PSAT Math Multiple-Choice Question 154: Answer and Explanation

Question: 154

The table below shows the daily attendance of a Physics and a Biology class each day of a particular week.Daily Attendance

Day	Physics	Biology
Monday	25	32
Tuesday	27	25
Wednesday	23	32
Thursday	31	21
Friday	25	28

Based on the information in the table, which of the following statements is true?

• A. Both the mode and the range for the Physics class are less than the mode and range for the Biology class.
• B. Both the mode and the range for the Physics class are greater than the mode and range for the Biology class.
• C. The mode for the Physics class is less than the mode for the Biology class, but the range for the Physics class is greater than the mode for the Biology class.
• D. The mode for the Physics class is greater than the mode for the Biology class, but the range for the Physics class is less than the mode for the Biology class.

Correct Answer: A

Explanation:

A

The question asks which statement is true, and the statements refer to mode and range. Begin with the easier statistic, which is mode. By definition, the mode of a list of numbers is the number that appears the most often. For the Physics class, 25 is the only number that appears more than once, so 25 is the mode. Similarly, for the Biology class, 32 in the only number that appears more than once, so 32 is the mode. Since the mode for Physics is less than the mode for Biology, eliminate (B) and (D). Now check the range, which is, by definition, the difference between the greatest and least number in a list. For the Physics class, the range is 31 - 23 = 8. For the Biology class, the range is 32 - 21 = 11. Since the range for the Physics class is less than the range for the Biology class, eliminate (C). The correct answer is (A).