If |x| + |y| = -x - y and xy does not equal 0, which of the following must be true?
x + y > 0
x + y < 0
x - y > 0
x - y < 0
x2 - y2 > 0
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MGMAT absolute numbers
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rommysingh
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sandipgumtya
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rommysingh
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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
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Matt@VeritasPrep
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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.
|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.
