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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 x^231 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).