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If x and y are non-zero integers and |x| + |y| = 32, what is

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If x and y are non-zero integers and |x| + |y| = 32, what is [#permalink]  10 Mar 2012, 01:26
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If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x – 12y = 0

(2) |x| – |y| = 16

please explain how A is sufficient I got C. on solving A i get 2 possible values of x and y and thus 2 values of XY
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Re: If x and y are non-zero integers [#permalink]  10 Mar 2012, 04:17
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devinawilliam83 wrote:
If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x – 12y = 0

(2) |x| – |y| = 16

please explain how A is sufficient I got C. on solving A i get 2 possible values of x and y and thus 2 values of XY

If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) $$-4x - 12y = 0$$ --> $$x+3y=0$$ --> $$x=-3y$$ --> $$x$$ and $$y$$ have opposite signs --> so either $$|x|=x$$ and $$|y|=-y$$ OR $$|x|=-x$$ and $$|y|=y$$ --> either $$|x|+|y|=-x+y=3y+y=4y=32$$: $$y=8$$, $$x=-24$$, $$xy=-24*8$$ OR $$|x|+|y|=x-y=-3y-y=-4y=32$$: $$y=-8$$, $$x=24$$, $$xy=-24*8$$, same answer. Sufficient.

(2) $$|x| - |y| = 16$$. Sum this one with th equations given in the stem --> $$2|x|=48$$ --> $$|x|=24$$, $$|y|=8$$. $$xy=-24*8$$ (x and y have opposite sign) or $$xy=24*8$$ (x and y have the same sign). Multiple choices. Not sufficient.

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Re: If x and y are non-zero integers [#permalink]  21 Sep 2013, 22:32
Bunuel wrote:
devinawilliam83 wrote:
If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x – 12y = 0

(2) |x| – |y| = 16

please explain how A is sufficient I got C. on solving A i get 2 possible values of x and y and thus 2 values of XY

If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) $$-4x - 12y = 0$$ --> $$x+3y=0$$ --> $$x=-3y$$ --> $$x$$ and $$y$$ have opposite signs --> so either $$|x|=x$$ and $$|y|=-y$$ OR $$|x|=-x$$ and $$|y|=y$$ --> either $$|x|+|y|=-x+y=3y+y=4y=32$$: $$y=8$$, $$x=-24$$, $$xy=-24*8$$ OR $$|x|+|y|=x-y=-3y-y=-4y=32$$: $$y=-8$$, $$x=24$$, $$xy=-24*8$$, same answer. Sufficient.

(2) $$|x| - |y| = 16$$. Sum this one with th equations given in the stem --> $$2|x|=48$$ --> $$|x|=24$$, $$|y|=8$$. $$xy=-24*8$$ (x and y have opposite sign) or $$xy=24*8$$ (x and y have the same sign). Multiple choices. Not sufficient.

Hi Bunel,

i have a doubt in ur explanation

|x|+|y|=32
For this the modulus sign wont have four cases?
(-x,+y), (+x,-y), (+x,+y), (-x,-y)

Rrsnathan.
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Re: If x and y are non-zero integers [#permalink]  22 Sep 2013, 03:35
Expert's post
rrsnathan wrote:
Bunuel wrote:
devinawilliam83 wrote:
If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x – 12y = 0

(2) |x| – |y| = 16

please explain how A is sufficient I got C. on solving A i get 2 possible values of x and y and thus 2 values of XY

If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) $$-4x - 12y = 0$$ --> $$x+3y=0$$ --> $$x=-3y$$ --> $$x$$ and $$y$$ have opposite signs --> so either $$|x|=x$$ and $$|y|=-y$$ OR $$|x|=-x$$ and $$|y|=y$$ --> either $$|x|+|y|=-x+y=3y+y=4y=32$$: $$y=8$$, $$x=-24$$, $$xy=-24*8$$ OR $$|x|+|y|=x-y=-3y-y=-4y=32$$: $$y=-8$$, $$x=24$$, $$xy=-24*8$$, same answer. Sufficient.

