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E
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Difficulty:
25%
(medium)
Question Stats:
72% (01:27) correct
28%
(01:13)
wrong
based on 201
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Is |xy| ≥ 1?
(1) x^2 + x = 0
(2) y^2 - y = 0
I thought that a statement like this would be xy>= 1 OR xy <= -1 ?? Please correct me if I'm wrong? Thanks in advance!
(1) x^2 + x = 0
(2) y^2 - y = 0
I thought that a statement like this would be xy>= 1 OR xy <= -1 ?? Please correct me if I'm wrong? Thanks in advance!
18 Oct 2014, 08:39
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Is |xy| ≥ 1?
(1) x^2 + x = 0 --> x(x + 1) = 0 --> x = 0 or x = -1. If x = 0, irrespective of y, |xy| = 0 < 1 but if x = -1, |xy| could be more than or equal to 1. Not sufficient.
(2) y^2 - y = 0 --> y(y - 1) = 0 --> y = 0 or y = 1. If y = 0, irrespective of x, |xy| = 0 < 1 but if y = 1, |xy| could be more than or equal to 1. Not sufficient.
(1)+(2) If either x or y is 0, then |xy| = 0 < 1 (NO answer) but if x = -1 and y = 1, then |xy| = 1 (YES answer). Not sufficient.
Answer: E.
(1) x^2 + x = 0 --> x(x + 1) = 0 --> x = 0 or x = -1. If x = 0, irrespective of y, |xy| = 0 < 1 but if x = -1, |xy| could be more than or equal to 1. Not sufficient.
(2) y^2 - y = 0 --> y(y - 1) = 0 --> y = 0 or y = 1. If y = 0, irrespective of x, |xy| = 0 < 1 but if y = 1, |xy| could be more than or equal to 1. Not sufficient.
(1)+(2) If either x or y is 0, then |xy| = 0 < 1 (NO answer) but if x = -1 and y = 1, then |xy| = 1 (YES answer). Not sufficient.
Answer: E.
P.S. Please name topics properly. Check rule 3 here: rules-for-posting-please-read-this-before-posting-133935.html
06 Sep 2016, 04:22
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