PSAT Math Multiple-Choice Question 384: Answer and Explanation

Question: 384

A group of 150 freshmen were randomly selected for a survey that asked whether they were excited to continue their foreign language studies in the next school year. Of this group, 93 said they were excited to continue, 37 said they were not excited to continue, and 20 said they did not know yet whether they were excited to continue. Using the data from this survey and the table, which of the following is most likely a valid conclusion?

• A. About 130 freshman students do not know yet whether they are excited to continue foreign language studies next year.
• B. About 240 freshman students are not excited to continue foreign language studies next year.
• C. About 440 freshman students are not excited to continue foreign language studies next year.
• D. About 740 freshman students are excited to continue foreign language studies next year.

Correct Answer: D

Explanation:

D

Difficulty: Medium

Category: Surveys and Data Samples

Strategic Advice: Find what you need about the group from the follow-up survey. Then, extrapolate to see which answer choice matches your calculations.

Getting to the Answer: First, determine the number of freshmen who fall into each of the three groups of the follow-up survey:

Percent excited to continue:

Percent not excited to continue:

Percent who do not know yet whether they are excited to continue:

There are 1,195 freshmen in the original survey, making the number excited to continue 0.62 × 1,195 = 740.9 ≈ 741; the number not excited to continue 0.2467 × 1,195 = 294.8 ≈ 295; and the number who do not know yet whether they are excited to continue 0.1333 × 1,195 = 159.3 ≈ 159. Choice (D) states that about 740 freshmen are excited to continue their foreign language studies, which matches these findings. Choice (D) is therefore correct.