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# What is the value of x ?

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Senior Manager
Joined: 10 Apr 2012
Posts: 276
Location: United States
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What is the value of x ? [#permalink]

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11 Feb 2013, 01:09
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Difficulty:

25% (medium)

Question Stats:

53% (01:55) correct 47% (00:38) wrong based on 137 sessions

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What is the value of x ?

(1) x^4=|x|
(2) x^2>x

M22-03

[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 39662
Re: What is the value of x ? [#permalink]

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11 Feb 2013, 01:18
1
KUDOS
Expert's post
guerrero25 wrote:
What is the value of x ?

(1) x^4=|x|
(2) x^2>x

M22-03

What is the value of $$x$$ ?

(1) $$x^4 = |x|$$. Square both sides: $$x^8=x^2$$ --> $$x^2(x^6-1)=0$$ --> $$x^2(x^3-1)(x^3+1)=0$$ --> $$x=-1$$, $$x=0$$, or $$x=1$$. Not sufficient.

(2) $$x^2> x$$. Rearrange and factor out $$x$$ to get $$x(x-1)>0$$. The roots are $$x=0$$ and $$x=1$$, "$$>$$" sign means that the given inequality holds true for: $$x<0$$ and $$x>1$$ (check here: x2-4x-94661.html#p731476, inequalities-trick-91482.html, everything-is-less-than-zero-108884.html?hilit=extreme#p868863, xy-plane-71492.html?hilit=solving%20quadratic#p841486). 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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Senior Manager
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Posts: 276
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Re: What is the value of x ? [#permalink]

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12 Feb 2013, 04:04
Bunuel wrote:
guerrero25 wrote:
What is the value of x ?

(1) x^4=|x|
(2) x^2>x

M22-03

What is the value of $$x$$ ?

(1) $$x^4 = |x|$$. Square both sides: $$x^8=x^2$$ --> $$x^2(x^6-1)=0$$ --> $$x^2(x^3-1)(x^3+1)=0$$ --> $$x=-1$$, $$x=0$$, or $$x=1$$. Not sufficient.

(2) $$x^2> x$$. Rearrange and factor out $$x$$ to get $$x(x-1)>0$$. The roots are $$x=0$$ and $$x=1$$, "$$>$$" sign means that the given inequality holds true for: $$x<0$$ and $$x>1$$ (check here: x2-4x-94661.html#p731476, inequalities-trick-91482.html, everything-is-less-than-zero-108884.html?hilit=extreme#p868863, xy-plane-71492.html?hilit=solving%20quadratic#p841486). Not sufficient.

(1)+(2) The only value of $$x$$ from (1) which is in the range from (2) is $$x=-1$$. Sufficient.

Thanks for the crystal clear approach .. Could you help me with a link here to grasp the concept on Absolute value type questions . I still get problems related to them wrong . Appreciate your help .

thanks again!
Math Expert
Joined: 02 Sep 2009
Posts: 39662
Re: What is the value of x ? [#permalink]

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12 Feb 2013, 05:33
1
KUDOS
Expert's post
2
This post was
BOOKMARKED
guerrero25 wrote:
Bunuel wrote:
guerrero25 wrote:
What is the value of x ?

(1) x^4=|x|
(2) x^2>x

M22-03

What is the value of $$x$$ ?

(1) $$x^4 = |x|$$. Square both sides: $$x^8=x^2$$ --> $$x^2(x^6-1)=0$$ --> $$x^2(x^3-1)(x^3+1)=0$$ --> $$x=-1$$, $$x=0$$, or $$x=1$$. Not sufficient.

(2) $$x^2> x$$. Rearrange and factor out $$x$$ to get $$x(x-1)>0$$. The roots are $$x=0$$ and $$x=1$$, "$$>$$" sign means that the given inequality holds true for: $$x<0$$ and $$x>1$$ (check here: x2-4x-94661.html#p731476, inequalities-trick-91482.html, everything-is-less-than-zero-108884.html?hilit=extreme#p868863, xy-plane-71492.html?hilit=solving%20quadratic#p841486). Not sufficient.

(1)+(2) The only value of $$x$$ from (1) which is in the range from (2) is $$x=-1$$. Sufficient.

Thanks for the crystal clear approach .. Could you help me with a link here to grasp the concept on Absolute value type questions . I still get problems related to them wrong . Appreciate your help .

thanks again!

Theory on Absolute Values: math-absolute-value-modulus-86462.html

PS questions on Absolute Values: search.php?search_id=tag&tag_id=58
DS questions on Absolute Values: search.php?search_id=tag&tag_id=37

Tough inequality and absolute value questions: inequality-and-absolute-value-questions-from-my-collection-86939.html

Hope it helps.
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Joined: 10 Apr 2012
Posts: 276
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Re: What is the value of x ? [#permalink]

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12 Feb 2013, 07:14
Hope it helps.[/quote]

Thanks GMATCLUB is my Bible
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Posts: 20
Re: What is the value of x ? [#permalink]

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09 Jan 2015, 17:35
For statement (2), why can't X<-1?
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Re: What is the value of x ? [#permalink]

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09 Jan 2015, 17:53
Hi All,

This DS question can be solved with a variety of Number Properties and TESTing VALUES:

We're asked for the value of X.

Fact 1: X^4 = |X|

While this certainly looks "scary", there can't be that many values that will "fit" this equation.

X = 0 is fairly obvious. Since we have a "fourth power" and an absolute value, I'd be looking for other solutions that are fairly close to 0 and possibly negative.

X = 1 and X = -1 also fit.
Fact 1 is INSUFFICIENT

Fact 2: X^2 > X

Here we can use a Number Property to our advantage - EVERY negative number, when squared, becomes positive.

So, X = ANY negative.

This is enough to prove that Fact 2 is INSUFFICIENT on its own, but I want to add a bit more detail to what X^2 > X means.

X CANNOT be 1, since 1^2 is NOT > 1.
X CANNOT be 0, since 0^2 is NOT > 0

X CANNOT be between 0 and 1 either (because of another Number Property - positive fractions, when squared, get SMALLER).
C CANNOT be 1/2, since (1/2)^2 is NOT > 1/2.

X CAN be > 1 though (choose any value greater than 1 and you can prove it).
Fact 2 is INSUFFICIENT

Combined, we know...
X = -1, 0 or 1
X CANNOT BE 0 OR 1
Thus, X can ONLY be -1
Combined, SUFFICIENT

[Reveal] Spoiler:
C

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Re: What is the value of x ? [#permalink]

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09 Jan 2015, 17:56
For statement 2, x can be < -1. In fact it can be x < 0 or x > 1 to meet the condition. Therefore, together with Statement 1, which translates to x= -1 or x=0 or x=1, x must be -1. You need both statements together to give the value of x.
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Re: What is the value of x ? [#permalink]

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24 Feb 2016, 12:57
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Re: What is the value of x ?   [#permalink] 24 Feb 2016, 12:57
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