If x^3

Question

If x^3 < x^2 , is x < 0 ? A) |x| > x^2 B) x > x^2

GMATinsight · Answer

Given: x^3 < x^2 i.e. x^3 - x^2 < 0 i.e. x^2(x - 1) < 0 But x^2 can NOT be negative as being square of a number i.e. x-1 < 0 i.e. x < 1 Question : is x < 0 ? Statement 1 : |x| > x^2 i.e. -1 < x < 1 NOT SUFFICIENT Statement 2 : x > x^2 i.e. 0 < x < 1 SUFFICIENT Answer: Option B P.S. I don't rate this question appropriate for GMAT practice as the GMAT question do NOT include any redundant information like x^3 < x^2 given in this question

jorgetomas9 · Answer

Excuse me, how do you solve the first equation?
 |x| > x^2 
Thank you.

GMATinsight · Answer

jorgetomas9

I prefer to avoid mathematically solving such expressions.

There are 4 critical ranges which are 
  0 to 1
greater than 1
0 to -1 and
Less than -1

I always prefer to test the given expression in these ranges to test the validity.

Here I see that  |x| > x^2

so point to be noted is  |x|  as well as  x^2  will always be positive for all values of x except zero.
also the absolute value of the number should become a smaller number when squared which happened in range  0 to 1

i.e. the expression will be valid in ranges   0 to 1 and 0 to -1

I HOPE THIS HELPS!!!

If x^3 < x^2, is x < 0 ?

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