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

Question

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. x^2 – y^2 > 0

WoundedTiger · Accepted Answer

Good question: 20 sec solution

We know that for any  |x|\geq{0}

We are told that  xy 
eq{0} that means neither x nor y is 0

Now in LHS we have |x|+|y|, which is greater than 0

So we have |x|+|y|> 0 or  -x-y >0  or -(x+y)>0 or x+y<0

Ans B

Bunuel · Answer

No. The absolute value of some expression is always non-negative: |some \ expression|\geq{0} , no matter whether that expression itself is positive, negative or 0. When x \le 0 then |x|=-x , or more generally when ext{some expression} \le 0 then | ext{some expression}| = -( ext{some expression}) . For example: |-5|=5=-(-5) ; When x \ge 0 then |x|=x , or more generally when ext{some expression} \ge 0 then | ext{some expression}| = ext{some expression} . For example: |5|=5 . Theory on Abolute Values: math-absolute-value-modulus-86462.html Absolute value tips: absolute-value-tips-and-hints-175002.html DS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=37 PS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=58 Hard set on Abolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html Hope it helps.

dmmk · Answer

Answer: B 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

Ashishmathew01081987 · Answer

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

saadis87 · Answer

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

Temurkhon · Answer

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

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

B

EMPOWERgmatRichC · Answer

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:

Show Spoiler

B

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

EgmatQuantExpert · Answer

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

arkanian86 · Answer

My second post ever...

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

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

sm1510 · Answer

Source: Manhattan GMAT

Bunuel · Answer

__________________________
Added the tag. Thank you.

0Lucky0 · Answer

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

Tejesh_Itha · Answer

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

playthegame · Answer

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?

Rod728 · Answer

If |x | + |y | = -x – y and xy does not equal 0, which of the following must be true?

|x | + |y | = -(x + y) It is easier to work with this expression since it is repeated in the answer choices.

Since xy =/ 0 then nor x nor are 0, so -> |x | + |y | must be positive, then -(x+y)>0 -> (x+y) <0

Answer B

ManishaPrepMinds · Answer

Solution:

Given |x| + |y| = -x - y and xy ≠ 0:

For |x| + |y| = -x - y to hold, both x and y must be negative.

Evaluate each option:

A. x + y > 0 — False, as x and y are both negative.
B. x + y < 0 — True, since the sum of two negative numbers is negative.
C. x - y > 0 — Not necessarily true; depends on relative values.
D. x - y < 0 — Not necessarily true; depends on relative values.
E. x^2 - y^2 > 0 — Not necessarily true; depends on relative values.

Conclusion: Only Choice B is always true.

Final Answer: (B) x + y < 0

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