PSAT Math Multiple-Choice Question 478: Answer and Explanation

Question: 478

David is trying to take up to 31 unique photos, one for each day in January. He has already taken 4 nature photos and 7 architectural photos. Which of the following inequalities represents all possible values of p if p represents the remaining number of photos David could take over the month of January?

• A. 0 ≤ 31 – (4 + 7) – p
• B. 31 ≤ p – 11
• C. 0 ≥ 31 – (4 + 7) – p
• D. 31 ≥ p – 11

Correct Answer: A

Explanation:

A

The question asks for an inequality that models a specific situation. Translate the English to math in bite-sized pieces. David is trying to take up to a certain number of photographs, p, so that he has up to 31 unique photographs. Since David can take up to 31 photographs and has already taken 11 photographs (4 nature photos and 7 architectural photos), these will need to be subtracted from the possible total of 31 as will the remaining photographs, p, he could take. This situation can be expressed as 31 – (4 + 7) – p. Eliminate (B) and (D). The difference between the remaining answers is the direction of the inequality symbol. To determine which is right, try picking a number for p and using it in the remaining answer choices. Set p = 2 and solve to get 31 – (4 + 7) – 2 = 18. Only (A) represents this situation since 0 ≤ 18. The correct answer is (A).