GMAT Practice Question: State X has 77 acres designated as wilderness, which is 0.0003 percent of its total acreage....
Question
State X has 77 acres designated as wilderness, which is 0.0003 percent of its total acreage. Which of the following expresses the total acreage of State X ?
- 3\left(10^{4}\right)(77)
- 3\left(10^{6}\right)(77)
- \frac{\left(10^{2}\right)(77)}{3}
- \frac{\left(10^{4}\right)(77)}{3}
- \frac{\left(10^{6}\right)(77)}{3}
Topics: word problems, percentages, conversions
Solution
Step 1
We first choose a variable for the total acreage of State X.
T = \text{total acreage of State X}
Step 2
We translate the statement \textbf{"77 acres designated as wilderness, which is 0.0003 percent of its total acreage"} into an equation.
77 = \frac{0.0003}{100} \times T
Step 3
We isolate the total acreage by dividing both sides by the percentage coefficient.
T = \frac{77}{\frac{0.0003}{100}}
Step 4
We simplify the percentage fraction in the denominator to scientific notation.
\frac{0.0003}{100} = 0.000003 0.000003 = 3 \times 10^{-6}
Step 5
We then simplify and express the total acreage in scientific notation.
T = \frac{77}{3 \times 10^{-6}} = \frac{77}{3} \times 10^{6}
Answer
E
