GRE Sample Test 4 Quantitative Reasoning 2

In this question, you have a fraction as a base and must consider various values for x, the exponent. Consider what happens when x = −1. We know that ${\left(\frac{1}{4}\right)}^{-1}$ = $\frac{1}{{\left(\frac{1}{4}\right)}^1}$ = 4.
Putting that into the full equation, we get $1-{\left(\frac{1}{4}\right)}^{\mathit{x}}$ = 1 - 4 = - 3
This is not greater than zero, and if x = −2, the result will be even lower, so choices (A) and (B) are out. Next, consider what happens when x = 0. Any base to the zero power equals 1; then
$1-{\left(\frac{1}{4}\right)}^{\mathit{x}}$ = 1 - 1 = 0.
You want the value of x that makes the expression greater than 0, so try x = 1: $1-{\left(\frac{1}{4}\right)}^{\mathit{x}}$ = $1-\left(\frac{1}{4}\right)$ = $\frac{3}{4}$. The answer is (D).