If x^2

Question

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

PS21231

Where does p lie if pÂ2 < p?

A. Between -1 and 0
B. Between -1 and 1
C. Between 0 and 1
D. It is always less than 0
E. It is always greater than 1

Ravixxx · Accepted Answer

x^{2}<x

x^{2}- x<0

x(x-1)<0

0<x<1

Answer C

yashikaaggarwal · Answer

Let's put values of x one by one

A) less than zero = -1/2
=> (-1/2)^2 & -1/2
=> 1/4>-1/2 (incorrect)

B) equal to zero 
=> 0^2 & 0 
=> 0=0 (incorrect)

C) between 0 & 1 = 1/2
=> (1/2)^2 & (1/2)
=> 1/4<1/2 ((correct))

D) equal to 1
=> 1^2 & 1
=> 1=1 (incorrect)

E) more than one = 2
=> (2)^2 & 2
=> 4>2 (incorrect)

Posted from my mobile device

BrentGMATPrepNow · Answer

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

GMATinsight · Answer

x^2 < x i.e. x^2 - x < 0 i.e. x (x-1) < 0 - Product of two things x and (x-1) is negative i,e, one of them must be negative and one must be positive - Since x-1 is smaller than x therefore x-1 must be negative and x must be positive x > 0 and x-1 < 0 x > 0 and x < 1 i.e. 0 < x < 1 Answer: Option C

ScottTargetTestPrep · Answer

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

Varane · Answer

If it was x^2>x
Then what would have been the answer?

Posted from my mobile device

bumpbot · Answer

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If x^2 < x, then x must be

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