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If xy < 0, what is the value of |x + y| ?
(1) |x| = 4
(2) |y| = 1
M36-109
(1) |x| = 4
(2) |y| = 1
M36-109
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15 Nov 2021, 04:38
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Bunuel
If xy < 0, what is the value of |x + y| ?
(1) |x| = 4
(2) |y| = 1
M36-109
(1) |x| = 4
(2) |y| = 1
M36-109
Official Solution:
If \(xy < 0\), what is the value of \(|x + y|\) ?
Notice that \(xy < 0\) means that \(x\) and \(y\) have different signs.
(1) \(|x| = 4\)
\(x\) is either 4 or -4. No info about \(y\). Not sufficient.
(2) \(|y| = 1\)
\(y\) is either 1 or -1. No info about \(x\). Not sufficient.
(1)+(2) Since \(x\) and \(y\) have different signs, then either \(x=4\) and \(y=-1\) or \(x=-4\) and \(y=1\) but in either case \(|x + y|=3\). Sufficient.
Answer: C
General Discussion
11 Dec 2018, 02:47
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Statement 1
|x|= 4 => x= 4, -4
Not sufficient
Statement 2
|y|= 1 => y= 1, -1
Not sufficient
St. 1+2
as we know xy<0
means x and y are of opposite sign. (4, -1) or (-4, 1)
In both cases |x+y|= 3
C is answer.
|x|= 4 => x= 4, -4
Not sufficient
Statement 2
|y|= 1 => y= 1, -1
Not sufficient
St. 1+2
as we know xy<0
means x and y are of opposite sign. (4, -1) or (-4, 1)
In both cases |x+y|= 3
C is answer.
