Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 28 Aug 2015, 19:05

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:
Manager
Joined: 21 Jul 2003
Posts: 67
Followers: 2

Kudos [?]: 17 [1] , given: 3

If x is a positive integer and x^2 is divisible by 32, then [#permalink]  24 Dec 2009, 02:59
1
KUDOS
8
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

69% (01:57) correct 31% (00:45) wrong based on 476 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
[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.
Math Expert
Joined: 02 Sep 2009
Posts: 29100
Followers: 4724

Kudos [?]: 49665 [5] , given: 7400

Re: Division & Factor [#permalink]  24 Dec 2009, 06:21
5
KUDOS
Expert's post
7
This post was
BOOKMARKED
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.
_________________
Manager
Joined: 09 May 2009
Posts: 202
Followers: 1

Kudos [?]: 143 [2] , given: 13

Re: Division & Factor [#permalink]  24 Dec 2009, 03:18
2
KUDOS
Imo C

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

GMAT is not a game for losers , and the moment u decide to appear for it u are no more a loser........ITS A BRAIN GAME

Math Expert
Joined: 02 Sep 2009
Posts: 29100
Followers: 4724

Kudos [?]: 49665 [1] , given: 7400

Re: If x is a positive integer and x^2 is divisible by 32, then [#permalink]  09 Mar 2014, 02:50
1
KUDOS
Expert's post
2
This post was
BOOKMARKED
Manager
Joined: 21 Jul 2003
Posts: 67
Followers: 2

Kudos [?]: 17 [0], given: 3

Re: Division & Factor [#permalink]  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.
Manager
Joined: 21 Jul 2003
Posts: 67
Followers: 2

Kudos [?]: 17 [0], given: 3

Re: Division & Factor [#permalink]  24 Dec 2009, 08:25
Thank you and it makes sense.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 6096
Followers: 340

Kudos [?]: 68 [0], given: 0

Re: If x is a positive integer and x^2 is divisible by 32, then [#permalink]  29 Oct 2013, 16:09
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Manager
Joined: 26 Jan 2014
Posts: 71
Followers: 1

Kudos [?]: 12 [0], given: 77

Re: If x is a positive integer and x^2 is divisible by 32, then [#permalink]  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.
Intern
Joined: 12 May 2014
Posts: 12
Followers: 0

Kudos [?]: 0 [0], given: 87

Re: If x is a positive integer and x^2 is divisible by 32, then [#permalink]  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 ?
Math Expert
Joined: 02 Sep 2009
Posts: 29100
Followers: 4724

Kudos [?]: 49665 [0], given: 7400

Re: If x is a positive integer and x^2 is divisible by 32, then [#permalink]  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.
_________________
Intern
Joined: 11 Nov 2013
Posts: 17
GMAT 1: 680 Q50 V31
Followers: 1

Kudos [?]: 9 [0], given: 17

Re: If x is a positive integer and x^2 is divisible by 32, then [#permalink]  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.
Intern
Joined: 30 Jul 2013
Posts: 28
Concentration: Technology, General Management
GMAT Date: 07-03-2015
GPA: 3.8
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 8 [0], given: 24

Re: If x is a positive integer and x^2 is divisible by 32, then [#permalink]  07 Apr 2015, 20:44
Hi Bunnel,

What if the question is as below:

If P is a positive integer and p^3 is divisible by 144, then the largest positive integer that must divide p is

How do we calculate using the "k" method when the cubeth root is asked for.
_________________

On the Kudos Spree.

If you like my post/comment please appreciate with kudos

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 3438
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 148

Kudos [?]: 925 [0], given: 56

Re: If x is a positive integer and x^2 is divisible by 32, then [#permalink]  08 Apr 2015, 22:22
Expert's post
Hi Pretz,

In the original question, we're essentially looking for the smallest multiple of 32 that is a perfect square....

32(2) = 64......which is 8^2.

Using prime factorization, we know that 32K = (2^5)K

By making K = 2, we have (2^5)(2) = 2^6

We can then break 2^6 into 2 equal "pieces": (2^3)(2^3) which equals (8)(8)

We're looking for the smallest multiple of 144 that is a perfect cube....

144K = (2^4)(3^2)K

By making K = 12, we have (2^4)(3^2)(2^2)(3) = (2^6)(3^3)

We can break this down into 3 equal "pieces": [(2^2)(3)][(2^2)(3)][(2^2)(3)] = (12)(12)(12)

GMAT assassins aren't born, they're made,
Rich
_________________

Re: If x is a positive integer and x^2 is divisible by 32, then   [#permalink] 08 Apr 2015, 22:22
Similar topics Replies Last post
Similar
Topics:
5 T is the set of all positive integers x such that x^2 is a multiple of 3 12 May 2015, 03:45
6 If x and y are positive integers, and 4x^2=3y, then which of 2 03 Aug 2014, 03:24
3 If x and y are positive integer and xy is divisible by 4 12 05 Nov 2012, 17:18
If x and y are positive integers and x^2 + y^2 = 100 3 18 Aug 2012, 14:22
20 If k and x are positive integers and x is divisible by 6 17 29 Oct 2010, 16:10
Display posts from previous: Sort by