(2) $$|x| - |y| = 16$$. Sum this one with th equations given in the stem --> $$2|x|=48$$ --> $$|x|=24$$, $$|y|=8$$. $$xy=-24*8$$ (x and y have opposite sign) or $$xy=24*8$$ (x and y have the same sign). Multiple choices. Not sufficient.

Hi Bunel,

i have a doubt in ur explanation

|x|+|y|=32
For this the modulus sign wont have four cases?
(-x,+y), (+x,-y), (+x,+y), (-x,-y)

Rrsnathan.

Generally yes. But from $$x=-3y$$ we can get that $$x$$ and $$y$$ have opposite signs, so we are left only with two cases (+, -) or (-, +).

Hope it's clear.
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Re: If x and y are non-zero integers and |x| + |y| = 32, what is [#permalink]  17 Oct 2013, 07:45
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If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x – 12y = 0

(2) |x| – |y| = 16

(1) -4x - 12y = 0 multiply by (-1)
4x + 12y = 0
4(x + 3y) = 0
x + 3y = 0 we are also told that |x| + |y| = 32, so the only values for x and y that satisfy both equations are x = 24 y = -8 or x = -24 y = 8 in both cases xy is the same (-24)(8) = (24)(-8) ==> Sufficient.

(2) |x| - |y| = 16 multiple values for xy possible, for example x = 24 y = 8 or x = -24 y = 8 ==> Not sufficient.

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Re: If x and y are non-zero integers [#permalink]  02 May 2014, 02:44
Bunuel wrote:
devinawilliam83 wrote:
If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x – 12y = 0

(2) |x| – |y| = 16

please explain how A is sufficient I got C. on solving A i get 2 possible values of x and y and thus 2 values of XY

If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) $$-4x - 12y = 0$$ --> $$x+3y=0$$ --> $$x=-3y$$ --> $$x$$ and $$y$$ have opposite signs --> so either $$|x|=x$$ and $$|y|=-y$$ OR $$|x|=-x$$ and $$|y|=y$$ --> either $$|x|+|y|=-x+y=3y+y=4y=32$$: $$y=8$$, $$x=-24$$, $$xy=-24*8$$ OR $$|x|+|y|=x-y=-3y-y=-4y=32$$: $$y=-8$$, $$x=24$$, $$xy=-24*8$$, same answer. Sufficient.

(2) $$|x| - |y| = 16$$. Sum this one with th equations given in the stem --> $$2|x|=48$$ --> $$|x|=24$$, $$|y|=8$$. $$xy=-24*8$$ (x and y have opposite sign) or $$xy=24*8$$ (x and y have the same sign). Multiple choices. Not sufficient.

Where did I go wrong..

|x| - |y| = 32
--> |-3y| - |y| = 32
--> 3y - |y| = 32
--> |y| = 32- 3y

y= -(32 - 3y)--> y= 16
y= 32 - 3y --> y= 8

Guess I am wrong here...But I dont understand why...Absolute value confuses me a lot...been thru GMAT CLub Book...not sufficient I guess
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Re: If x and y are non-zero integers [#permalink]  02 May 2014, 09:21
Expert's post
JusTLucK04 wrote:
Bunuel wrote:
devinawilliam83 wrote:
If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x – 12y = 0

(2) |x| – |y| = 16

please explain how A is sufficient I got C. on solving A i get 2 possible values of x and y and thus 2 values of XY

If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) $$-4x - 12y = 0$$ --> $$x+3y=0$$ --> $$x=-3y$$ --> $$x$$ and $$y$$ have opposite signs --> so either $$|x|=x$$ and $$|y|=-y$$ OR $$|x|=-x$$ and $$|y|=y$$ --> either $$|x|+|y|=-x+y=3y+y=4y=32$$: $$y=8$$, $$x=-24$$, $$xy=-24*8$$ OR $$|x|+|y|=x-y=-3y-y=-4y=32$$: $$y=-8$$, $$x=24$$, $$xy=-24*8$$, same answer. Sufficient.

(2) $$|x| - |y| = 16$$. Sum this one with th equations given in the stem --> $$2|x|=48$$ --> $$|x|=24$$, $$|y|=8$$. $$xy=-24*8$$ (x and y have opposite sign) or $$xy=24*8$$ (x and y have the same sign). Multiple choices. Not sufficient.

