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# If x^2/4 is an integer greater than 50 and x is a positive i

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If x^2/4 is an integer greater than 50 and x is a positive i [#permalink]  09 Aug 2017, 15:19
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53% (01:14) correct 46% (01:11) wrong based on 13 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 $$x^2$$?

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256

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Re: If x^2/4 is an integer greater than 50 and x is a positive i [#permalink]  11 Aug 2017, 21:16
how could it possible????

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Re: If x^2/4 is an integer greater than 50 and x is a positive i [#permalink]  12 Aug 2017, 02:27
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$$\frac{x^2}{4} > 50$$

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.

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Re: If x^2/4 is an integer greater than 50 and x is a positive i [#permalink]  08 Jul 2018, 01:27
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.
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Re: If x^2/4 is an integer greater than 50 and x is a positive i [#permalink]  08 Jul 2018, 11:38
Expert's post
Please read carefully my explanation on why I considered 16 as a number and above.

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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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$$x^2/4>50$$ 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.

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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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