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If x is positive integer, is √2x an integer?

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If x is positive integer, is √2x an integer?

1) x/2 is an integer squared
2) x/200 is an integer squared
[Reveal] Spoiler: OA

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Re: If x is positive integer, is √2x an integer? [#permalink]

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MathRevolution wrote:
If x is positive integer, is √2x an integer?

1) x/2 is an integer squared
2) x/200 is an integer squared


(1) we have \(\frac{x}{2}=k^2\) so \(x=2k^2\).

Hence, \(\sqrt{2x}=\sqrt{2 \times 2k^2}=\sqrt{4k^2}=2k\), is an integer. Sufficient.

(2) we have \(\frac{x}{200}=k^2\) so \(x=200k^2=2 \times (10k)^2\).

Hence, \(\sqrt{2x}=\sqrt{2 \times 2 (10k)^2}=\sqrt{4 \times (10k)^2}=2 \times 10k =20k\), is an integer. Sufficient.

The answer is D.
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Re: If x is positive integer, is √2x an integer? [#permalink]

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New post 23 Nov 2016, 00:19
==> In the original condition, there is 1 variable (x). Therefore, D is most likely to be the answer.
For con 1), from x=2t^2, you get √2x = √(2*2t^2 ) =2t, hence yes, it is sufficient.
For con 2), from x=200s^2, you get √2x = √(2*200s^2 ) =20s, hence yes, it is sufficient.
Therefore, the answer is D.

Answer: D
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If x is positive integer, is √2x an integer? [#permalink]

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New post 14 Oct 2017, 06:47
Hello Moderators/MathRevolution,

Do you think the question needs to be made math friendly?

The reason is, the way it is written looks to convey - "Is \(\sqrt{2}*x\) an integer?". However, from the OE it seems that the stem means "Is \(\sqrt{(2*x)}\) an integer?"

Do correct me if I am wrong.

PS: Note that even if the stem is read as \(\sqrt{2}*x\) I still got D. The answer I got is 'x is not an integer' for both cases.Suggesting modification so that the stem matches the OE.

Thanks in advance!

MathRevolution wrote:
If x is positive integer, is √2x an integer?

1) x/2 is an integer squared
2) x/200 is an integer squared

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If x is positive integer, is √2x an integer?   [#permalink] 14 Oct 2017, 06:47
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