If |x | + |y | = -x y and xy does not equal 0, which of the followin

Took me about 2 mins to complete. Feedback's are welcome, if I have missed or omitted anything from my method

Question stem mentions \(|X | + |Y| = -X -Y\) --> from this you can drive that only possibility to satisfy the equation is when \(X & Y\) both are negative.
Example: Assume \(X=-2\) and \(Y=-1\)
Then, substitute in the given equation \(LHS = |-2|+|-1| = 2+1\) & \(RHS = -(-2)-(-1) = 2+1 = 3\)
Therefore, \(LHS = RHS\)

Now, that you know \(X & Y\) both are negative, substitute in each option-->

option A: \(X + Y > 0\), therefore, \(-ve + -ve\) will always be less than zero, hence does not satisfy the equation.
option B: \(X+Y < 0\), therefore, \(-ve + -ve\) will always be less than zero, hence satisfies the equation.
option C: \(X - Y > 0\), therefore, \((-ve) - (-ve)\) can be less than zero or more than zero, hence does not satisfy the equation.
option D: \(X - Y < 0\), therefore, \((-ve) - (-ve)\) can be less than zero or more than zero, hence does not satisfy the equation.
option E: \(X^2-Y^2 > 0\), therefore, \((-ve)^2 - (-ve)^2 = (+ve) - (+ve)\) can be less than zero or more than zero, hence does not satisfy the equation.

Since only option B Satisfies the equation, the correct answer choice is option B

Given that, |x | + |y | = -x – y
LHS = |x | + |y |, implies that LHS > 0 {because mod is always +ve }

This implies that RHS > 0 i.e. -x – y > 0
- (X + Y ) > 0

Multiply by -1 on both sides and flip inequality sign

we get (X + Y ) < 0. Hence answer is B

Isnt the rule |x|>0 when x is positive and |x|<0 when X is negative
(I know im mistaken, but I dont know where so please do point out )

so shouldn't -(x+y)<0

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

means that x+y<0 for their negative to be positive

B

Hi All,

This question can be solved by TESTing VALUES.

We're told that |X| + |Y| = -X -Y and that neither variable equals 0. We're asked which of the following answers MUST be true (which really means "which of the following is ALWAYS TRUE no matter how many different examples we come up with....?)

As complicated as this might look, it's really just telling us to use NEGATIVE values for X and Y. From the answer choices (and their focus on the relationship to 0), we should look to pick the SAME number for BOTH variables...

IF....
X = -1
Y = -1

Answer A: X+Y > 0 -1 -1 = -2 is NOT > 0. NOT the answer
Answer B: X+Y < 0 -1 - 1 = -2 IS < 0. This is a MATCH
Answer C: X-Y > 0 -1 +1 = 0 is NOT > 0. NOT the answer
Answer D: X-Y < 0 -1 +1 = 0 is NOT < 0. NOT the answer
Answer E: X^2 – Y^2 > 0 1 - 1 = 0 is NOT > 0. NOT the answer

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Going through the solutions posted above, I realized that while most students did answer the question right, some missed out on an important nuance:

It is incorrect to say that an absolute value expression is always positive.

The correct statement is:

An absolute value expression is always non-negative.

This means, |x| ≥ 0 (please note that I wrote ≥ here in this first expression, not just >)

Similarly, |y| ≥ 0

However,we are given here that xy doesn't equal 0. This means x ≠ 0 and y ≠ 0.

This is the reason why we can write |x| > 0
and |y| > 0

Adding the two inequalities, we get: |x| + |y| > 0

This means -x - y > 0 (since |x| + |y| = -x-y)
Or, -(x+y) > 0

That is, x+ y < 0

Here is a variation of the above question that highlights the importance of the green statement above:

If |x | + |y | = -x – y, which of the following can be true?

I. x + y < 0
II. x + y = 0
III. xy = 0

(A) I only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III

Hope this helped!

Best Regards

Japinder

My second post ever...

|x| + |y| is always > 0;

Therefore -x - y > 0
-1*(x + y) > 0
x + y < 0

Source: Manhattan GMAT

__________________________
Added the tag. Thank you.

The answer to the question that you posted above would be Option (E) ? Yes?

Bunuel

Here is my solution, Is my analysis right?

1. x>0 and y>0 => x+y = -(x+y) not possible so this is wrong
2. x>0 and y<0 => x+y = -(x-y) => x = 0 wrong
3. x<0 and y>0 => x+y = -(-x+y) => y = 0 wrong
4. x<0 and y<0 => x+y = -(-x-y) => they are equal so x<0 and y<0 is correct

therefore x+y<0 always => B

­It took me 3:16 to get this answer right. I am wondering if there is any basic concept I should review to bring down time on Modulus. People who are taking the GMAT focus are you seeing absolute value questions and of what kind?