Question

To be eligible for a particular ride at an amusement park, a person must be at least 12 years old and must be between 50 and 80 inches tall, inclusive. Let age represent a person’s age, in years, and let height represent the person’s height, in inches. Which of the following expressions evaluates to true if and only if the person is eligible for the ride? a) (age ≥ 12) AND ((height ≥ 50) AND (height ≤ 80)) b) (age ≥ 12) AND ((height ≤ 50) AND (height ≥ 80)) c) (age ≥ 12) AND ((height ≤ 50) OR (height ≥ 80)) d) (age ≥ 12) OR ((height ≥ 50) AND (height ≤ 80))

Answer 1

Answer: A

Explanation:

This is a system of inequalities... so let's start with age. They said "at least 12 years old", which means that the person CAN BE 12. So this person must be 12+. So this inequality is represented as (age ≥ 12)- 12 or older.

Height: they say that the person must be between 50 & 80 inches tall, INCLUSIVE- which means that the person CAN BE 50 or 80 incles tall as well. Let's start with 50. The person must be 50 inches or taller, so that's represented as (height ≥ 50). The person must also be 80 inches or less, which is represented as (height ≤ 80). Now, we must remember that you need to be within ALL of these inequalities to be able to ride the ride, so NONE OF THESE are either/or statements. The person MUST BE 12 or older, they MUST BE 50 inches or more, and they MUST BE 80 incles or less. Hence, our answer is A.

Hope that helped!