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If x is an integer, is x odd?

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Joined: 02 Sep 2009
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If x is an integer, is x odd?  [#permalink]

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20 Dec 2015, 06:02
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45% (medium)

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55% (01:00) correct 45% (00:56) wrong based on 190 sessions

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If x is an integer, is x odd?

(1) x + 4 is an odd integer.
(2) x/3 is NOT an even integer.

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Re: If x is an integer, is x odd?  [#permalink]

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20 Dec 2015, 09:37
Bunuel wrote:
If x is an integer, is x odd?

(1) x + 4 is an odd integer.
(2) x/3 is NOT an even integer.

(A) - (1) IS SUFFICIENT, (2) IS NOT

(1) x+4 is odd. Therefore, x+2 is odd, and so is x+0 (i.e. x). Basically, adding a multiple of two to any integer keeps its odd/even'ness' the same.

(2) x/3 is not an even integer. So, it could be - a fraction OR an odd integer. Consider x = 7 . Then x/3 is a fraction. Similarly, x=8 gives x/3 as a fraction. However, x=15 gives an odd quotient. NOT SUFFICIENT.
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Re: If x is an integer, is x odd?  [#permalink]

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26 Oct 2017, 12:35
Bunuel wrote:
If x is an integer, is x odd?

(1) x + 4 is an odd integer.
(2) x/3 is NOT an even integer.

(1) x + even = odd ---> x - odd ---> sufficient
(2) x/3 can be either odd integer or a fraction
2.1. x/3=5 ---> x = 15 ---> yes
2.2. x/3 = 0,5 ---> x = 1,5 ---> no

(2_new). x/3 is an integer, not even
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Re: If x is an integer, is x odd?  [#permalink]

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06 Dec 2018, 06:06
Bunuel wrote:
If x is an integer, is x odd?

(1) x + 4 is an odd integer.
(2) x/3 is NOT an even integer.

x is an integer
Question : is x odd or not.

Statement 1 : x+4 is odd..
Also odd - even = odd
So, odd - 4 = odd = x
SUFFICIENT

Statement 2: x/3 is not even .. So x/3 can be fraction or odd .
If x/3 is odd , definitely x will be odd. For e.g. x/3 = 3 -> x = 9
If x/3 is a fraction, x may be odd or even. For e.g. if x/3 = 2/3 a fraction -> x=2
Also if x/3 = 7/3 a fraction -> x = 7
NOT SUFFICIENT

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Re: If x is an integer, is x odd?  [#permalink]

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06 Dec 2018, 09:42
If x is an integer, is x odd?

(1) x + 4 is an odd integer.
(2) x/3 is NOT an even integer.

1)odd + odd is always even,and even +even is always even but odd + even is always odd. so we know that 4 is even that means that x must be odd.
2) odd*even=even even*even=even so we dont know for sure.

Re: If x is an integer, is x odd?   [#permalink] 06 Dec 2018, 09:42
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