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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] New post 09 Aug 2017, 15:19
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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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[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] New post 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] New post 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] New post 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] New post 08 Jul 2018, 11:38
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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] New post 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.

So the answer is 256.
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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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