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# Is x odd?

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Is x odd? [#permalink]  15 Jul 2012, 03:30
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Is x odd?

(1) 2x - 1 is odd
(2) x^3 is odd
[Reveal] Spoiler: OA

Last edited by Bunuel on 15 Jul 2012, 03:41, edited 1 time in total.
Edited the question.
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Re: Is x odd? [#permalink]  15 Jul 2012, 03:51
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Is x odd?

(1) 2x - 1 is odd --> $$2x-1=odd$$ --> $$2x=even$$ --> $$x=\frac{even}{2}$$ --> $$x$$ is an integer. Now, $$x=\frac{even}{2}$$ could be even (consider $$x=\frac{even}{2}=\frac{4}{2}=2=even$$) as well as odd (consider $$x=\frac{even}{2}=\frac{2}{2}=1=odd$$). Not sufficient.

(2) x^3 is odd. If $$x=integer$$ then in order $$x^3=odd$$ to hold true, it must be odd (answer YES), but $$x$$ could also be some irrational number, for example $$x=\sqrt[3]{5}$$ (answer NO). Not sufficient.

(1)+(2) Since from (1) $$x=integer$$ then from (2) we have that $$x=odd$$. Sufficient.

Hope it's clear.
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Re: Is x odd? [#permalink]  16 Jul 2012, 10:18
@Bunuel:

I don't understand your approach for the first argument:

$$2x-1=odd$$

If the result muss be odd, so x must be even. It will be even if x is 2 or greater than 2. If x is odd the result won't be odd. If I say x = 1 so the result will be Zero. But Zero is neither even nor odd. So the satetement is sufficient ?
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Re: Is x odd? [#permalink]  16 Jul 2012, 12:06
Expert's post
Alexmsi wrote:
@Bunuel:

I don't understand your approach for the first argument:

$$2x-1=odd$$

If the result muss be odd, so x must be even. It will be even if x is 2 or greater than 2. If x is odd the result won't be odd. If I say x = 1 so the result will be Zero. But Zero is neither even nor odd. So the satetement is sufficient ?

Several things:

1. $$2x-1=odd$$ --> $$2x=odd+1=odd+odd=even$$ --> so $$2x=even$$ --> $$x=\frac{even}{2}=integer$$. Hence $$2x-1=odd$$ just means that $$x$$ is an integer (it can be even as well as odd).

2. If $$x=1$$the result wont be zero, it'l be 1, so odd: $$2*1-1=2-1=1=odd$$.

3. Zero is an even integer. Zero is nether positive nor negative, but zero is definitely an even number.

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even (in fact zero is divisible by every integer except zero itself).

Or in another way: an even number is an integer of the form $$n=2k$$, where $$k$$ is an integer. So for $$k=0$$ --> $$n=2*0=0$$.

Hope it's clear.
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Re: Is x odd? [#permalink]  05 Sep 2015, 04:35
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Re: Is x odd?   [#permalink] 05 Sep 2015, 04:35
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