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The graphs of y=x^4 and y=|x| 1ntersect each other at three points (-1,1), (0,0) and (1,1), then A is wrong. Any x<0 or x>1 satisfies the inequality x^2>x, then B is wrong. Both statements together uniquely determine the value x=-1, so C is the answer.

Last edited by nvgroshar on 31 Dec 2009, 14:21, edited 1 time in total.

(1) x^4 = |x|. This statement implies that x=-1, x=0, or x=1. Not sufficient.

(2) x^2> x. Rearrange and factor out x to get x(x-1)>0. The roots are x=0 and x=1, ">" sign means that the given inequality holds true for: x<0 and x>1. Not sufficient.

(1)+(2) The only value of x from (1) which is in the range from (2) is x=-1. Sufficient.

(1) x^4 = |x|. This statement implies that x=-1, x=0, or x=1. Not sufficient.

(2) x^2> x. Rearrange and factor out x to get x(x-1)>0. The roots are x=0 and x=1, ">" sign means that the given inequality holds true for: x<0 and x>1. Not sufficient.

(1)+(2) The only value of x from (1) which is in the range from (2) is x=-1. Sufficient.

Answer: C.

Bunuel/Karishma I dont understand the following:

The roots are x=0 and x=1, ">" sign means that the given inequality holds true for: x<0 and x>1.

shouldn't x(x-1)>0 mean that x>0 or (x-1)>0 ? Please explain why it means x<0 ?
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

(1) x^4 = |x|. This statement implies that x=-1, x=0, or x=1. Not sufficient.

(2) x^2> x. Rearrange and factor out x to get x(x-1)>0. The roots are x=0 and x=1, ">" sign means that the given inequality holds true for: x<0 and x>1. Not sufficient.

(1)+(2) The only value of x from (1) which is in the range from (2) is x=-1. Sufficient.

Answer: C.

Bunuel/Karishma I dont understand the following:

The roots are x=0 and x=1, ">" sign means that the given inequality holds true for: x<0 and x>1.

shouldn't x(x-1)>0 mean that x>0 or (x-1)>0 ? Please explain why it means x<0 ?