Is x^2 x^3 (1) x^3 0 (2) x ≠ 1

Question

Is  x^2 > x^3  ?

(1)  x^3 > 0

(2)  x
eq{1}

Nipungupta9081 · Answer

IMO E

(1) x^3 > 0

This tells us X is positive = X could be 0 or 1.

X^2 = X^3 ------- INSUFFICIENT

(2) x≠1

X could be 0 or -1. --------- INSUFFICIENT

Joining both Statements

X^3 > 0 and X ≠ 1

Still cant get a definite value ------ INSFUFFIENT

Joining 1 + 2

Still INSUFFICIENT

rocky620 · Answer

(1)  x^3  > 0 
means that x is +ve.
If x is greater than 1 than we get no.
If x is less than 1 than we get yes; x= \frac{1}{2} ,  x^2 = \frac{1}{4}  and  x^3 = \frac{1}{8} ;  x^2 > x^3

Insufficient.

(2) x≠1 
Clearly insufficient as we do not know the polarity of x.

1+2 
Statement 1 still stands
Insufficient.

Option E

manasi05 · Answer

Question stem asks if x^2>x^3
Let's simplify the expression

x^2 - x^3 >0
x^2(1-x)>0
For this expression to be greater than 0 we should have both the terms x^2 and 1-x positive or negative. As x^2 is always nonnegative so 1-x needs to be positive as well for the expression to be greater than 0
So 1-x>0
1>x
So basically we have to find if x<1

Statement 1:
x^3>0
This tells us that x>0
The answer will be yes for range 0<x<1 but will be no for x>1
Hence Insufficient
Statement 2
x≠1
This only tells us that x can be any value other than 1. Not sufficient

Combining 2 statements also does not give us a definite answer. The answer will be yes for range 0<x<1 but will be no for x>1

Hence the answer is E

achloes · Answer

Bunuel   KarishmaB   JeffTargetTestPrep   ScottTargetTestPrep   avigutman

Could one of the experts validate my reasoning please?

Pushing the question stem got me the following:

Is x^2 > 0 or is x > 1?

"x^2 > 0" doesn't tell us much as x could be positive or negative so I focused on whether x > 1. Is this the right approach?

S1. x^3 > 0 
So x is positive but could be greater or lesser than 1 
Insufficient

S2. x is not equal to 1 
Clearly insufficient

Combining S1 and S2: 
Still insufficient as x could be any value other than 1

Therefore, E

Bunuel · Answer

Your rephrasing of the question is not accurate. "Is x^2 > x^3?" can be rephrased as: Is 1 > x and x ≠ 0? https://gmatclub.com/forum/download/file.php?id=71023 I recall you providing links to study inequality theory. Without a solid foundation, there's a risk of repeatedly making the same mistakes. Here are those links once again: 9. Inequalities Theory Inequalities Made Easy! Inequalities: Tips and hints Arithmetic with Inequalities Wavy Line Method Application - Complex Algebraic Inequalities Solving Quadratic Inequalities: Graphic Approach Inequalities - Quadratic Inequalities Graphic approach to problems with inequalities Inequalities trick INEQUATIONS(Inequalities) Part 1 INEQUATIONS(Inequalities) Part 2 Questions Inequality and absolute value questions from my collection DS Questions PS Questions For more check Ultimate GMAT Quantitative Megathread Hope it helps. download.gif

Is x^2 > x^3 (1) x^3 > 0 (2) x ≠ 1

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