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(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 \(x(x-1) \gt 0\). The roots are \(x=0\) and \(x=1\), "\(\gt\)" sign means that the given inequality holds true for: \(x \lt 0\) and \(x \gt 1\). Not sufficient.
(1)+(2) The only value of \(x\) from (1) which is in the range from (2) is \(x=-1\). Sufficient.
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
Bunuel wrote:
Official Solution:
(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 \(x(x-1) \gt 0\). The roots are \(x=0\) and \(x=1\), "\(\gt\)" sign means that the given inequality holds true for: \(x \lt 0\) and \(x \gt 1\). Not sufficient.
(1)+(2) The only value of \(x\) from (1) which is in the range from (2) is \(x=-1\). Sufficient.
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
Bunuel wrote:
Official Solution:
(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 \(x(x-1) \gt 0\). The roots are \(x=0\) and \(x=1\), "\(\gt\)" sign means that the given inequality holds true for: \(x \lt 0\) and \(x \gt 1\). Not sufficient.
(1)+(2) The only value of \(x\) from (1) which is in the range from (2) is \(x=-1\). Sufficient.
+1 for C. From the first statement x=-1,0, or 1. From second statement , x<0 or x>1. Each statement alone is not sufficient. Combine the two, x=-1. Hence option C.
_________________
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
Bunuel wrote:
Official Solution:
(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 \(x(x-1) \gt 0\). The roots are \(x=0\) and \(x=1\), "\(\gt\)" sign means that the given inequality holds true for: \(x \lt 0\) and \(x \gt 1\). Not sufficient.
(1)+(2) The only value of \(x\) from (1) which is in the range from (2) is \(x=-1\). Sufficient.
I too have exactly the same question as the previous person...I went through the links provided and still cannot understand why in statement 2, x is not either greater than 0 or greater than 1. I then got confused as to how you got to the answer being x= (-1).
Would really appreciate a breakdown of the above queries please.
I too have exactly the same question as the previous person...I went through the links provided and still cannot understand why in statement 2, x is not either greater than 0 or greater than 1. I then got confused as to how you got to the answer being x= (-1).
Would really appreciate a breakdown of the above queries please.
Thanks,
Tosin
This is explained in detail in the links provided.
x > 0 or x > 1 doe not make any sense. Is x > 0? So, could it be 0.5? Or is x > 1?
\(x(x-1) \gt 0\) --> x and x - 1 have the same sign.
x > 0 and x - 1 > 0 --> x > 0 and x > 1. Simultaneously to be true x > 1 has to be true. x < 0 and x - 1 < 0 --> x < 0 and x < 1. Simultaneously to be true x < 0 has to be true.
So, \(x(x-1) \gt 0\) is true for x < 0 and x > 1.
_________________
I too have exactly the same question as the previous person...I went through the links provided and still cannot understand why in statement 2, x is not either greater than 0 or greater than 1. I then got confused as to how you got to the answer being x= (-1).
Would really appreciate a breakdown of the above queries please.
Thanks,
Tosin
This is explained in detail in the links provided.
x > 0 or x > 1 doe not make any sense. Is x > 0? So, could it be 0.5? Or is x > 1?
\(x(x-1) \gt 0\) --> x and x - 1 have the same sign.
x > 0 and x - 1 > 0 --> x > 0 and x > 1. Simultaneously to be true x > 1 has to be true. x < 0 and x - 1 < 0 --> x < 0 and x < 1. Simultaneously to be true x < 0 has to be true.
Yes, |0| = 0. An absolute value show the distance from 0. For example, |-3| = 3 means that -3 is 3 units from 0. How far is 0 from 0? What is the distance from 0 to 0? It's 0.
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69% (00:49) correct 
