PSAT Math Multiple-Choice Question 634: Answer and Explanation

Question: 634

Katie is interested in running a marathon, which is 26.2 miles long. She just finished a 5-kilometer race, and she wants to see how many 5K races she would have to complete in order to equal a full marathon. Given that there are approximately 0.62 miles in 1 kilometer, how many complete 5K races would Katie have to finish to go at least the distance of a marathon?

• A. 6
• B. 8
• C. 9
• D. 10

Correct Answer: C

Explanation:

(C) Let's first convert the marathon distance to kilometers:

If Katie has to run 42.26 km and if she's doing it 5 km at a time, she would need to run:

races

Therefore, she would need to run a minimum of 9 whole races to run the distance of a marathon.

Alternatively, you could have done dimensional analysis for the last step, canceling out units that you don't want and leaving only the units that you do want. Katie wants to go 42.26 km, and she's running 5 km/race. Cancel out kilometers, so that we're left with number of races:

We again need to round up to 9 so that Katie runs the full marathon distance.