If x^2 < x, then x must be

[BTGModeratorVI]

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

Answer: C
Source: GMAT prep

[Brent@GMATPrepNow]

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

Answer: 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

[Scott@TargetTestPrep]

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

Answer: C

Solution:

In order for x^2 to be less than x, then x must be a number between 0 and 1. For example, if x = 1/2, then x^2 = (½)^2 = 1/4. Since 1/4 < 1/2, we see that x^2 < x for this example, and the equation holds true for any positive fraction (i.e., a value between 0 and 1).

Answer: C