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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

Re: If |x | + |y | = -x – y and xy does not equal 0, which of the followin [#permalink]

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17 Oct 2014, 09:54

If x is <0, then |x| = -x , so From the given equation we can figure out that x and y are both negative numbers . thus, -ve + (-Ve) will always be <0 hence B.

Bunuel please let me know if my approach is wrong !

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

Good question: 20 sec solution

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

We are told that \(xy \neq{0}\)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

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

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 \(\text{some expression} \le 0\) then \(|\text{some expression}| = -(\text{some expression})\). For example: \(|-5|=5=-(-5)\);

When \(x \ge 0\) then \(|x|=x\), or more generally when \(\text{some expression} \ge 0\) then \(|\text{some expression}| = \text{some expression}\). For example: \(|5|=5\).

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

I assumed the only possible value of x and y to be negative as positive value will not satisfy the given information. Taking X as -1 and Y as -1. Now, |-1|+|-1| = - (-1) + -(-1) == > 2 = 2. Based on this I chose ‘B’ as answer. (–X) + (-Y) <0.

IMHO that's the perfect , shortest and the best approach to deal with the Particular problem, though there are numerous approaches for solving this problem as discussed above..

Answer will hence (B) be ( Same approach) _________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

If |x | + |y | = -x – y and xy does not equal 0, which of the followin [#permalink]

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25 Jul 2016, 01:14

Bunuel wrote:

Tough and Tricky questions: Absolute Values.

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

|x | + |y | = -x – y Lets solve LHS Anything that comes out of mod is positive so |x|+|y| = postive so |x|+|y| >0

Lets solve RHS -x-y -(x+y)

LHS =RHS -(x+y)>0 -1(x+y)>0

Now since we know that our expression is positive we can remove the -1 by multiplying both side of the inequality with -1 and flipping the inequality sign (Don't forget whenever we multiply an equality with a negative number we have to flip the sign !!) -1*-1(x+y)<0 * (-1) 1(x+y)<0 x+y<0

This is a correct match with our option B B is the answer.
_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly. FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

Re: If |x | + |y | = -x – y and xy does not equal 0, which of the followin [#permalink]

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16 May 2017, 08:05

Bunuel wrote:

Tough and Tricky questions: Absolute Values.

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

I thought about the question as under: LHS---> distance of x from zero + distance of y from zero i.e. something positive RHS---> it MUST be positive, a quick glance over the options reveals B as the amswer....

took about 20 seconds

Pl correct me if i have been plain lucky kudos if i it helps