M7MBA wrote: ↑

Thu Nov 18, 2021 10:15 am

Last school year, each of the 200 students at a certain high school attended the school for the entire year. If there were 8 cultural performances at the school during the last school year, what was the average (arithmetic mean) number of students attending each cultural performance?

(1) Last school year, each student attended at least one cultural performance
(2) Last school year, the average number of cultural performances attended per student was 4.

Answer: B

Source: Official Guide

Target question: What was the average (arithmetic mean) number of students attending each cultural performance?

Given: 200 students. 8 cultural performances

Statement 1: Last school year, each student attending at least one cultural performance
There are several scenarios that satisfy statement 1. Here are two:
Case a: every student attended exactly 1 performance last year. So, the TOTAL attendance was 200 last year, which means the average number of attendees for each performance = 200/8 = 25
Case b: every student attended exactly 2 performances last year. So, the TOTAL attendance was 400 last year, which means the average number of attendees for each performance = 400/8 = 50
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Last school year, the average number of cultural performance attended per student was 4.
So, the TOTAL attendance was last year = (200)(4) = 800
This means the average number of attendees for each performance = 800/8 = 100
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B