4th Edition,Math Strategy Guide3 Problemset Page no.187,Q9

[rahul_var25]

Is X3>x2 ? "x3 read as X cube and x2 as x square".

1. x>0
2. x2>x

Rephrasing : x3>x2
x3-x2>0
x2(x-1)>0 this means either both are +ve or both are -ve. Since x2 can never be -ve, therefore
(x-1)>0 or x>1 ?

from satement 1) X is positive but it cannot tell anything about x>1 b'coz it could 0<x<1 . Insufficient

from satement 2) X2>0 or X2-X>0 or x(x-1)>0
x>0 and x>1 from here we can infer that "x>1" . So the answer should be B . B'coz it seems sufficient.

But in guide answer is C.

CAN ANYONE EXPLAIN ME. THANK yOU.

[JohnHarris]

Hi rahul,

A good approach but you stumbled a bit. Just as in the rephrasing of the question, statement two leads to two possibilities of the two factors which must both be examined, i.e.
from satement 2) X2>0 or X2-X>0 or x(x-1)>0
implies we have x and x-1 are either both positive or both negative. From statement 2 alone we do not know that x is greater than zero. So we must allow both of those possibilities. So both x and x-1 could be negative, say, for example, -1/10 and -11/10 in which case x^3 < x^2 and statement two alone is not sufficient.

When you put bot statement (1) and statement (2) together, you can then say, since x is greater than zero [from (1)], x must be greater than 1 [from (2)] and the two statements together are sufficient.

[tim]

Thanks John. One additional thing the original poster missed is that x^2 need not always be positive - you have to consider the possibility that x=0. Of course, statement 1 deals with this quite effectively once you combine the statements..