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# If x, y and z are different integers, is x divisible by 11?

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If x, y and z are different integers, is x divisible by 11? [#permalink]

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12 Feb 2013, 05:54
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Difficulty:

65% (hard)

Question Stats:

42% (02:03) correct 58% (01:01) wrong based on 59 sessions

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If x, y and z are different integers, is x divisible by 11?

(1) xyz is divisible by 22 and 33
(2) yz is divisible by 72
[Reveal] Spoiler: OA

Last edited by Bunuel on 12 Feb 2013, 05:55, edited 1 time in total.
Edited the question and added the OA.
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Re: If x, y and z are different integers, is x divisible by 11? [#permalink]

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12 Feb 2013, 06:01
Expert's post
If x, y and z are different integers, is x divisible by 11?

(1) xyz is divisible by 22 and 33. Given that xyz is a multiple of 22=2*11 and 33=3*11, thus xyz is a multiple of 2*3*11=66. Now, if x=1 and yz=66, the answer is NO but if x=11 and yz=66, the answer is YES. Not sufficient.

(2) yz is divisible by 72. Nothing about x. Not sufficient.

(1)+(2) Still insufficient, for example if x=1 and yz=66*72, the answer is NO but if x=11 and yz=66*72, the answer is YES. Not sufficient.

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Re: If x, y and z are different integers, is x divisible by 11? [#permalink]

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12 Feb 2013, 09:02
Statement 1: either x could be 11 or y could be 11 or z could be 11. Insufficient.

Statement 2: No information about x. Insufficient.

Combined 1+2: x could be 1 and y could be 66 and z could be 72 or x could be 11 y could be 66 and z could be 72. Answer E.
Re: If x, y and z are different integers, is x divisible by 11?   [#permalink] 12 Feb 2013, 09:02
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