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Is x^2 greater than x? 1) x^2 is greater than 1 2) x is

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Is x^2 greater than x? 1) x^2 is greater than 1 2) x is [#permalink] New post 31 Oct 2010, 16:39
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Is x^2 greater than x?

1) x^2 is greater than 1

2) x is greater than -1


I was doing this question and did not particularly like the explanation that was given. Was my approach of rephrasing this question appropriate?

I rephrased it this way:
x^2 > x
x^2 - x > 0
x(x-1) > 0

Then from this i deduced that both of those phrases would have to be either positive or both would have to be negative. I felt that statement 1) allowed me to determine that but statement 2) did not. Was my approach correct?
[Reveal] Spoiler: OA
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Re: Quant Review 2nd Edition: DS 81 [#permalink] New post 31 Oct 2010, 16:52
Expert's post
jscott319 wrote:
Is x^2 greater than x?

1) x^2 is greater than 1

2) x is greater than -1


I was doing this question and did not particularly like the explanation that was given. Was my approach of rephrasing this question appropriate?

I rephrased it this way:
x^2 > x
x^2 - x > 0
x(x-1) > 0

Then from this i deduced that both of those phrases would have to be either positive or both would have to be negative. I felt that statement 1) allowed me to determine that but statement 2) did not. Was my approach correct?


Yes it was.

Is x^2 > x? --> is x(x-1)>0? --> is x in the following ranges: x<0 or x>1?

(1) x^2 is greater than 1 --> x^2>1 --> x<-1 or x>1. Sufficient.

(2) x is greater than -1 --> x>-1. Not sufficient.

Answer: A.
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Re: Quant Review 2nd Edition: DS 81 [#permalink] New post 31 Oct 2010, 17:07
Bunuel wrote:
jscott319 wrote:
Is x^2 greater than x?

1) x^2 is greater than 1

2) x is greater than -1


I was doing this question and did not particularly like the explanation that was given. Was my approach of rephrasing this question appropriate?

I rephrased it this way:
x^2 > x
x^2 - x > 0
x(x-1) > 0

Then from this i deduced that both of those phrases would have to be either positive or both would have to be negative. I felt that statement 1) allowed me to determine that but statement 2) did not. Was my approach correct?


Yes it was.

Is x^2 > x? --> is x(x-1)>0? --> is x in the following ranges: x<0 or x>1?

(1) x^2 is greater than 1 --> x^2>1 --> x<-1 or x>1. Sufficient.

(2) x is greater than -1 --> x>-1. Not sufficient.

Answer: A.


Great Thank You!

I am curious though, and maybe I was not fully aware with this in my understanding. How do you conclude to determine the ranges? x<0 or x>1? Should it be x>0 ?
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Re: Quant Review 2nd Edition: DS 81 [#permalink] New post 31 Oct 2010, 17:24
Expert's post
jscott319 wrote:
Bunuel wrote:
jscott319 wrote:
Is x^2 greater than x?

1) x^2 is greater than 1

2) x is greater than -1


I was doing this question and did not particularly like the explanation that was given. Was my approach of rephrasing this question appropriate?

I rephrased it this way:
x^2 > x
x^2 - x > 0
x(x-1) > 0

Then from this i deduced that both of those phrases would have to be either positive or both would have to be negative. I felt that statement 1) allowed me to determine that but statement 2) did not. Was my approach correct?


Yes it was.

Is x^2 > x? --> is x(x-1)>0? --> is x in the following ranges: x<0 or x>1?

(1) x^2 is greater than 1 --> x^2>1 --> x<-1 or x>1. Sufficient.

(2) x is greater than -1 --> x>-1. Not sufficient.

Answer: A.


Great Thank You!

I am curious though, and maybe I was not fully aware with this in my understanding. How do you conclude to determine the ranges? x<0 or x>1? Should it be x>0 ?


x(x-1)>0 as you noted either both multiples are positive or both are negative:
x<0 and x-1<0, or x<1 --> x<0;
x>0 and x-1>0, or x>1 --> x>1;

So x(x-1)>0 holds true when x<0 or x>1.

