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!!
Answer: C
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
