Last school year, each of the 200 students at a certain high school at

Hello Rickooreo,

You have translated Statement 2 incorrectly and thus, have confused yourself.
Statement 2: “Last school year, the average number of cultural performances attended per student was 4.”

We shall look at the incorrect translation you have used, followed by an example to help you understand the correct idea completely, and then finally the correct translation.
Let’s start one-by-one.

INCORRECT TRANSLATION

While analyzing statement 2, you considered only the students who attended at least 1 cultural performance as proven by your formula for average: \(\frac{(Total number of student attendees at all the cultural performances)}{(Number of students who attended at least 1 cultural performance)}\)
This shows that you translated statement 2 as “the average number of cultural performances attended per student attending at least 1 performance was 4.”
Can you notice how this differs from the original statement?
Statement 2 talked about the average per student. This is ALL the students in the school and not just those who attended the cultural performances.

Look at the following example to understand this more deeply:

EXAMPLE

Suppose 5 students planted 15, 10, 0, 7, 13 plants respectively during an environment drive.

• Now, if I ask you to calculate the average number of plants planted per student, what would you do?
  
  • \(\frac{(Number of all plants)}{4}\) or \(\frac{(Number of all plants)}{5}\)?
• Well, we would obviously consider all 5 students! Just because one student planted no plants, it doesn’t mean he will not be considered in average calculations.

Having thoroughly understood this, let’s look at the correct translation now.

CORRECT TRANSLATION

As in the example shown above, when calculating the average number of cultural performances attended per student, we must consider all the students in the school.
Hence, the average would be calculated as: \(\frac{(Total number of student attendees at all the cultural performances)}{(Total Number of students in the school)}\)
So, even if only 100 students attended at least one cultural performance, the average would still be calculated for all 200 students.
4 = \(\frac{Total number of student attendees at all the cultural performances}{Total Number of students in the school}\)
4 = \(\frac{(Total number of student attendees at all the cultural performances)}{200}\)
Total number of student attendees at all the cultural performances = 200 x 4 = 800

Here on, you already know how to get the final answer. I hope this resolves your confusion and you will not make this error in the future. 😊

Best Regards,
Ashish Arora
Quant Expert, e-GMAT