PSAT Math Multiple-Choice Question 608: Answer and Explanation

Question: 608

A person can ride a roller coaster at an amusement park if he or she is between 36 and 72 inches tall. Which of the following inequalities models all possible values of permitted heights in inches for the ride?

• A. |x - 36| < 72
• B. |x - 38| < 34
• C. |x - 30| < 42
• D. |x - 54| < 18

Correct Answer: D

Explanation:

(D) Recognize that those who are allowed to ride are the ones who aren't too far in either direction from the mean of the permitted heights. If you take the mean height of the constraints, you get:

72 - 54 = 18 and 36 - 54 = -18. Therefore, anyone who is less than 18 units away from 54 is allowed to ride, which is what choice (D) says.

If you didn't recognize this, you could use the process of elimination. You could pick heights that aren't allowed to ride. If you plug in a height that isn't allowed to ride but the inequality is still true, then you'd know that you could eliminate the choice. For instance:

Choice (A): |35 - 36| = 1. Since 1 is less than 72, we can rule out this answer choice.

Choice (B): |35 - 38| = 3. Since 3 is less than 34, we can rule out this answer choice as well.

Choice (C): |35 - 30| = 5. Since 5 is less than 42, we're left with choice (D).