GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Oct 2019, 10:45

### 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

# Is x^2 greater than x ?

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 24 Jun 2012
Posts: 363
Location: Pakistan
GPA: 3.76
Is x^2 greater than x ?  [#permalink]

### Show Tags

02 Jul 2017, 07:44
1
00:00

Difficulty:

35% (medium)

Question Stats:

68% (01:37) correct 32% (02:01) wrong based on 57 sessions

### HideShow timer Statistics

Is x^2 greater than x ?

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

_________________
Push yourself again and again. Don't give an inch until the final buzzer sounds. -Larry Bird
Success isn't something that just happens - success is learned, success is practiced and then it is shared. -Sparky Anderson
-S
Math Expert
Joined: 02 Aug 2009
Posts: 8004
Is x^2 greater than x ?  [#permalink]

### Show Tags

02 Jul 2017, 09:38
sananoor wrote:
Is x^2 greater than x ?

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

hi

so we are looking for $$x^2>x.....x^2-x>0......x(x-1)>0$$
two cases..
a) x is positive and x-1>0 0r x>1..
b) x is negative and x-1<0 or x<1... or x<0..

lets see the statements..

1) $$x^2>2x...x^2-2x>0...x(x-2)>0$$
so we have two ranges.. x>2 or x<0..
it suffices to answer as YES
suff

2) $$2x^2>x....x(2x-1)>0$$..
here we get $$x>\frac{1}{2}$$ and $$x<0$$..
but x can be between $$\frac{1}{2}$$ and 1..
so insufficient

A
_________________
Intern
Joined: 27 Apr 2015
Posts: 39
GMAT 1: 370 Q29 V13
Re: Is x^2 greater than x ?  [#permalink]

### Show Tags

13 Jan 2018, 08:42
sananoor wrote:
Is x^2 greater than x ?

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

To Find is $$x^2 > x$$ ------ equ (1)
=> on simplifying we have
=> $$(x^2-x)>0$$
=> OR $$x(x-1)>0$$
=> Above hold true in 2 case- both x & (x-1) are +ve or both -ve
=> case 1 both x & (x-1) are +ve implies x>0 & x-1>0 or x>1
=> case 2 both x & (x-1) are -ve implies x<0 & x-1<0 or x<1
Thus equ (1) hold true if x<0 OR x>1

Statement 1 $$x^2>2x$$
=> OR $$x^2-2x>0$$
=> OR $$x(x-2)>0$$ ------ equ (2)
=> Above hold true in 2 case- both x & (x-2) are +ve or both -ve
=> case 1 both x & (x-2) are +ve implies x>0 & x-2>0 or x>2
=> case 2 both x & (x-2) are -ve implies x<0 & x-2<0 or x<2
Thus equ (2) hold true if x<0 OR x>2
BUT these values x<0 OR x>2 hold TRUE for equ (1) too. THEREFORE SUFFICIENT

Statement 2 $$2x^2>x$$
=> OR $$2x^2-x>0$$
=> OR $$x(2x-1)>0$$ ------ equ (3)
=> Above holds true in 2 case- both x & (2x-1) are +ve or both -ve
=> case 1 both x & (2x-1) are +ve implies x>0 & 2x-1>0 or $$x>\frac{1}{2}$$
=> case 2 both x & (2x-1) are -ve implies x<0 & 2x-1<0 or $$x<\frac{1}{2}$$
Thus equ (3) hold true if x<0 OR $$x>\frac{1}{2}$$
Now when x<0 OR x>1 equ (1) is ALSO TRUE
BUT for $$\frac{1}{2}<x<1$$ equ (1) FAILs.
Since no UNIQUE answer THEREFORE IN-SUFFICIENT

Hence 'A'

Thanks
Dinesh
Re: Is x^2 greater than x ?   [#permalink] 13 Jan 2018, 08:42
Display posts from previous: Sort by