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# The positive integer p is divisible by 11. If √p is an integer divisib

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Joined: 06 Jul 2013
Posts: 43
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The positive integer p is divisible by 11. If √p is an integer divisib  [#permalink]

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Updated on: 05 Jul 2018, 11:10
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Difficulty:

45% (medium)

Question Stats:

43% (00:32) correct 57% (01:36) wrong based on 7 sessions

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The positive integer p is divisible by 11. If √p is an integer divisible by 3, which of the following must be a factor of p/11?

(A) 9
(B) 14
(C) 15
(D) 33
(E) 99

Originally posted by TippingPoint93 on 05 Jul 2018, 10:49.
Last edited by Bunuel on 05 Jul 2018, 11:10, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Joined: 02 Sep 2009
Posts: 49430
The positive integer p is divisible by 11. If √p is an integer divisib  [#permalink]

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05 Jul 2018, 11:10
1
TippingPoint93 wrote:
The positive integer p is divisible by 11. If √p is an integer divisible by 3, which of the following must be a factor of p/11?

(A) 9
(B) 14
(C) 15
(D) 33
(E) 99

√p = 3k;

p = 9k^2. So, p is a multiple of 9.

Since we also know that p is a multiple of 11 too, then p must be a multiple of both 9 and 11, so a multiple of the LCM of 9 and 11, which is 99.

p/11 = 99x/11 = 9x. Thus, p/11 must be a multiple of 9.

P.S. Please provide the OA when posting a question.
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Joined: 06 Jul 2013
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Location: United States
Re: The positive integer p is divisible by 11. If √p is an integer divisib  [#permalink]

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05 Jul 2018, 11:24
Bunuel wrote:
TippingPoint93 wrote:
The positive integer p is divisible by 11. If √p is an integer divisible by 3, which of the following must be a factor of p/11?

(A) 9
(B) 14
(C) 15
(D) 33
(E) 99

√p = 3k;

p = 9k^2. So, p is a multiple of 9.

Since we also know that p is a multiple of 11 too, then p must be a multiple of both 9 and 11, so a multiple of the LCM of 9 and 11, which is 99.

p/11 = 99x/11 = 9x. Thus, p/11 must be a multiple of 9.

P.S. Please provide the OA when posting a question.

Thanks for the response, Bunuel. Apologies for the lack of OA. I had posted from my phone. The OA is A.

Could you please tell me where I’ve gone wrong?

If 11 is a factor of p, and sqrt(p) is an integer, then doesn’t that mean that 11 is also a factor of sqrt(p)? And hence p/11 would also be a multiple of 11? Making 3x11=33 also a possible answer?

Sent from my iPhone using GMAT Club Forum mobile app
Re: The positive integer p is divisible by 11. If √p is an integer divisib &nbs [#permalink] 05 Jul 2018, 11:24
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# The positive integer p is divisible by 11. If √p is an integer divisib

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