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16 Sep 2014, 01:15
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16 Sep 2014, 01:15
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Official Solution:
What is the value of \(x\) ?
(1) \(x^4 = |x|\).
This statement implies that \(x = -1\), \(x = 0\), or \(x = 1\). Not sufficient.
(2) \(x^2 \gt x\).
Rearrange and factor out \(x\) to get \(x(x - 1) > 0\). The roots are \(x = 0\) and \(x = 1\). The "\(>\)" sign indicates that the solution lies to the left of the smaller root and to the right of the larger root; therefore, the given inequality holds true for: \(x < 0\) and \(x > 1\). Not sufficient.
(1) + (2) The only value of \(x\) from (1) that is within the range from (2) is \(x = -1\). Sufficient.
Answer: C
What is the value of \(x\) ?
(1) \(x^4 = |x|\).
This statement implies that \(x = -1\), \(x = 0\), or \(x = 1\). Not sufficient.
(2) \(x^2 \gt x\).
Rearrange and factor out \(x\) to get \(x(x - 1) > 0\). The roots are \(x = 0\) and \(x = 1\). The "\(>\)" sign indicates that the solution lies to the left of the smaller root and to the right of the larger root; therefore, the given inequality holds true for: \(x < 0\) and \(x > 1\). Not sufficient.
(1) + (2) The only value of \(x\) from (1) that is within the range from (2) is \(x = -1\). Sufficient.
Answer: C
09 Nov 2014, 21:42
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Thanks for Explanation! I did not understand following part
" The roots are x=0 and x=1, \("\gt"\) sign means that the given inequality holds true for: \(x \lt 0\) and \(x \gt 1\)."
I thought \(x(x-1) \gt 0\) would mean \(x \gt 0\) and \(x \gt 1\)
Please suggest. Also how did we get -1 as final answer. As per statement (2) \(x \gt 1\).
Thanks
" The roots are x=0 and x=1, \("\gt"\) sign means that the given inequality holds true for: \(x \lt 0\) and \(x \gt 1\)."
I thought \(x(x-1) \gt 0\) would mean \(x \gt 0\) and \(x \gt 1\)
Please suggest. Also how did we get -1 as final answer. As per statement (2) \(x \gt 1\).
Thanks
Bunuel