Where did I go wrong..

|x| - |y| = 32
--> |-3y| - |y| = 32
--> 3y - |y| = 32
--> |y| = 32- 3y

y= -(32 - 3y)--> y= 16
y= 32 - 3y --> y= 8

Guess I am wrong here...But I dont understand why...Absolute value confuses me a lot...been thru GMAT CLub Book...not sufficient I guess

It's $$|x| + |y| = 32$$, not |x| - |y| = 32.

From (1): $$x=-3y$$ --> $$|x| + |y| = 32$$ --> $$|-3y| + |y| = 32$$ --> $$3|y| + |y| = 32$$ --> $$4|y|=32$$ --> $$|y|=8$$ --> $$y=8$$ or $$y=-8$$.

If $$y=8$$, then $$x=-3y=-24$$ --> $$xy=(-24)8$$.
If $$y=-8$$, then $$x=-3y=24$$ --> $$xy=24(-8)$$.

Both cases give the same value of xy.

Hope it's clear.
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Re: If x and y are non-zero integers and |x| + |y| = 32, what is [#permalink]  03 Aug 2014, 16:06
Bunuel wrote:
devinawilliam83 wrote:
If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x – 12y = 0

(2) |x| – |y| = 16

please explain how A is sufficient I got C. on solving A i get 2 possible values of x and y and thus 2 values of XY

If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) $$-4x - 12y = 0$$ --> $$x+3y=0$$ --> $$x=-3y$$ --> $$x$$ and $$y$$ have opposite signs --> so either $$|x|=x$$ and $$|y|=-y$$ OR $$|x|=-x$$ and $$|y|=y$$ --> either $$|x|+|y|=-x+y=3y+y=4y=32$$: $$y=8$$, $$x=-24$$, $$xy=-24*8$$ OR $$|x|+|y|=x-y=-3y-y=-4y=32$$: $$y=-8$$, $$x=24$$, $$xy=-24*8$$, same answer. Sufficient.

(2) $$|x| - |y| = 16$$. Sum this one with th equations given in the stem --> $$2|x|=48$$ --> $$|x|=24$$, $$|y|=8$$. $$xy=-24*8$$ (x and y have opposite sign) or $$xy=24*8$$ (x and y have the same sign). Multiple choices. Not sufficient.

Hi Bunuel,

Couple of things to clarify:

I understand that you're saying that x and y have opposite signs, but in the equation above, if the absolute value sign is around the equation in the question stem, how can the "minus" be brought outside for either x OR y? meaning, how does it become 4y = 32 vs. -4y = 32. I'm not sure how you can just drop the abs value sign?

Thanks
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Re: If x and y are non-zero integers and |x| + |y| = 32, what is [#permalink]  01 Oct 2014, 07:41
Note that one need not determine the values of both x and y to solve this problem; the value of product xy will suffice.

(1) SUFFICIENT: Statement (1) can be rephrased as follows:

-4x – 12y = 0
-4x = 12y
x = -3y

If x and y are non-zero integers, we can deduce that they must have opposite signs: one positive, and the other negative. Therefore, this last equation could be rephrased as

|x| = 3|y|

We don’t know whether x or y is negative, but we do know that they have the opposite signs. Converting both variables to absolute value cancels the negative sign in the expression x = -3y.

We are left with two equations and two unknowns, where the unknowns are |x| and |y|:

|x| + |y| = 32
|x| – 3|y| = 0

Subtracting the second equation from the first yields

4|y| = 32
|y| = 8

Substituting 8 for |y| in the original equation, we can easily determine that |x| = 24. Because we know that one of either x or y is negative and the other positive, xy must be the negative product of |x| and |y|, or -8(24) = -192.

(2) INSUFFICIENT: Statement (2) also provides two equations with two unknowns:

|x| + |y| = 32
|x| - |y| = 16

Solving these equations allows us to determine the values of |x| and |y|: |x| = 24 and |y| = 8. However, this gives no information about the sign of x or y. The product xy could either be -192 or 192.

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Re: If x and y are non-zero integers and |x| + |y| = 32, what is   [#permalink] 01 Oct 2014, 07:41
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