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# M22-03

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Math Expert
Joined: 02 Sep 2009
Posts: 43335

Kudos [?]: 139526 [0], given: 12794

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16 Sep 2014, 00:15
Expert's post
1
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Difficulty:

25% (medium)

Question Stats:

69% (00:48) correct 31% (01:14) wrong based on 85 sessions

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What is the value of $$x$$ ?

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

(2) $$x^2 \gt x$$
[Reveal] Spoiler: OA

_________________

Kudos [?]: 139526 [0], given: 12794

Math Expert
Joined: 02 Sep 2009
Posts: 43335

Kudos [?]: 139526 [0], given: 12794

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16 Sep 2014, 00:15
Expert's post
2
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BOOKMARKED
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.

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Kudos [?]: 139526 [0], given: 12794

Intern
Joined: 16 Feb 2014
Posts: 7

Kudos [?]: 1 [0], given: 8

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09 Nov 2014, 20:42
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.

Kudos [?]: 1 [0], given: 8

Math Expert
Joined: 02 Sep 2009
Posts: 43335

Kudos [?]: 139526 [0], given: 12794

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10 Nov 2014, 01:57
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.

Inequality tips: tips-and-hints-for-specific-quant-topics-with-examples-172096.html#p1379270
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Kudos [?]: 139526 [0], given: 12794

Intern
Joined: 01 Oct 2014
Posts: 23

Kudos [?]: [0], given: 3

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21 Jun 2016, 06:13
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Not able to understand the explanation

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Math Expert
Joined: 02 Sep 2009
Posts: 43335

Kudos [?]: 139526 [0], given: 12794

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21 Jun 2016, 06:18
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Not able to understand the explanation

Please check alternate solutions here: what-is-the-value-of-x-147037.html
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Kudos [?]: 139526 [0], given: 12794

Senior Manager
Joined: 08 Jun 2015
Posts: 365

Kudos [?]: 27 [0], given: 106

Location: India
GMAT 1: 640 Q48 V29

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27 Dec 2017, 07:31
+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.
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Re: M22-03   [#permalink] 27 Dec 2017, 07:31
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# M22-03

Moderators: chetan2u, Bunuel

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