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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # If x^2/4 is an integer greater than 50 and x is a positive i  Question banks Downloads My Bookmarks Reviews Important topics
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TAGS: Moderator  Joined: 18 Apr 2015
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If x^2/4 is an integer greater than 50 and x is a positive i [#permalink]
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Expert's post 00:00

Question Stats: 64% (01:10) correct 35% (01:11) wrong based on 17 sessions

If $$\frac{x^2}{4}$$ is an integer greater than 50 and x is a positive integer, then what is the smallest possible value for $$x^2$$?

[Reveal] Spoiler: OA
256

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Re: If x^2/4 is an integer greater than 50 and x is a positive i [#permalink]
how could it possible????

Posted from my mobile device  Moderator  Joined: 18 Apr 2015
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Re: If x^2/4 is an integer greater than 50 and x is a positive i [#permalink]
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Expert's post
$$\frac{x^2}{4} > 50$$

50*4 = 200 which means that $$x^2$$ must be > 200.

The only number > 200 AND at the same time the smallest possible value is 16. $$16^2 = 256$$

Notice also that X must be a number divisible by 4.

Hope this helps.

Regards
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Re: If x^2/4 is an integer greater than 50 and x is a positive i [#permalink]
Carcass wrote:
$$\frac{x^2}{4} > 50$$

50*4 = 200 which means that $$x^2$$ must be > 200.

The only number > 200 AND at the same time the smallest possible value is 16. $$16^2 = 256$$

Notice also that X must be a number divisible by 4.

Hope this helps.

Regards

Thanks Carcass, it's clear. But why you started off from 16? Why if the number is extremely large? I think this could works with small numbers, but it might get knotty with complex once.
Moderator  Joined: 18 Apr 2015
Posts: 5877
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Kudos [?]: 1154 , given: 5471

Re: If x^2/4 is an integer greater than 50 and x is a positive i [#permalink]
Expert's post
Please read carefully my explanation on why I considered 16 as a number and above.

Regards
_________________ Intern  Joined: 04 May 2017
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Re: If x^2/4 is an integer greater than 50 and x is a positive i [#permalink]
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$$x^2/4>50$$ and $$x^2,x^2/4$$ is an integer <-> $$x^2>200$$ and $$x^2$$ are an integers.

We see that $$14^2=196, 15^2=225, 16^2=256$$, but $$14^2=196<250$$, $$15^2=225$$ is not divisible by 4.

So the answer is 256.
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Do not pray for an easy life, pray for the strength to endure a difficult one - Bruce Lee Re: If x^2/4 is an integer greater than 50 and x is a positive i   [#permalink] 10 Jul 2018, 01:56
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