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02 Oct 2008, 06:47
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
70% (01:14) correct
30%
(01:18)
wrong
based on 2322
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Is x^2 – y^2 a positive number?
(1) x – y is a positive number.
(2) x + y is a positive number.
DS48302.01
(1) x – y is a positive number.
(2) x + y is a positive number.
DS48302.01
I chose (A) for this one. If x - y > 0 then x > y. So x2-y2 will be a +ve number.
the OA is C though x2 - y2 = (x+y)(x-y)
the OA is C though x2 - y2 = (x+y)(x-y)
31 Oct 2014, 04:40
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topmbaseeker
Is x^2 – y^2 a positive number?
(1) x – y is a positive number.
(2) x + y is a positive number.
(1) x – y is a positive number.
(2) x + y is a positive number.
I chose (A) for this one. If x - y > 0 then x > y. So x2-y2 will be a +ve number.
the OA is C though x2 - y2 = (x+y)(x-y)
the OA is C though x2 - y2 = (x+y)(x-y)
Is x^2 – y^2 a positive number?
Is x^2 - y^2 > 0? is x^2 > y^2? --> is |x| > |y|? So, the question asks whether x is further from 0 than y.
(1) x – y is a positive number --> x > y. One number is greater than another. Also, insufficient to say which one is further from 0. For example, if x = 2 and y = 1, then x is further but if x = 2 and y = -3, then y is further. Not sufficient.
(2) x + y is a positive number. The sum of two numbers is greater than 0. Clearly insufficient to say which one is further from 0.
(1)+(2) Is x^2 - y^2 > 0? 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 positive values, must be greater than 0. Sufficient.
Answer: C.
Hope it's clear.
General Discussion
09 Apr 2016, 07:41
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Almost all data sufficiency questions (and generally most problem solving questions) benefit from the "dumb" approach. I'll elaborate on that in a second but first, as a trigger, you should ALWAYS attempt to rearrange the question they give you especially when you see exponents. When you see x^2 – y^2 you should immediately realize that it equals (x + y)(x - y).
Now for the dumb approach:
The question asks is (x + y)(x - y) > 0. The dumb approach says that you take this problem and translate it to the simplest terms possible. "Is a number times a number positive?" For this to be true, both numbers must either be positive or negative. That's why you need to both statements. And knowing number properties such as "a positive times a positive is a positive" or "an odd number to any power is odd" will save you the hassle of plugging and chugging.
Now for the dumb approach:
The question asks is (x + y)(x - y) > 0. The dumb approach says that you take this problem and translate it to the simplest terms possible. "Is a number times a number positive?" For this to be true, both numbers must either be positive or negative. That's why you need to both statements. And knowing number properties such as "a positive times a positive is a positive" or "an odd number to any power is odd" will save you the hassle of plugging and chugging.
