If x is a positive integer and x^2 is divisible by 32, then

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If x is a positive integer and x^2 is divisible by 32, then [#permalink]

24 Dec 2009, 03:59

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Question Stats:

57% (05:42) correct

42% (00:30) wrong

based on 9 sessions

If x is a positive integer and x^2 is divisible by 32, then the largest positive integer that must divide x is

(A) 2
(B) 6
(C) 8
(D) 12
(E) 16

Last edited by Bunuel on 03 Jan 2013, 08:03, edited 1 time in total.

Renamed the topic and edited the question.

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Re: Division & Factor [#permalink]

24 Dec 2009, 04:18

Imo C

32=2^5
nearest squre =2^6=8^2
hence x=8 and the lagest int dividing 8 is 8
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Manager

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Re: Division & Factor [#permalink]

24 Dec 2009, 06:46

Thank you for solving. However I am confused why not x is divisible by16.

if x is 16 then x^2 is 256 which is divisible by 32. Appreciate your help.

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Re: Division & Factor [#permalink]

24 Dec 2009, 07:21

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prasadrg wrote:

Thank you for solving. However I am confused why not x is divisible by16.

if x is 16 then x^2 is 256 which is divisible by 32. Appreciate your help.

The largest positive integer that must divide x, means for lowest value of x which satisfies the given statement in the stem.

Given: 32k=x^2, where k is an integer \geq1 (as x is positive).

32k=x^2 --> x=4\sqrt{2k}, as x is an integer \sqrt{2k}, also must be an integer. The lowest value of k, for which \sqrt{2k} is an integer is when k=2 --> \sqrt{2k}=\sqrt{4}=2 --> x=4\sqrt{2k}=4*2=8

Hope it's helps.
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Manager

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Re: Division & Factor [#permalink]

24 Dec 2009, 09:25

Thank you and it makes sense.

Re: Division & Factor [#permalink] 24 Dec 2009, 09:25

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If x is a positive integer and x^2 is divisible by 32, then

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If x is a positive integer and x^2 is divisible by 32, then

If x is a positive integer and x^2 is divisible by 32, then

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