PSAT Math Multiple-Choice Question 393: Answer and Explanation

Question: 393

A runner is training for a marathon. His goal is to run an average of 5 miles per day for the first 10 days of his training. The dot plot above shows the number of miles he ran each day during the first 9 days. How many miles must he run on the 10th day to reach his goal?

• A. 5
• B. 5.5
• C. 6
• D. 6.5

Correct Answer: C

Explanation:

C

Difficulty: Medium

Getting to the Answer: Understanding how averages and sums are connected is the key to answering a question like this. If the average of 10 numbers is 5, then the sum of the 10 numbers must be 50 (because ). Use the dot plot to find the total number of miles the runner has already run. Then, subtract this number from 50. The runner has already run 3.5 + 2(4) + 2(4.5) + 5 + 2(6) + 6.5 = 44 miles, so he needs to run 50 - 44 = 6 miles on the 10th day. Choice (C) is correct.