Lesson: Fractional Exponents

Rate this video: 
5

Comment on Fractional Exponents

Please help me with this one.

Is 3^(a²/b) < 1 ?
(1) a < 0
(2) b < 0
gmat-admin's picture

TARGET QUESTION: Is 3^(a²/b) < 1 ?

This is a great candidate for REPHRASING the target question. Notice that, if order for 3^k < 1, it must be the case that k < 0.

So, in order for 3^(a²/b) < 1, it must be the case that a²/b < 0 (i.e,, a²/b must be negative). So, let's REPHRASE our target question as....

REPHRASED TARGET QUESTION: Is a²/b < 0?

STATEMENT 1: (1) a < 0
There are several values a and b that satisfy statement 1. Here are two:
CASE A: a = -1 and b = -1. In this case a²/b = (-1)²/(-1) = -1. Here, a²/b < 0
CASE B: a = -1 and b = 1. In this case a²/b = (-1)²/(1) = 1. Here, a²/b > 0
Since we cannot answer the REPHRASED TARGET QUESTION with certainty,
statement 1 is NOT sufficient.

STATEMENT 2: b < 0
There are several values a and b that satisfy statement 2. Here are two:
CASE A: a = 1 and b = -1. In this case a²/b = (1)²/(-1) = -1. Here, a²/b < 0
CASE B: a = 0 and b = -1. In this case a²/b = (0)²/(-1) = 0. Here, a²/b = 0 (in other words, a²/b is NOT less than 0)
Since we cannot answer the REPHRASED TARGET QUESTION with certainty,
statement 2 is NOT sufficient.

STATEMENTS 1 and 2 COMBINED
If a < 0, then a CANNOT equal 0, which means a² is POSITIVE
If b < 0, then b is NEGATIVE
So, a²/b = POSITIVE/NEGATIVE = NEGATIVE
In other words, a²/b < 0
Since we can answer the REPHRASED TARGET QUESTION with certainty, the combined statements are sufficient.
Answer: C

Add a comment

Tweet about our course!

If you're enjoying our video course, help spread the word on Twitter.

Ask on Beat The GMAT

If you have any questions, ask them on the Beat The GMAT discussion forums. The average response time is typically less than 30 minutes.

Learning Guide

Our step-by-step Learning Guide will help direct your studies and ensure that you cover everything that the GMAT tests.