For alternate approach check "How to solve quadratic inequalities": x2-4x-94661.html#p731476

Hope it helps.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 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 NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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

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Re: Quant Review 2nd Edition: DS 81 [#permalink] New post 31 Oct 2010, 18:39
Ah of course, I think I was just mixingup my own thinking and the 'solvinf for x' approach that is also done when solving for a quadratic. Thanks for straightening my thinking and thanks for the link!
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Re: Quant Review 2nd Edition: DS 81 [#permalink] New post 01 Nov 2010, 07:53
Yes that is already noted as the OA

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Re: Quant Review 2nd Edition: DS 81 [#permalink] New post 18 Mar 2011, 04:06
Let me see if I can explain this in an easy manner...
Statement tells us that x<0 or x>1 - see bunuel's explanation.
OR statement also says...x can be a positive integer or a positive fraction greater than 1. Also, x can be a negative integer or a negative fraction (Basically x<0)
Statement 1. YES - sufficient.
Statement 2. NO - Insuff. This is because x>-1 can be any number such as 0.5 (which does not solve our problem)
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Re: Quant Review 2nd Edition: DS 81 [#permalink] New post 18 Mar 2011, 06:23
thesfactor wrote:
Let me see if I can explain this in an easy manner...
Statement tells us that x<0 or x>1 - see bunuel's explanation.
OR statement also says...x can be a positive integer or a positive fraction greater than 1. Also, x can be a negative integer or a negative fraction (Basically x<0)
Statement 1. YES - sufficient.
Statement 2. NO - Insuff. This is because x>-1 can be any number such as 0.5 (which does not solve our problem)


Few Tips
1. √x ≥ x for (0 ≤ x ≤ 1)
2. √x ≤ x for (1 ≤ x)
3. x³ ≤ x for (x ≤ -1) and (0 ≤ x ≤ 1)
4. x³ ≥ x for (-1 ≤ x ≤ 0) and (1 ≤ x)
5. x^2 >=x for (1 ≤ x)

So OA should be A..(Case 5)
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Re: Quant Review 2nd Edition: DS 81 [#permalink] New post 06 Dec 2011, 07:58
"
x(x-1)>0 as you noted either both multiples are positive or both are negative:
x<0 and x-1<0, or x<1 --> x<0;
x>0 and x-1>0, or x>1 --> x>1;

So x(x-1)>0 holds true when x<0 or x>1.

For alternate approach check "How to solve quadratic inequalities": x2-4x-94661.html#p731476

Hope it helps."

Hi Bunuel, sorry I did not understand how the ranges/limits change?

For x(x-1) > 0 to hold true,
either
x > 0 and x > 1
or
x < 0 and x < 1

How then does x(x-1) > 0 hold true when x < 0 and x > 1?
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Re: Is x^2 greater than x? 1) x^2 is greater than 1 2) x is [#permalink] New post 06 Dec 2011, 08:33
1. if x>1 then x^2 always greater than x
x= 2, x^2=4
2. x>-1
x=0
x^2 = x^2
x = 3
x^2>x
insufficient.
Ans. A
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Re: Is x^2 greater than x? 1) x^2 is greater than 1 2) x is [#permalink] New post 14 Dec 2011, 10:44
+1 A

The numbers in the range between - 1 and 1 have a particular behavior in exponent problems.
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Re: Is x^2 greater than x? 1) x^2 is greater than 1 2) x is [#permalink] New post 14 Aug 2013, 05:13
Hi Bunuel, How would do this sum in your way. The official answer, which is quite confusing is below. I am unable to understand it completely. I did the sum by evaluation the combinations in regions
{ x<-1 } , { -1<x<0} , { 0<x<1} , {x,1}

Is x^2 greater than x ?

(1) x is less than -1.
(2) x^2 is greater than 1.
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Re: Is x^2 greater than x? 1) x^2 is greater than 1 2) x is [#permalink] New post 14 Aug 2013, 05:16
Expert's post
irda wrote:
Hi Bunuel, How would do this sum in your way. The official answer, which is quite confusing is below. I am unable to understand it completely. I did the sum by evaluation the combinations in regions
{ x<-1 } , { -1<x<0} , { 0<x<1} , {x,1}

Is x^2 greater than x ?

(1) x is less than -1.
(2) x^2 is greater than 1.


Check here: is-x-2-greater-than-x-147172.html
_________________

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

PLEASE READ AND FOLLOW: 11 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 NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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: Is x^2 greater than x? 1) x^2 is greater than 1 2) x is   [#permalink] 14 Aug 2013, 05:16
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