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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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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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You tried your best and you failed miserably. The lesson is 'never try'. -Homer Simpson

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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(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.

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