Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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.

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)

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]

Show Tags

17 Oct 2013, 08:45

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.

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..

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]

Show Tags

03 Aug 2014, 17:06

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]

Show Tags

01 Oct 2014, 08:41

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.

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

Show Tags

25 May 2015, 21:21

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

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

Show Tags

25 May 2015, 23:04

1

This post received KUDOS

Expert's post

Hi All,

This question has some interesting 'pattern-matching shortcuts' built into it that you can take advantage of IF you take enough notes.

We're told that X and Y are NON-0 INTEGERS and |X| + |Y| = 32. We're asked for the value of (X)(Y).

Before dealing with the two Facts, it's worth noting that the prompt provides a significant limitation on the possible values of X and Y. Since the absolute values will turn negative results into positive ones, and the variables CANNOT be 0, there really are NOT that many possible values for X and Y.

+-1 and +-31 +-2 and +-30 +-3 and +-29 Etc.

We can use this to our advantage when dealing with the two Facts....

Fact 1: -4X - 12Y = 0

Here, we can do some algebra to simplify the equation...

-4X = 12Y -X = 3Y

This tells us that one variable MUST be POSITIVE and one MUST be NEGATIVE. When we include the absolute value equation given in the prompt, we know that one absolute value must be 3 times the value of the other....

That leaves us with two options for X and Y.... X = +24 and Y = -8 or X = -24 and Y = +8

Either way, we get the SAME PRODUCT: -192 Fact 1 is SUFFICIENT

Fact 2: |X| – |Y| = 16

Here, we can use the work we did in Fact 1 to save us some time (and help us create some new possibilities)...

IF... X = +24, Y = -8, the answer to the question is -192

IF... X = +24, Y = +8, the answer to the question is +192 Fact 2 is INSUFFICIENT

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

Show Tags

21 May 2016, 04:48

Bunuel wrote:

Bunuel wrote:

devinawilliam83 wrote:

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 (-, +).

Hope it's clear.

But how did u eliminate the other two cases (+x,+y) and (-x,-y) Solving x+y=32 and x+3y=0 gives x=48,y=-16 Solving -x-y=32 and x+3y=0 gives x=-48, y=16 this also says both x and y are of opposite signs.

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

Show Tags

21 May 2016, 05:00

Expert's post

sa18 wrote:

But how did u eliminate the other two cases (+x,+y) and (-x,-y) Solving x+y=32 and x+3y=0 gives x=48,y=-16 Solving -x-y=32 and x+3y=0 gives x=-48, y=16 this also says both x and y are of opposite signs.

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

Show Tags

25 May 2016, 22:49

I am going to only examine statement #1

|x|+|y|=32. statement #1: x=-3y. Let us substitute this in the prompt. |-3y|+|y| = 32 if y> 0 then -(-3*y)+y=32 (-3*y is negative inside absolute value, so to obtain positive we need to multiply by -1) => y = 8. substituting to get x = -24 and so xy=-192

what if y<0 then |-3y|+|y|=32 => -3*y -y=32 (here we retained the -3y outside because y is negative already) => -4y=32 => y=-8. x=24 and again xy=-192 In both cases, we get y=-8.

so only one possible value of x*y . ----------------------------------------------------------------------------------------

another way when x>0 and y>0 x+y=32 so now x=-3y -3y+y=32=> y=-16. so this is not possible

when x>0 and y<0 x-y=32 and x=-3y=> y=-8 ok then x= 24. x*y = -192

when x<0 y >0 y-x=32, substituting x=-3y=> y=8 . So then x = -24. x*y = -192

when x<0, y<0 -y-x=32. and x=-3y => -y-(-3y) = 32 =>2y = 32 => y=16. not feasible so the only answer possible is x*y = -192 .. Sufficient

gmatclubot

If x and y are non-zero integers and |x| + |y| = 32, what is
[#permalink]
25 May 2016, 22:49

Excellent posts dLo saw your blog too..!! Man .. you have got some writing skills. And Just to make an argument = You had such an amazing resume ; i am glad...

So Much $$$ Business school costs a lot. This is obvious, whether you are a full-ride scholarship student or are paying fully out-of-pocket. Aside from the (constantly rising)...

They say you get better at doing something by doing it. then doing it again ... and again ... and again, and you keep doing it until one day you look...

I barely remember taking decent rest in the last 60 hours. It’s been relentless with submissions, birthday celebration, exams, vacating the flat, meeting people before leaving and of...