PSAT Math Multiple-Choice Question 543: Answer and Explanation

Question: 543

A new video game is being tested by a focus group. A group of researchers randomly selected people to evaluate, on a check system, the game they just played. The results of the evaluation are shown in the table below.

Video Game Evaluations

Rating	# of People
√–	14
√	29
√+	13
√++	18

A total of 240 people played the video game. Based on the results of the evaluations, about how many people who played the video would have evaluated it as a √+ or higher?

• A. 197
• B. 100
• C. 42
• D. 31

Correct Answer: B

Explanation:

B

The question asks for an estimate of the number of people in a group who would have rated a game at a certain level or higher based on an evaluation completed by a portion of the group. Since the people were randomly selected, the results found in the evaluation should match that of the larger group. To extrapolate the evaluation results, set up a proportion being sure to match up units. In this case, the proportion is based on the ratings of a video game given by members of the group. The total number of people that completed the survey was 14 + 29 + 13 + 18 = 74. Of those, 13 people rating the video game √+ and 18 people rating the video game √++, so the number of people who rated it with a √+ or higher was 13 + 18 = 31. The proportion becomes . Cross-multiply to get 74x = 7,440. Divide both sides by 74 to get x = 100.54. The question asks for an approximation, so round this to 100. The correct answer is (B).