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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 [#permalink] New post 24 Dec 2009, 02:59
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 26 Jun 2013, 00:46, edited 2 times in total.
Renamed the topic and edited the question.
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Re: Division & Factor [#permalink] New post 24 Dec 2009, 03:18
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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Re: Division & Factor [#permalink] New post 24 Dec 2009, 05:46
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] New post 24 Dec 2009, 06:21
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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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Re: Division & Factor [#permalink] New post 24 Dec 2009, 08:25
Thank you and it makes sense.
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Re: If x is a positive integer and x^2 is divisible by 32, then [#permalink] New post 29 Oct 2013, 16:09
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Re: If x is a positive integer and x^2 is divisible by 32, then [#permalink] New post 09 Mar 2014, 02:39
Very interesting question.

Here is the similar problem link:
if-n-is-a-positive-integer-and-n-2-is-divisible-by-72-then-129929-20.html#p1341433

I got one of the questions wrong and then got another right, I think some problem has been discussed in the above link on the first page.

Hope it helps.
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Re: If x is a positive integer and x^2 is divisible by 32, then [#permalink] New post 09 Mar 2014, 02:50
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samsmalldog wrote:
Very interesting question.

Here is the similar problem link:
if-n-is-a-positive-integer-and-n-2-is-divisible-by-72-then-129929-20.html#p1341433

I got one of the questions wrong and then got another right, I think some problem has been discussed in the above link on the first page.

Hope it helps.


Similar questions to practice:

if-n-is-a-positive-integer-and-n-2-is-divisible-by-96-then-127364.html
if-n-is-a-positive-integer-and-n-2-is-divisible-by-72-then-90523.html
n-is-a-positive-integer-and-k-is-the-product-of-all-integer-104272.html
if-n-and-y-are-positive-integers-and-450y-n-92562.html
if-m-and-n-are-positive-integer-and-1800m-n3-what-is-108985.html
if-x-and-y-are-positive-integers-and-180x-y-100413.html
if-x-is-a-positive-integer-and-x-2-is-divisible-by-32-then-88388.html
if-5400mn-k-4-where-m-n-and-k-are-positive-integers-109284.html
if-n-is-a-positive-integer-and-n-2-is-divisible-by-72-then-129929.html

Hope it helps.
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Re: If x is a positive integer and x^2 is divisible by 32, then [#permalink] New post 02 Jul 2014, 22:11
Hello Bunuel

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

Why are we looking for the smallest value of x ?
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Re: If x is a positive integer and x^2 is divisible by 32, then [#permalink] New post 05 Jul 2014, 06:15
Expert's post
parul1591 wrote:
Hello Bunuel

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

Why are we looking for the smallest value of x ?


Because we need the largest positive integer that MUST divide x. So, we should find the least value of x for which x^2 is divisible by 32, and if that x is divisible by some number then so will be every other x's (MUST condition will be satisfied). The least positive x for which x^2 is divisible by 32 is 8 (8^2 = 64, which is divisible by 32). So, even if x = 8 it is divisible by 8 but not divisible by 6, 12 or 16.

Check similar problems in my post above.
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: If x is a positive integer and x^2 is divisible by 32, then [#permalink] New post 06 Jul 2014, 10:34
Simply put x = 8 and get the answer. If you put a number greater than 8, then you would have less options to eliminate and more to check.
Re: If x is a positive integer and x^2 is divisible by 32, then   [#permalink] 06 Jul 2014, 10:34
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