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# Is √(56x) an integer?

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Is √(56x) an integer? [#permalink]  01 Dec 2013, 16:36
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Difficulty:

55% (hard)

Question Stats:

57% (02:26) correct 43% (01:13) wrong based on 92 sessions
Is √(56x) an integer?

(1) x is a multiple of 14.
(2) 28 is not a factor of x.
[Reveal] Spoiler: OA

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Re: Is √(56x) an integer? [#permalink]  02 Dec 2013, 01:06
Expert's post
Is √(56x) an integer?

$$\sqrt{56x}=2\sqrt{14x}$$.

(1) x is a multiple of 14. If x=14, then the answer is YES but if x=14*3, then the answer is NO. Not sufficient.

(2) 28 is not a factor of x. Consider the same examples. Not sufficient.

(1)+(2) Consider the same examples. Not sufficient.

Answer: E.
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Re: Is √(56x) an integer? [#permalink]  06 Jan 2014, 09:16
honchos wrote:
Is √(56x) an integer?

(1) x is a multiple of 14.
(2) 28 is not a factor of x.

OK here's the deal

We need to know if X has at least 2 and a 7^2 for 56x to be a perfect square

Statement 1

Is a multiple of 2*7, OK, thanks for the info but we are still missing one 7

Statement 2

Not a factor of 2^2*7. Well OK, doesn't have a square power of 2 but could as well have a square power of 7. I need more info

Statement 1 and 2 together

Well we are still missing that 7!!

Answer is E

Cheers!
If it helps Kudos me ok?

J
Re: Is √(56x) an integer?   [#permalink] 06 Jan 2014, 09:16
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# Is √(56x) an integer?

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