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# Is x an integer?

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Senior Manager
Status: May The Force Be With Me (D-DAY 15 May 2012)
Joined: 06 Jan 2012
Posts: 257
Location: India
Concentration: General Management, Entrepreneurship

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04 Feb 2012, 10:43
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Is x an integer?

(1) x/2 is an integer
(2) 2x is an integer

I used a fraction (4/2) in A to prove that X is not an integer but OA is different
[Reveal] Spoiler: OA

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Last edited by Bunuel on 12 Jun 2013, 03:19, edited 2 times in total.
Edited the question
Manager
Joined: 03 Oct 2009
Posts: 59
Re: X is an integer? [#permalink]

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04 Feb 2012, 11:01
Is X an integer?

A] X/2 is an integer
Sufficient, X is a multiple of 2.

B] 2X is an integer
Not sufficient, for instance x = .5 and 2x = 1.
Math Expert
Joined: 02 Sep 2009
Posts: 44412
Re: X is an integer? [#permalink]

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04 Feb 2012, 12:10
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boomtangboy wrote:
Is X an integer?

A] X/2 is an integer
B] 2X is an integer

I used a fraction (4/2) in A to prove that X is not an integer but OA is different

Is x an integer?

(1) x/2 is an integer. For x/2 to be an integer x must be an integer --> $$\frac{x}{2}=integer$$ --> $$x=2*integer=integer$$, as you can see $$x$$ is not only an integer but an even integer. Sufficient.

(2) 2x is an integer --> x may or may not be an integer, for instance $$x=0.5$$ or $$x=1$$. Basically $$x$$ is of a type $$\frac{integer}{2}$$, hence $$x$$ may be an integer itself or half of an integer 0.5, 1.5, ... Not sufficient.

As for your example: 4/2=2=integer, so 4/2 is just another way of writing integer 2, like 6/3 or 8/4. Also notice that any integer can be expressed as the ratio of 2 integers.

Hope it's clear.
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Re: Is x an integer? [#permalink]

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15 Sep 2017, 07:33
Hello from the GMAT Club BumpBot!

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Re: Is x an integer?   [#permalink] 15 Sep 2017, 07:33
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