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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, 15:21, 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 ?