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S be the set of all positive integers n such that n^2

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GRE Prep Club Legend
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Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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S be the set of all positive integers n such that n^2 [#permalink] New post 04 Jan 2016, 16:45
Expert's post
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Question Stats:

42% (00:56) correct 57% (02:14) wrong based on 14 sessions
Let S be the set of all positive integers n such that \(n^2\) is a multiple of both 24 and 108. Which of the following integers are divisors of every integer n in S ?

Indicate all such integers.

A. 12
B. 24
C. 36
D. 72

Practice Questions
Question: 14
Page: 159
Difficulty: hard


[Reveal] Spoiler: OA
A,C

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GRE Prep Club Legend
GRE Prep Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 123

Kudos [?]: 1971 [0], given: 397

Re: S be the set of all positive integers n such that n^2 [#permalink] New post 04 Jan 2016, 18:48
Expert's post
Now here we are looking for a Set S of numbers n such that \(n^2\) is multiple of 24 and 108.

Lets take one such case Least Common Multiple of 108 and 24 is 216.

\(n^2\) = 216
n = 6\(\sqrt{6}\).

This is not an integer however if we multiply 216 by any number it is still divisible by 24 and 108. So we multiply by 6 and repat the above steps to find n. So n =36.

Now n= 36 is one of the number in set S.

Hence all the options that divide n =36 are correct. Hence option A and C.
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Intern
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Re: S be the set of all positive integers n such that n^2 [#permalink] New post 29 Mar 2016, 09:38
can you please show the exact repeated steps please?
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Re: S be the set of all positive integers n such that n^2 [#permalink] New post 15 May 2016, 21:09
LCM of 108 and 24 is 216 = 2^3*3^3. As n^2 is a square, the least value n^2 can take is 2^4*3^4 = 6*216 = 36 * 36, so n should be at least 36 or multiples of 36. So any factor of 36 should always divide n. Hence A and C are correct.
Re: S be the set of all positive integers n such that n^2   [#permalink] 15 May 2016, 21:09
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S be the set of all positive integers n such that n^2

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