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If x, y, and z are integers, what is the remainder when xyz is divided

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Joined: 02 Sep 2009
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Kudos [?]: 135294 [0], given: 12686

If x, y, and z are integers, what is the remainder when xyz is divided [#permalink]

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New post 18 Apr 2016, 01:17
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Kudos [?]: 135294 [0], given: 12686

Expert Post
Math Expert
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Joined: 02 Aug 2009
Posts: 5337

Kudos [?]: 6097 [0], given: 121

Re: If x, y, and z are integers, what is the remainder when xyz is divided [#permalink]

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New post 18 Apr 2016, 03:34
Bunuel wrote:
If x, y, and z are integers, what is the remainder when xyz is divided by 2?

(1) 6xy is even.
(2) 9zx is even.



We have to find if xyz is EVEN or ODD..
firstly XYZ must be x*y*z and not three digit number otherwise it would have been specified

(1) 6xy is even.
It is possible that xy is also even ans will be 0..
Nothing is known of z and xy could also be ODD, that is 6xy may be EVEN because of 6.. ans can be 1
Insuff


(2) 9zx is even.
xz is clearly EVEN here..
xyz will be EVEN and remainder will be 0..
Suff


B
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6097 [0], given: 121

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Kudos [?]: 7 [0], given: 141

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Re: If x, y, and z are integers, what is the remainder when xyz is divided [#permalink]

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New post 19 Apr 2016, 00:21
We have to find if atleast one of the numbers is even or not
Statement 1: 6xy is even.
X and Y may or may not be even
For example x=1, Y= 1 6xy = even even when X,Y are odd,
Suppose X=2, Y= 5 still 6xy is even
So X,Y may or may not be even NS

Statement 2:
9XZ = even, it means at least one og X or Z is even.
So, xyz will be divisible by 2

Option B

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Re: If x, y, and z are integers, what is the remainder when xyz is divided [#permalink]

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New post 17 Aug 2017, 06:30
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Kudos [?]: 287 [0], given: 0

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Re: If x, y, and z are integers, what is the remainder when xyz is divided [#permalink]

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New post 17 Aug 2017, 07:44
Very simple trick for above question

Statement 1: 6xy can be even because of 6 or xy.
Not sufficient

Statement 2: 9xz is even because of either x or z
Hence remainder always 0
Sufficient
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Kudos [?]: 16 [0], given: 18

Re: If x, y, and z are integers, what is the remainder when xyz is divided   [#permalink] 17 Aug 2017, 07:44
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