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# M22-03

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Math Expert
Joined: 02 Sep 2009
Posts: 51072

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16 Sep 2014, 00:15
1
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Difficulty:

25% (medium)

Question Stats:

69% (00:49) correct 31% (01:13) wrong based on 138 sessions

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What is the value of $$x$$ ?

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

(2) $$x^2 \gt x$$

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Math Expert
Joined: 02 Sep 2009
Posts: 51072

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16 Sep 2014, 00:15
1
1
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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Joined: 16 Feb 2014
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09 Nov 2014, 20:42
1
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.

Math Expert
Joined: 02 Sep 2009
Posts: 51072

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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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Joined: 01 Oct 2014
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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
Math Expert
Joined: 02 Sep 2009
Posts: 51072

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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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Joined: 08 Jun 2015
Posts: 436
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38
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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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Intern
Joined: 13 Oct 2017
Posts: 39

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16 Feb 2018, 05:51
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.

Inequality tips: http://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
Math Expert
Joined: 02 Sep 2009
Posts: 51072

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16 Feb 2018, 05:57
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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Joined: 13 Oct 2017
Posts: 39

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17 Feb 2018, 02:58
Bunuel wrote:
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.

Thanks a lot...now understood.
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Joined: 15 Nov 2016
Posts: 282

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10 Jul 2018, 22:17
is the absolute value of zero, zero?
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Math Expert
Joined: 02 Sep 2009
Posts: 51072

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10 Jul 2018, 22:22
1
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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Joined: 28 Sep 2018
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16 Nov 2018, 00:37
wouldnt this ans insufficient when x=2,-2
if this is the case, then x could still satisfy both condition.

thank you
Math Expert
Joined: 02 Sep 2009
Posts: 51072

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16 Nov 2018, 01:01
mmildlyy wrote:
wouldnt this ans insufficient when x=2,-2
if this is the case, then x could still satisfy both condition.

thank you

How does 2 or -2 satisfy x^4 = |x| ?
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Re: M22-03 &nbs [#permalink] 16 Nov 2018, 01:01
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# M22-03

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