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Re: If x and y are non-zero integers [#permalink]
10 Mar 2012, 04:17

3

This post received KUDOS

Expert's post

3

This post was BOOKMARKED

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.

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.

Answer: A.

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)

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.

Answer: A.

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)

Please clarify me.

Thanks in Advance, 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 (-, +).

Re: If x and y are non-zero integers and |x| + |y| = 32, what is [#permalink]
17 Oct 2013, 07:45

2

This post received KUDOS

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.

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.

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 _________________

Appreciate the efforts...KUDOS for all Don't let an extra chromosome get you down..

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.

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.

Answer: A.

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?

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.

The correct answer is A. _________________

Consider +1 Kudos Please

gmatclubot

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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