1) 9X^2 is divisible by 4.
(2) 3X + 2 is divisible by 8.

Given x > 0

Question: Is X even?

Smallest even number greater that 0" is 2.

St 1: 9 is not divisible by 4, therefore, 9x^2 is only divisible by "4" If X^2 is divisible by "4".

Hence X can be 2, 4, 8 etc. EVEN. Sufficient

St 2: 3X + 2 is divisible by 8.

An ODD number can't be divisible by "8", Therefore X is even and thereby 3X is even.

Sufficient

(D)
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Re: If X is a positive integer, is X even?   [#permalink] 27 Mar 2018, 06:35
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