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Is x an integer?

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Is x an integer? [#permalink] New post 08 Dec 2005, 05:33
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Is x an integer?

(1) \(\frac{x}{2}\) is an integer
(2) 2x is an integer

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-x-an-integer-127043.html
[Reveal] Spoiler: OA
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Re: Is x an integer? [#permalink] New post 08 Dec 2005, 06:02
The answer is A.

Your contention that x could be 1/2 means that x/2 would be 1/4 and this is not an integer while they say that x/2 is an integer.

Thus, if x/2 is an integer, x has to be an integer as well and thus we have A as the answer.
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Re: Is x an integer? [#permalink] New post 08 Dec 2005, 06:08
You are right...it just clicked. Dumb mistake on my end. Dumb mistakes are my worse enemy!
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Re: Is x an integer? [#permalink] New post 08 Dec 2005, 06:14
manta_ray wrote:
Here is a DS question (Question 28 in the GMAT Review Official Guide 11th edition):

Is x an integer?

(1) x/2 is an integer

(2) 2x is an integer

My answer was E, neither is sufficient.

My rationale:
For (1) x could be 1/2 which would make x/2 an integer or x could be 4 which would make x/2 an integer

For (2) x could be 1/2 or 4 causing 2x to be an integer.

In both cases x could be an integer or a fraction. Therefore neither (1) nor (2) is sufficient for answering the question.

BUT in the answer guide the answer is A. Can someone please shed light on why the answer is A. The explaination is a poor one in the book I'm using.

Thanks!
CM

For x=1/2 x/2=1/4 I think Try to check with calculator :wink:
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Re: Is x an integer? [#permalink] New post 06 Feb 2008, 00:02
lmshaw wrote:
Hey guys, I am confused at this DS question...hope u can help clarify it for me.

#28 pg. 280
Is x an integer?
(1) x/2 is an integer
(2) 2x is an integer

The answer is A.

So you can plug in 6 for x, and that will satisfy statement 1. But can't you also plug in 3/2 for x? The answer will be 3, which will still satisfy statement 1. So if x can both be an integer and non-integer, A can't be the answer right?

I don't know...it's past midnight here. Maybe I'm just getting delirious...??


plugging 3/2 in a will give 3/4 (since its x/2), which is not an integer. The answer should be (A)
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Re: Is x an integer? [#permalink] New post 06 Feb 2008, 00:09
oh god you're right! i am delirious. thanks!
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Re: Is x an integer? [#permalink] New post 06 Feb 2008, 04:53
lmshaw wrote:
Hey guys, I am confused at this DS question...hope u can help clarify it for me.

#28 pg. 280
Is x an integer?
(1) x/2 is an integer
(2) 2x is an integer

The answer is A.

So you can plug in 6 for x, and that will satisfy statement 1. But can't you also plug in 3/2 for x? The answer will be 3, which will still satisfy statement 1. So if x can both be an integer and non-integer, A can't be the answer right?

I don't know...it's past midnight here. Maybe I'm just getting delirious...??

we always want the minimum values for the numerator in divisibility questions. the min of x/2 is 2. all numerators will be multiples of 2 so x is an integer.
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Re: Is x an integer? [#permalink] New post 26 Mar 2015, 17:14
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Re: Is x an integer? [#permalink] New post 27 Mar 2015, 04:03
Expert's post
manta_ray wrote:
Is x an integer?

(1) \(\frac{x}{2}\) is an integer
(2) 2x is an integer


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.

Answer: A.

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-x-an-integer-127043.html
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Re: Is x an integer?   [#permalink] 27 Mar 2015, 04:03
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