If x^2 < x, then x must be

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

by Brent@GMATPrepNow » 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!!

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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