lenagmat wrote:Which of the folloing describes value of x^2-x when x is between 0 and 1?
A). 1>x^2-x>0
B). 1>x^2-x>=-1/4
C). 0>x^2-x>=-1/4
D). 1>x^2-x>-1
E). 0>x^2->=-1
Since 0<x<1, x²-x = (smaller positive fraction) - (greater positive fraction).
Thus, x²-x<0.
Eliminate answer choice whose range includes positive values.
Eliminate A, B and D.
Since x² and x are both fractions are between 0 and 1, the distance between them must be less than 1: |x²-x| < 1.
Thus, it is not possible that x²-x = -1.
Eliminate E.
The correct answer is
C.
A less GMAT-friendly approach:
The graph of y= x²-x opens upward, since the coefficient of x² is positive.
The minimum value of y= x²-x occurs when its first derivative = 0.
The first derivative of x²-x is 2x-1.
Setting 2x-1 equal to 0, we get:
2x-1 = 0.
x = 1/2.
Thus, the minimum value of x²-x occurs when x = 1/2:
y = (1/2)² - 1/2 = -1/4.
As shown above, when 0<x<1, x²-x<0.
Thus, the range is -1/4≤x<0.
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