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MGMAT absolute numbers

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by sandipgumtya » Thu Sep 17, 2015 10:05 pm
X and Y both have to be negative.so B it is i think.What's OA?
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by rommysingh » Fri Sep 18, 2015 1:18 pm
thats right.
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by [email protected] » Sat Sep 19, 2015 10:42 am
Hi rommysingh,

This question can be solved with Number Properties or by TESTing VALUES.

We're told that |X| + |Y| = -X - Y and the (X)(Y) does not equal 0. We're asked which of the following MUST be true...

IF...
X = -2
Y = -2
|-2| + |-2| = -(-2) - (-2)
4 = 4

X + Y = (-2) + (-2) = -4
X - Y = (-2) - (-2) = 0
X^2 - Y^2 = (-2)^2 - (-2)^2 = 0

Answer A: NOT TRUE
Answer B: TRUE
Answer C: NOT TRUE
Answer D: NOT TRUE
Answer E: NOT TRUE

Final Answer: B

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by Matt@VeritasPrep » Thu Sep 24, 2015 11:14 am
We have

|x| + |y| + x + y = 0

Since xy ≠ 0, we must have x ≠ 0 and y ≠ 0.

Let's consider a few cases.

If x > 0, then x + |x| > 0.

If y > 0, then y + |y| > 0.

Since we're told that the sum of the two of these is 0, neither of these can be true. If one of them is positive, then the other must be negative, but a + |a| can NEVER be negative for any value of a.

Hence we must have x < 0, which gives x + |x| = 0, and y < 0, which gives y + |y| = 0.

So x and y are both negative, and B must be true.
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