Digital PSAT Math Practice Question 301: Answer and Explanation

Question: 301

A conference planner will have equal representation of male and female representatives at a breakout session in a meeting room. The session will go ahead as long as people are in the room. Fire marshal regulations stipulate that no more than 60 people are permitted in the room at a given time. Assuming that the breakout session is proceeding and that no other people are in the meeting room other than the m male participants and w female participants, what are the constraints on the values of m and w?

• A.
• B.
• C.
• D.

Correct Answer: B

Explanation:

(B) Let m be the number of male participants and w be the number of female participants. You know that no more than 60 people are permitted in the room. So, the total number of males and females in the room must be 60 or less. In other words, m + w ≤ 60. You are also told that there will be an equal number of males and females at the session, so necessarily, m = w. Finally, you know that the breakout session will occur, so there must be at least one person in the room. But, there are an equal number of males and females present, so there must actually be at least 2 people in the room. In particular, there must be at least one male and one female in the room. So, m > 0 and w > 0. Hence, your constraints are