PSAT Math Multiple-Choice Question 153: Answer and Explanation

Question: 153

The table below shows the maximum weights that each of eight people at a gym can bench press.Bench Press Weights

Person	Pounds
Aaron	40
Beth	30
Carey	110
Donna	230
Ethan	130
Fay	70
Gino	60
Helen	170

What is the difference between the maximum weight, in pounds, that Helen can bench press and the median weight, in pounds, of all eight people?

• A. 10
• B. 65
• C. 70
• D. 80

Correct Answer: D

Explanation:

D

The question asks for the difference between the maximum weight that Helen can lift and the median, so find the median. The median of a list of numbers is the middle number when all values are arranged in order. In lists with an even number of items, the median is the average of the middle two numbers. Put the maximum weights in order from least to greatest: 30, 40, 60, 70, 110, 130, 170, 230. Find the middle number by crossing out numbers in pairs starting from the outside. Cross out 30 and 230. Cross out the next least and next greatest: 40 and 170. Cross out the next least and next greatest: 60 and 130. Only 70 and 110 remain. Since there is no single middle number, find the average of the middle two to get as the median. Find the difference between this value and the maximum weight that Helen can lift. The maximum weight that Helen can lift is 170 pounds, so the difference is 170 - 90 = 80. The correct answer is (D).