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

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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, 00:17
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A
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E

Difficulty:

  45% (medium)

Question Stats:

53% (00:47) correct 47% (01:19) wrong based on 210 sessions

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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 18 Apr 2016, 02:34
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


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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 18 Apr 2016, 23:21
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, 06:44
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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Re: If x, y, and z are integers, what is the remainder when xyz is divided  [#permalink]

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New post 10 Jan 2019, 06:08
i am trying to get my head around this question, please correct me where I go wrong:

a) 6xy=EVEN, regardless what xy is, if we have 6 (EVEN), result would always be EVEN, so R=0. Example: 6*2*2=24, 6*3*3=54, 6*2*3=36
I can't understand why A is not sufficient (

b) 9zx=EVEN, so for it to be EVEN we need at least one even number, and then it would divide by 2 with R=0. Sufficient

Explanation above indicated that we don't have information about z, so A is insufficient, but do we have to now what Z is, no matter what, because we have 6, it would result in EVEN and would divide by 2 with R0

please help....
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Re: If x, y, and z are integers, what is the remainder when xyz is divided &nbs [#permalink] 10 Jan 2019, 06:08
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If x, y, and z are integers, what is the remainder when xyz is divided

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