## If x^2 < x, then x must be

##### This topic has expert replies
Moderator
Posts: 6599
Joined: 07 Sep 2017
Followed by:20 members

### If x^2 < x, then x must be

by BTGmoderatorDC » Sat May 14, 2022 5:14 pm

00:00

A

B

C

D

E

## Global Stats

If x^2 < x, then x must be

A. less than 0
B. equal to 0
C. between 0 and 1
D. equal to 1
E. greater than 1

OA C

Source: GMAT Prep

### GMAT/MBA Expert

GMAT Instructor
Posts: 16088
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1267 members
GMAT Score:770

### Re: If x^2 < x, then x must be

by [email protected] » Sun May 15, 2022 10:25 am
BTGmoderatorDC wrote:
Sat May 14, 2022 5:14 pm
If x^2 < x, then x must be

A. less than 0
B. equal to 0
C. between 0 and 1
D. equal to 1
E. greater than 1

OA C

Source: GMAT Prep
Given: x² < x
Subtract x from both sides to get: x² - x < 0
Factor: x(x - 1) < 0

We can already see that, when x = 0, we get: 0(0 - 1) < 0, which results in 0 < 0, which doesn't work. ELIMINATE B
Likewise, when x = 1, we get: 1(1 - 1) < 0, which results in 0 < 0, which doesn't work. ELIMINATE D

At this point we can apply a little bit of number sense.

If x is between 0 and 1, then x is POSITIVE, and (x - 1) is NEGATIVE, which means x(x - 1) < 0 becomes POSITIVE(NEGATIVE) < 0, which works!!