The correct answer is B.See the question again >
Which value is bigger?
The exponent in this question is astronomical—a good indicator that we should Compare rather than Calculate. There is no way that the GRE wants us to calculate the 231st root of a number. Instead, our job will be to use what we know about the properties of exponents to compare the value of x with -1. First, we can infer from the centered information that x is a negative number, since only negative numbers would "stay negative" when raised to an odd power. Based on this knowledge, we know that x is negative, but is it less than -1?
Let's think about what would happen if x were between 0 and -1. If that were the case, and we raised it to a big power, the value would just get closer to closer to zero. In order for x231 to equal -4000, x must be more negative than -1.
Therefore, even though we can't calculate the value of x, we can compare it to -1 and know that Quantity A is less than Quantity B. The correct answer is (B).
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