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

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Math Expert
Joined: 02 Sep 2009
Posts: 46283
If x, y and z are different integers, is x divisible by 11? [#permalink]

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11 May 2016, 00:17
3
5
00:00

Difficulty:

65% (hard)

Question Stats:

54% (01:09) correct 46% (01:08) wrong based on 63 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

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Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1
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If x, y and z are different integers, is x divisible by 11? [#permalink]

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11 May 2016, 01:54
1
Is x divisible by 11?

St1: xyz is divisible by 22 and 33 --> xyz is a multiple of 66
Let xyz = 66
x * y * z can be 11 * 2 * 3 or 2 * 3 * 11 or 1 * 6 * 11.
x may or may not be divisible by 11
Not Sufficient

St2: yz is divisible by 72 --> yz = 72k.
Not Sufficient as we have no information about x

Combining St1 and St2:
xyz = 66K --- (1)
yz = 72k --- (2)

(1)/(2) --> $$\frac{xyz}{yz}$$ = $$x$$ = $$\frac{11K}{12k}$$

If K = 12, k = 1 then x = 11 --> Is x divisible by 11? Yes
If K = 12, k = 11 then x = 1 --> Is x divisible by 11? No
Not Sufficient

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2642
GRE 1: 323 Q169 V154
Re: If x, y and z are different integers, is x divisible by 11? [#permalink]

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24 Aug 2016, 02:27
Amazing question Bunuel
Here we need to check if x is divisible by 11
I used the concept of test cases here
Statement 1 => let x=1 y=66 z=2=> NO x/11≠integer
let x=11 y=66 z=1 => Yes x/11=integer
Not sufficient
Statement 2 => no clue of x => not suff
Statement 1 +statement 2=> x=1,y=72*66, z=2 => No
else X can be 11 too => YES

Not suff

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

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08 Oct 2017, 12:53
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).

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Re: If x, y and z are different integers, is x divisible by 11?   [#permalink] 08 Oct 2017, 12:53
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