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26 Sep 2014, 10:05
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C
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61% (01:39) correct
39%
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26 Sep 2014, 10:36
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Is x^2 > y^2?
Is x^2 > y^2? --> is |x| > |y|? So, the question asks whether x is further from 0 than y.
(1) x + y < 0. The sum of two numbers is less than 0. Clearly insufficient to say which one is further from 0.
(2) x - y < 0 --> x < y. One number is less than another. Also, insufficient to say which one is further from 0. For example, if x = 1 and y = 2, then y is further but if x = -2 and y = 1, then x is further. Not sufficient.
(1)+(2) Is x^2 > y^2? Can be rephrased as "is (x - y)(x + y) > 0?" (1) says that x + y < 0 and (2) says that x - y < 0, thus their product, the product of two negative values, must be greater than 0. Sufficient.
Answer: C.
Hope it's clear.
Is x^2 > y^2? --> is |x| > |y|? So, the question asks whether x is further from 0 than y.
(1) x + y < 0. The sum of two numbers is less than 0. Clearly insufficient to say which one is further from 0.
(2) x - y < 0 --> x < y. One number is less than another. Also, insufficient to say which one is further from 0. For example, if x = 1 and y = 2, then y is further but if x = -2 and y = 1, then x is further. Not sufficient.
(1)+(2) Is x^2 > y^2? Can be rephrased as "is (x - y)(x + y) > 0?" (1) says that x + y < 0 and (2) says that x - y < 0, thus their product, the product of two negative values, must be greater than 0. Sufficient.
Answer: C.
Hope it's clear.
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26 Sep 2014, 10:07
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ok so that is how I resolved, but it is not correct:
x + y < 0
x<-y
hence if x must be less than -y, and that must be a negative, and since x is more than negative y, then x^2 must be also more than y^2
but it is incorrect.
can someone explain why?
PS
I did not consider the fact that y can be negative, in this case, x is positive, and since we have 2 outcomes, the statement 1 alone is insufficient.
x + y < 0
x<-y
hence if x must be less than -y, and that must be a negative, and since x is more than negative y, then x^2 must be also more than y^2
but it is incorrect.
can someone explain why?
PS
I did not consider the fact that y can be negative, in this case, x is positive, and since we have 2 outcomes, the statement 1 alone is insufficient.
