Welcome! Check out our free B-School Guides to learn how you compare with other applicants.

## number properties

This topic has 1 expert reply and 4 member replies
sud21 GMAT Destroyer!
Joined
12 Nov 2011
Posted:
308 messages
Followed by:
3 members
number properties Fri Jan 13, 2012 6:39 am
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
Is x>1?
1). x^2<x
2). x<rootx

source search engines

Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
sud21 GMAT Destroyer!
Joined
12 Nov 2011
Posted:
308 messages
Followed by:
3 members
Sat Jan 14, 2012 11:59 am
St.1 x^2<x, this is possible when x is a fraction, that is, a positive fraction less than 1 but greater than 0.

If x=1/2 then x^2=1/4 which is less than x=1/2.

If x=-1/2 then x^2=1/4 which is more than x=-1/2, thus not meeting the condition.

Thus we can say that x can never be greater than 1 but it will be less than 1 but greater than 0.

Since it is asked that whether x>1, we can say it as a no, so, sufficient.

St.2 x<rootx, squaring both sides we get x<x^2 which is same as St.1 provided x is a positive number. Sufficient.

Ans.D

neelgandham Community Manager
Joined
13 May 2011
Posted:
1060 messages
Followed by:
46 members
Thanked:
305 times
Test Date:
October 15th 2012
Target GMAT Score:
740
Sat Jan 14, 2012 12:11 pm
sud21 wrote:
St.2 x<rootx, squaring both sides we get x<x^2 which is same as St.1 provided x is a positive number. Sufficient.
Ans.D
To add to the explanation, you cannot always square the terms of an equation without knowing the sign of the terms . x < y, DOESNOT always imply x^2 < y^2

x<y, => x^2 < y^2, if x,y >0
x<y, => x^2 > y^2, if x,y <0

_________________
Anil Gandham
Welcome to BEATtheGMAT
My Quant Blog | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now’s online course at http://www.gmatprepnow.com/

mj78ind Really wants to Beat The GMAT!
Joined
28 Dec 2009
Posted:
265 messages
Followed by:
1 members
Thanked:
26 times
GMAT Score:
760
Sat Jan 14, 2012 2:19 pm
sud21 wrote:
Is x>1?
1). x^2<x
2). x<rootx

source search engines
Stmt 1 - can be reduced to
x^2 - x < 0, which is x(x-1)<0,
the two roots are 0 and 1. Check for x <0, 0<x<1 and x >1.
We find that the condition holds only when 0<x<1, thus x > 1? Can be answered with an unequivocal NO. Hence sufficient.

Stmt 2 - x < root (x), thus we know x >0 and x<1 since a negative number can not have a real root (GMAT does not deal with imaginary numbers) and only numbers < 1 are such that their roots are bigger than themselves. Thus sufficient.

Hence D. Sorry solved the question right and forgot when both are sufficient independently we gotta choose D!! and not C

_________________
Call me 1 - (412) 897 6727 (US) or leave a msg on BTG for GMAT advise / questions.
http://www.beatthegmat.com/760-done-deal-debrief-especially-for-2nd-timers-updated-t66740.html

Last edited by mj78ind on Sun Jan 15, 2012 7:01 am; edited 1 time in total

### GMAT/MBA Expert

Anurag@Gurome GMAT Instructor
Joined
02 Apr 2010
Posted:
3835 messages
Followed by:
466 members
Thanked:
1749 times
GMAT Score:
770
Sat Jan 14, 2012 10:14 pm
Another approach to solve this kind of problem is interpretation of graphs and the approach is very quick and easy if you are familiar with graphs of standard functions.

If we plot the graphs of x, x², and √x on the same axes, we will get the following diagram

From the graph, it is very clear that x² is less than x, i.e. the yellow line is below the red one only for 0 < x < 1. And x is less than √x, i.e. the blue line is above the red one is only for 0 < x < 1.

Hence, to satisfy any of the two statements x must be less than 1. Hence, both statements are individually sufficient to answer the question with NO.

_________________
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

GMAT with Gurome

Thanked by: mankey
amit.trivedi@ymail.com GMAT Destroyer!
Joined
09 Nov 2010
Posted:
934 messages
Followed by:
14 members
Thanked:
59 times
Test Date:
N.A
Target GMAT Score:
750
Thu Mar 15, 2012 10:37 pm
Is x>1?
1). x^2<x
2). x<rootx

The answer is D. Got it in less than 2 mins...

_________________
IT IS TIME TO BEAT THE GMAT

LEARNING, APPLICATION AND TIMING IS THE FACT OF GMAT AND LIFE AS WELL... KEEP PLAYING!!!

Whenever you feel that my post really helped you to learn something new, please press on the 'THANK' button.

### Best Conversation Starters

1 varun289 40 topics
2 guerrero 21 topics
3 sana.noor 20 topics
4 killerdrummer 19 topics
5 sanaa.rizwan 14 topics
See More Top Beat The GMAT Members...

### Most Active Experts

1 Brent@GMATPrepNow

GMAT Prep Now Teacher

203 posts
2 GMATGuruNY

The Princeton Review Teacher

140 posts
3 Jim@StratusPrep

Stratus Prep

100 posts
4 Anju@Gurome

Gurome

99 posts