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M22-03

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Bunuel
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M22-03 [#permalink] New post   16 Sep 2014, 01:15
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What is the value of \(x\) ?


(1) \(x^4 = |x|\)

(2) \(x^2 \gt x\)
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Bunuel
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Re M22-03 [#permalink] New post   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
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Re: M22-03 [#permalink] New post   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

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.


Answer: C
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Bunuel
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Re: M22-03 [#permalink] New post   10 Nov 2014, 02:57
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Sky78 wrote:
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.


Answer: C


Check links below.

Solving Quadratic Inequalities - Graphic Approach: solving-quadratic-inequalities-graphic-approach-170528.html
Inequality tips: tips-and-hints-for-specific-quant-topics-with-examples-172096.html#p1379270
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Re: M22-03 [#permalink] New post   16 Feb 2018, 06:51
Bunuel wrote:
Sky78 wrote:
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.


Answer: C


Check links below.

Solving Quadratic Inequalities - Graphic Approach: https://gmatclub.com/forum/solving-quadr ... 70528.html
Inequality tips: https://gmatclub.com/forum/tips-and-hint ... l#p1379270



Hi Bunuel,

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
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Bunuel
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Re: M22-03 [#permalink] New post   16 Feb 2018, 06:57
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ttaiwo wrote:
Hi Bunuel,

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.
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Re: M22-03 [#permalink] New post   10 Jul 2018, 23:17
is the absolute value of zero, zero?
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Re: M22-03 [#permalink] New post   10 Jul 2018, 23:22
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ENEM wrote:
is the absolute value of zero, zero?


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.

Hope it's clear.
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Re: M22-03 [#permalink] New post   08 May 2023, 05:39
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M22-03 [#permalink]
08 May 2023, 05:39
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