Hard Statistics Question for the SAT with Solution

Today I would like to give a solution to the statistics problem I presented last Wednesday. The original post can be found here: Hard Statistics Question for the SAT

Level 5 Statistics

In Dr. Steve’s AP Calculus BC class, students are given a grade between 0 and 100, inclusive on each exam. Jason’s average (arithmetic mean) for the first 3 exams was 90. What is the lowest grade Jason can receive on his 4th exam and still be able to have an average of 90 for all 7 exams that will be given?

Solution by changing averages to sums: The sum of the first 3 exam grades was 90 ⋅ 3 = 270.

We want the sum of Jason’s 7 exam grades to be 90 ⋅ 7 = 630.

So, we need the sum of the grades on the last three exams to be

630 – 270 = 360.

The maximum grade is 100, and so the most Jason can score on the last 3 exams is 100 ⋅ 3 = 300.

Therefore, on the 4th exam he must score at least 360 – 300 = 60.

Note: To see more details on the strategy used here, go to this page: Changing Averages to Sums

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