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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5062
GMAT 1: 800 Q59 V59
GPA: 3.82
If x is positive integer, is √2x an integer? [#permalink]

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21 Nov 2016, 02:01
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45% (medium)

Question Stats:

65% (01:22) correct 35% (02:09) wrong based on 118 sessions

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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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"Only $79 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior CR Moderator Status: Long way to go! Joined: 10 Oct 2016 Posts: 1351 Location: Viet Nam Re: If x is positive integer, is √2x an integer? [#permalink] ### Show Tags 21 Nov 2016, 02:54 2 This post received KUDOS 3 This post was BOOKMARKED 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. _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5062 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: If x is positive integer, is √2x an integer? [#permalink] ### Show Tags 23 Nov 2016, 01:19 ==> 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 3 month Online Course"
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If x is positive integer, is √2x an integer? [#permalink]

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14 Oct 2017, 07:47
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.

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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Joined: 26 Jun 2017
Posts: 167
Location: Russian Federation
Concentration: General Management, Strategy
WE: Information Technology (Other)
Re: If x is positive integer, is √2x an integer? [#permalink]

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23 Jan 2018, 07:20
susheelh wrote:
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.

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

The same here. Agree with susheelh 100%.
Re: If x is positive integer, is √2x an integer?   [#permalink] 23 Jan 2018, 07:20
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