PSAT Math Multiple-Choice Question 657: Answer and Explanation

Question: 657

Which of the following is a logical conclusion about the data about Sam's age and height percentile?

I. Sam's height grew exponentially quickly between ages 12 and 18.

II. Sam's height relative to that of other men was lower when he was less than 5 years old than when he was between 10 and 15 years old.

III. Sam continued to experience changes in his height between the ages of 18 and 22.

• A. I only
• B. II only
• C. II and III only
• D. I, II, and III

Correct Answer: B

Explanation:

(B) Go through each possibility.

Option I: Sam's height percentile actually decreased between ages 12 and 18, so it's extremely unlikely that he experienced exponential growth. By ruling this out, we can eliminate choices (A) and (D).

Option II: When Sam was less than 5 years old, his height percentile ranged between about the 42nd percentile and the 50th percentile. Between the ages of 10 and 15, he ranged between the 54th and 60th percentile. Therefore, he was taller than more men during these later years, making this statement true.

Option III: We can't say for sure that Sam's height changed between these years, although it's probable. Percentiles measure only your status compared to others. We know only that Sam's height compared to others changed, not that his absolute height changed.

Therefore, the answer is choice (B).