PSAT Math Grid-Ins Question 35: Answer and Explanation

Question: 35

In a certain marathon, 45 percent of the runners were men and the rest were women. The official timekeeper determined that 64 percent of the men and 68 percent of the women completed the marathon in under four hours.

What percent of the runners who completed the marathon in under four hours were women? (Ignore the percent symbol when entering your answer. For example, if the answer is 35.2%, enter 35.2.)

Correct Answer: 56.4 or 56.5

Explanation:

56.4 or 56.5

The question asks for the percent of runners completing the marathon in under four hours that were women. The question doesn't give an actual number for the runners, but percent information about the unknown total is given. Therefore, plug in for the unknown total. Make the total number of runners 1,000. If 45 percent of the runners were men, then 0.45 × 1,000 = 450 of the runners were men. If the rest were women, then 1,000 - 450 = 550 of the runners were women. If 64 percent of the men completed the marathon in under four hours, then 0.64 × 450 = 288 of the men completed the marathon in under four hours. Similarly, if 68 percent of the women completed the marathon in under four hours, then 0.68 × 550 = 374 women completed the marathon in under four hours. The total number of runners who completed the marathon in under four hours is 288 + 374 = 662, so the percent becomes percent of the runners who completed the marathon in less than four hours. The correct answer can be expressed as 56.4 or 56.5.