Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 25 Apr 2015, 19:19

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:
Intern
Joined: 31 Aug 2010
Posts: 44
Followers: 0

Kudos [?]: 6 [0], given: 2

Is x^2 greater than x? 1) x^2 is greater than 1 2) x is [#permalink]  31 Oct 2010, 16:39
2
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

71% (01:39) correct 29% (00:51) wrong based on 121 sessions
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
Math Expert
Joined: 02 Sep 2009
Posts: 27056
Followers: 4184

Kudos [?]: 40358 [0], given: 5420

Re: Quant Review 2nd Edition: DS 81 [#permalink]  31 Oct 2010, 16:52
Expert's post
1
This post was
BOOKMARKED
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.

_________________
Intern
Joined: 31 Aug 2010
Posts: 44
Followers: 0

Kudos [?]: 6 [0], given: 2

Re: Quant Review 2nd Edition: DS 81 [#permalink]  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.

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 $$x>0$$ ?
Math Expert
Joined: 02 Sep 2009
Posts: 27056
Followers: 4184

Kudos [?]: 40358 [0], given: 5420

Re: Quant Review 2nd Edition: DS 81 [#permalink]  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.

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.
_________________
Intern
Joined: 31 Aug 2010
Posts: 44
Followers: 0

Kudos [?]: 6 [0], given: 2

Re: Quant Review 2nd Edition: DS 81 [#permalink]  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!
Intern
Joined: 31 Aug 2010
Posts: 44
Followers: 0

Kudos [?]: 6 [0], given: 2

Re: Quant Review 2nd Edition: DS 81 [#permalink]  01 Nov 2010, 07:53
Yes that is already noted as the OA

Posted from my mobile device
Manager
Joined: 19 Dec 2010
Posts: 145
Followers: 2

Kudos [?]: 19 [0], given: 12

Re: Quant Review 2nd Edition: DS 81 [#permalink]  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)
Manager
Joined: 05 Jan 2011
Posts: 178
Followers: 3

Kudos [?]: 38 [0], given: 8

Re: Quant Review 2nd Edition: DS 81 [#permalink]  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)
Intern
Joined: 24 May 2011
Posts: 22
Followers: 0

Kudos [?]: 6 [0], given: 5

Re: Quant Review 2nd Edition: DS 81 [#permalink]  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?
Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 662
Followers: 36

Kudos [?]: 346 [0], given: 38

Re: Is x^2 greater than x? 1) x^2 is greater than 1 2) x is [#permalink]  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
_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1725
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Followers: 73

Kudos [?]: 433 [0], given: 109

Re: Is x^2 greater than x? 1) x^2 is greater than 1 2) x is [#permalink]  14 Dec 2011, 10:44
+1 A

The numbers in the range between - 1 and 1 have a particular behavior in exponent problems.
_________________

"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

My Integrated Reasoning Logbook / Diary: my-ir-logbook-diary-133264.html

GMAT Club Premium Membership - big benefits and savings

Intern
Joined: 17 Dec 2012
Posts: 32
Followers: 1

Kudos [?]: 12 [0], given: 34

Re: Is x^2 greater than x? 1) x^2 is greater than 1 2) x is [#permalink]  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.
Math Expert
Joined: 02 Sep 2009
Posts: 27056
Followers: 4184

Kudos [?]: 40358 [0], given: 5420

Re: Is x^2 greater than x? 1) x^2 is greater than 1 2) x is [#permalink]  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
_________________
Senior Manager
Joined: 28 Apr 2014
Posts: 291
Followers: 0

Kudos [?]: 26 [0], given: 46

Re: Is x^2 greater than x? 1) x^2 is greater than 1 2) x is [#permalink]  28 Apr 2014, 20:05
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?

I think it can be answered by a bit intuitively as below:-

X^2 will be always greater than equal to 0. ( Square of a number is always positive).

Now taking the two options one by one. x^2 will be greater than 1 only when x>1 ( square of a decimal i.e 0.0~0.9 will increase the decimal place , for 0.2^2 = 0.04). Option 1 looks correct.

Exploring option 2 - For x>-1 we have to be careful that on number line , the closer one gets to zero , the bigger the number is. So extrapolating for say -0.2 ( which is greater than -1) would give value of 0.04 ( square of a negative number is positive) BUT now there is no end range. So even 1.1 is greater than -1. This makes this information insufficient.

Obviously all this thought process will be done in mind so could be possibly fast compared to quadratic way.
Re: Is x^2 greater than x? 1) x^2 is greater than 1 2) x is   [#permalink] 28 Apr 2014, 20:05
Similar topics Replies Last post
Similar
Topics:
1 Is x^2>x (1) x^2 is greater than 1 (2) x is greater than -1 2 14 May 2012, 09:39
Is x^2 greater than x? (1) x^2 is greater than x^3 (2) x^2 2 03 Jun 2008, 07:21
Is x^2 greater than x? (1) x^2 is greater than 1. (2) x is 2 21 May 2008, 02:13
1 Is x^2 greater than x ? (1) x^2 is greater than 1. (2) x is 8 15 May 2008, 17:16
Is x^2 greater than x? 1) x^2 is greater than 1 2) x is 5 18 Oct 2006, 12:24
Display posts from previous: Sort by