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What is the value of x ?

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What is the value of x ? [#permalink] New post 11 Feb 2013, 00:09
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A
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Difficulty:

  35% (medium)

Question Stats:

56% (01:54) correct 44% (00:34) wrong based on 81 sessions
What is the value of x ?

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

M22-03

please explain ..

thanks in advance
[Reveal] Spoiler: OA
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Re: What is the value of x ? [#permalink] New post 11 Feb 2013, 00:18
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Expert's post
guerrero25 wrote:
What is the value of x ?

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

M22-03

please explain ..

thanks in advance


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.

Answer: C.
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Re: What is the value of x ? [#permalink] New post 12 Feb 2013, 03:04
Bunuel wrote:
guerrero25 wrote:
What is the value of x ?

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

M22-03

please explain ..

thanks in advance


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.

Answer: C.


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!
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Re: What is the value of x ? [#permalink] New post 12 Feb 2013, 04:33
1
This post received
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Expert's post
1
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

please explain ..

thanks in advance


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.

Answer: C.


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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: What is the value of x ? [#permalink] New post 12 Feb 2013, 06:14
Hope it helps.[/quote]

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Re: What is the value of x ? [#permalink] New post 09 Jan 2015, 16:35
For statement (2), why can't X<-1?
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Re: What is the value of x ? [#permalink] New post 09 Jan 2015, 16:53
Expert's post
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

Final Answer:
[Reveal] Spoiler:
C


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Re: What is the value of x ? [#permalink] New post 09 Jan 2015, 16:56
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] 09 Jan 2015, 16:56
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