Bunuel wrote:

Considering the positions on the number line above, which of the following could be a value for x?

A. 5/3

B. 3/5

C. -2/5

D. -5/2

E. none

lets see the values x can take..

1) \(x^3<x^2.................x^3-x^2<0...............x^2(x-1)<0...................\)

this means \(x<1\) as \(x^2\) cannot be negative...

2) \(x<x^3............. x^3-x>0...........x(x^2-1)>0.........\)...

so both x and x^2-1 will be of the same sign..

a) if x is +ive, \(x^2-1>0...............x^2>1............ x>1... OR ...x<-1.......\) BUT x is +ive so x>1..

But we have seen above x<1.. so this is not possible

b) if x is -ive, \(x^2-1<0...............x^2<1............ x<1... OR ...x>-1.......\) BUT x is -ive so x lies between -1 and 0.....

From above 2 points, x lies between -1 and 0..... so x is -3/5

C

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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