PSAT Math Multiple-Choice Question 100: Answer and Explanation

Question: 100

P = 2,500 + 135x

The population of County Y, in thousands, can be modeled by the above equation, in which x represents the number of years since the 2010 census. What does the number 135 represent in this equation?

• A. Every year the population of County Y increases by 135 people.
• B. Every 135 years that passes, the population of County Y increases by 2,500 people.
• C. Every 135 years that passes, the population of County Y increases by 250,000 people.
• D. Every year the population of County Y increases by 135,000 people.

Correct Answer: D

Explanation:

D

The question asks for the meaning of a number in context. Start by reading the final question, which asks for the meaning of the number 135. Then label the parts of the equation with the information given. The variable x is the number of years since the 2010 census, so P must be the population of County Y, in thousands. The equation becomes population (thousands) = 2,500 + 135(years since 2010). Next, use Process of Elimination to get rid of answer choices that are not consistent with the labels. Choice (A) refers to an increase in population per year, and the 135 is multiplied by years in the equation. This is consistent with the labels, so keep (A) but check the remaining answers just in case. Choices (B) and (C) both refer to the population increasing by a certain amount every 135 years, so these answers are not consistent with the labels. Eliminate (B) and (C). Choice (D) also refers to an increase in population per year, so keep (D). The difference between (A) and (D) is the value of the increase. The equation represents the population in thousands, so 135 should be multiplied by 1,000 to give 135,000 as the actual population increase. Eliminate (A). The correct answer is (D).