GMAT Math: Data Sufficiency – Inequalities^(Exponents) – What You Need To Know

Step 1) The first thing I notice is that one exponent is odd and the other is even. So I immediately know what it’s testing.

Step 2) I know I need to check positive and negative…but I also need to check fractions as well.

Check positive/negative:
If x = 2, then of course x^3 > x^2 [GOOD]
If x= -2, then x^3 is NOT > x^2 [NO GOOD]

So (A) and (D) are no good since there’s inconsistency here with GOOD/NO GOOD.
For now, I don’t need to check fractions. Just evaluate (2) for now.

Step 3) Evaluating (2): x^2 > x
Genearlly, squaring a number means it gets bigger. BUT–I know there’s an exception–FRACTIONS!
If x = 1/2, then (1/2)^2 = (1/4) 
So when you square a fraction, it actually gets smaller!
OK, so (2) is telling us: “Let’s use only non-fractions.”

Obviously, if we plug in a normal number like 3, it’s gonna be a [TRUE] statement.
What happens if we plugin a negative number to x^3 > x^2?
Try x=-2. Well, then you’d get -8>+4 [FALSE].
So with x=+2, you get TRUE, but with x=-2, you get FALSE. .

So since you sometimes get FALSE and sometimes get TRUE—then you know this conflict means (B) is NO GOOD!


Step 4) But what about if you combine (1) and (2) together.

Well, (1) basically tells us we can restrict x to be positive.
(2) basically tells us we can restrict x to be only non-fractions.

So what if we only use x values that are positive AND non-fractions. That means x>1.

Can we answer this original question definitively?

Is x^3 > X^2? 

Well, when we only use x>1, then this statement is ALWAYS true. So voila!

When we combine (1) and (2) we can restrict the scope of possible X’s to only those that are POSITIVE and NON-FRACTIONS–which means x>1.

Turns out this works out great. So we can choose (C) is the final answer.

Table of Contents | See Pricing

Verbal Videos: Sentence Correction | Critical Reasoning | Reading Comprehension
Quant Videos: Problem Solving | Data Sufficiency