If |x| + |y| = -x – y and xy does not equal 0

[MMS]

If |x| + |y| = -x - y and xy does not equal 0, which of the following must be true?
A) x + y > 0
B) x + y < 0
C) x - y > 0
D) x - y < 0
E) x2 - y2 > 0

I really didn't quite understand the explanation provided in the CAT, could someone please assist me with how to go about this.

The way I thought (not sure if its the right approach) about this was
|x| + |y| = (-x) + (- y)
Therefore, both x and y are negative. I could rewrite (and add) these as...
-x<0 and -y<0. Adding those would be -x-y<0, got stuck after this ...

Thanks for your help

[RonPurewal]

The way I thought (not sure if its the right approach) about this was
|x| + |y| = (-x) + (- y)
Therefore, both x and y are negative.

correct up to here.

I could rewrite (and add) these as...
-x<0 and -y<0.

no.
if x and y are negative, then x and y themselves are negative. hence the correct answer, x + y > 0.

--

on another note, be sure to stay focused on the problem!
there is no answer choice that contains both -x and -y, so there's no point in trying to create a construction containing both of those quantities.
(incidentally, if x and y are negative then -x and -y are positive.)

[nt2011]

What is OA for this problem?

I thought if x < 0 and y <0, x + y < 0.

Ron,

Could you please explain how x+y > 0?

[tim]

you're right. the answer is B) x+y < 0
i think Ron just hit the wrong button; those are right next to each other on the keyboard..

[nocheivyirene]

If |x| + |y| = -x - y and xy does not equal 0, which of the following must be true?
A) x + y > 0
B) x + y < 0
C) x - y > 0
D) x - y < 0
E) x2 - y2 > 0

|x| + |y| = -x - y
|x| + |y| = -(x+y)

I know that |x| + |y| is always (+). But the other side is -(x+y).
To make it positive, we multiple (-) with (-).

Thus, (x+y) is (-) or x+y < 0

Answer: B

[nt2011]

Thank you Tim and nocheivyirene

[tim]

:)

[m.manavsingh]

Hi All,

I still have a small query regarding the solution posted here.

Yes, based on the expression x+y must be <0. I was trying to verify this using some numbers and ran into a bit of trouble.

If X=-3 and Y=2, then X+Y = -3+2= -1 which is <0. But the LHS equates to 5 whereas the RHS equates to 1. Thus this particular set of values does not satisfy the requirement.

The statement only seems to be true when both X and Y are negative individually.

Am I going wrong in my approach here ??

[RonPurewal]

Hi All,

I still have a small query regarding the solution posted here.

Yes, based on the expression x+y must be <0. I was trying to verify this using some numbers and ran into a bit of trouble.

If X=-3 and Y=2, then X+Y = -3+2= -1 which is <0. But the LHS equates to 5 whereas the RHS equates to 1. Thus this particular set of values does not satisfy the requirement.

The statement only seems to be true when both X and Y are negative individually.

Am I going wrong in my approach here ??

the prompt equation implies that both variables are individually negative, not just that their product is negative.

[m.manavsingh]

Ron,

Thanks for the reply.

I am still missing to see how did you deduce that both X and Y should be negative?

I am just trying to understand if there is something that I am missing in my interpretation of the question stem here.

[tim]

|x| + |y| = -x - y

if you have a hard time seeing from this statement that x and y are both negative, just try all four possibilities, keeping in mind that neither x nor y may be 0:

x and y are both positive
x + y = -x - y
only works if 2x + 2y = 0, which cannot happen as x and y are both positive

x is negative and y is positive
-x + y = -x - y
works only when y = 0, which cannot happen as it contradicts the given information

x is positive and y is negative
x - y = -x - y
works only when x = 0, which cannot happen as it contradicts the given information

x and y are both negative
-x - y = -x - y
true tautologically

[chetna.response]

thanks Tim.
good explanation.

[jnelson0612]

thanks Tim.
good explanation.

Glad it helped you. Tim does indeed give good explanations. :-)