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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, 01:17
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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, 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


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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, 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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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, 07:08
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  [#permalink]

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New post 08 Apr 2019, 23:32
nuraisma wrote:
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....


Same Issue here as well
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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 09 Apr 2019, 01:36
louhit wrote:
nuraisma wrote:
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....


Same Issue here as well


6xy is even, meaning 6 times xy is even. But we don't know if xy is even on its own. It could 3*1 = 3, which is odd. Now if Z were odd, we would have a range of possibilities for remainders when xyz/2. Hence it is insufficient.
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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 09 Apr 2019, 01:53
swatato wrote:
louhit wrote:
nuraisma wrote:
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....


Same Issue here as well


6xy is even, meaning 6 times xy is even. But we don't know if xy is even on its own. It could 3*1 = 3, which is odd. Now if Z were odd, we would have a range of possibilities for remainders when xyz/2. Hence it is insufficient.


Thanks for the reply. I totally get your explanation but what i am struggling to understand that if 6 is multiplied by x and y, the result will always be even. Why do we need to determine x and y nature. Because as per your example 6 multiplied by 3 and 1 will give 18 which is still give remainder 0. Sorry if i am making this tough but need bit of clarity if i am able to understand the question/solution right or not. Thanks

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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 09 Apr 2019, 02:08
Quote:
Quote:
6xy is even, meaning 6 times xy is even. But we don't know if xy is even on its own. It could 3*1 = 3, which is odd. Now if Z were odd, we would have a range of possibilities for remainders when xyz/2. Hence it is insufficient.


Thanks for the reply. I totally get your explanation but what i am struggling to understand that if 6 is multiplied by x and y, the result will always be even. Why do we need to determine x and y nature. Because as per your example 6 multiplied by 3 and 1 will give 18 which is still give remainder 0. Sorry if i am making this tough but need bit of clarity if i am able to understand the question/solution right or not. Thanks

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Because the question is asking you for the remainder when xyz is divided by 2. Not 'what is the remainder when 6xy divided by 2'

If xy are odd and by some chance z is odd too, then you will have a range of remainders, not one, single answer, which is what the question is asking you for.

Unless you know clearly what x, y and z are in terms of even/odd, you will not be able to answer the main question: What is the remainder when xyz is divided by 2.
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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 09 Apr 2019, 02:11
swatato wrote:
Quote:
Quote:
6xy is even, meaning 6 times xy is even. But we don't know if xy is even on its own. It could 3*1 = 3, which is odd. Now if Z were odd, we would have a range of possibilities for remainders when xyz/2. Hence it is insufficient.


Thanks for the reply. I totally get your explanation but what i am struggling to understand that if 6 is multiplied by x and y, the result will always be even. Why do we need to determine x and y nature. Because as per your example 6 multiplied by 3 and 1 will give 18 which is still give remainder 0. Sorry if i am making this tough but need bit of clarity if i am able to understand the question/solution right or not. Thanks

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Because the question is asking you for the remainder when xyz is divided by 2. Not 'what is the remainder when 6xy divided by 2'

If xy are odd and by some chance z is odd too, then you will have a range of remainders, not one, single answer, which is what the question is asking you for.

Unless you know clearly what x, y and z are in terms of even/odd, you will not be able to answer the main question: What is the remainder when xyz is divided by 2.



Isint z = 6 from statement 1? Which means xyz is even ?
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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 09 Apr 2019, 02:14
louhit wrote:
swatato wrote:
Quote:

Thanks for the reply. I totally get your explanation but what i am struggling to understand that if 6 is multiplied by x and y, the result will always be even. Why do we need to determine x and y nature. Because as per your example 6 multiplied by 3 and 1 will give 18 which is still give remainder 0. Sorry if i am making this tough but need bit of clarity if i am able to understand the question/solution right or not. Thanks

Posted from my mobile device



Because the question is asking you for the remainder when xyz is divided by 2. Not 'what is the remainder when 6xy divided by 2'

If xy are odd and by some chance z is odd too, then you will have a range of remainders, not one, single answer, which is what the question is asking you for.

Unless you know clearly what x, y and z are in terms of even/odd, you will not be able to answer the main question: What is the remainder when xyz is divided by 2.



Isint z = 6 from statement 1? Which means xyz is even ?


Nope. z is not 6. It doesn't say that anywhere in the statement. For DS questions statements must be interpreted as they are presented.
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Re: If x, y, and z are integers, what is the remainder when xyz is divided   [#permalink] 09 Apr 2019, 02:14
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