Explanation

First, solve for x:

\(-(x)^3 = 64\)
\((x)^3 = -64\)

The GRE calculator will not do a cube root. As a result, cube roots on the GRE tend to be quite small and easy to puzzle out. What number times itself three times equals –64? The answer is x = –4.

Since x is negative, Quantity A is positive (a negative number times itself four times is positive) and Quantity B is negative (a negative number times itself five times is negative). No further calculations are needed to conclude that Quantity A is greater.

Notice that solving for the value of x here was not strictly necessary. Knowing that the cube root of a negative number is negative gives you all the information you need to solve.

We know, −(x)^3=64
=> x=-4 (x is negative)
(negative x)^(even number) = always positive
(negative x)^(odd number) = always negative

so (negative x)^4 > (negative x)^5
Quantity A will be greater

if \(-(x^3) = 64\), then \(x=-4\).

\(x^4\) = positive number
\(x^5\) = negative number

Quantity A is greater.

No calculation is necessary.