number properties

[sud21]

Is X^2 < X^3?
1). X<X^2
2). X<1

[sam2304]

Is X^2 < X^3?
1). X<X^2
2). X<1

x^2 < x^3
x^2 - x^3 < 0
is x^2(1 - x) < 0 ?
x^2 < 0 or 1-x < 0.
x^2 cannot be negative as it an even power. So 1 - x < 0 => 1 < x => x >1.

Is x > 1 ?

1.x < x^2 => x - x^2 < 0
x(1 - x) < 0
Either of them can be -ve for the value to be < 0.
x < 0 or x > 1. So we cannot say whether x > 1 or not. INSUFF.

B. X < 1. So the answer to the question is a NO. SUFF.

IMO B.

[ArunangsuSahu]

See my explanation:

Statement 1:
x-x^2<0
or x(x-1) >0
x< 0 or x>1
x<0...-> x^2>x^3
x>1 ---> x^2<x^3

So INSUFFICIENT..

Statement 2:
x<1
Case 1: x=0...-> x^2=x^3
Case 2: x=1/2 -> x^2 > x^3
case 3: x=-1/2 or -3 ---> x^2> x^3

so x^2 is never less than x^3

SUFFICIENT

[sam2304]

@arunangsusahu: Can you explain where i go wrong in my approach ?

[ArunangsuSahu]

@sam...You are right..

This is a Yes or No question so x^2 can be equal to greater than x^3 if x<1 but definitely not less than
(B) is the answe