How to Solve tricky GMAT Negative Fraction with Exponents?

To answer questions that involve negative fractions and exponents, you have to know the following rules:

1) Fraction with one in the numerator always obeys the following rule

1/High Number < 1/Low Number

What confuses test takers is the definition of High Number and Low Number when it comes to negative denominator

2) For negative numbers, remember this one rule

-5 < -3

- (Higher Positive Number) < - (Lower Positive Number)

3) When it comes to negative fraction, the rule reverses

-(1/High Number) > - (1/Low Number)

4) Even power of negative fraction is positive and odd power of negative fraction is negative

(-(a/b)) ^n is positive if n is even and negative is n is odd

Q) If a = -1/4 & b = -1/3, which of the following is true?

a) a^2 < b^3
b) a^3 > b^2
c) a^4 > b^6
d) a^3 < b^3
e) a^2 < b^4

Solution

Once you know the four rules, it becomes easier to eliminate answer choices. The question asks us to find the cube and square of two negative fractions a and b

a=-1/4 b=-1/3

According to Rule 3

a > b

If you look at the answer choices, a is represented as a^2 a^3 and a^4

And b is represented as b^2 b^3 b^4 , b^5 and b^6

Arrange the signs of the fraction, before solving it

a^2 = +
a^3 = -
a^4 = +
b^2 = +
b^3 = -
b^4 = +
b^5 = -
b^6 = +

Now eliminate answer choice based on signs

+ > -

Eliminate A, B and D

Answer Choices remaining C and D

c) a^4 > b^6
e) a^2 < b^4

Let us look at answer Choice D as both are relatively smaller powers

Solving e)

1/16 <   1/81

This is false. Hence, answer choice C is the Correct Answer. By adopting process of elimination techniques, you can avoid lengthy calculations.