aniketm.87@gmail.com wrote:

Prof Liu gave the same quiz to the students in her morning class and in her afternoon class. the average score for the two classes combined was 84. which class had more students ?

(1) The average score for the students in the morning class was 80

(2) the average score for the students in the afternoon class was 86

This is a great question testing the foundations of weighted averages. We must remember that the weighted average will always be closer to the average of the group that has a larger quantity. Let’s test this theory with a simple example.

Let’s say there are 5 women in a room with an average age of 40 and 3 men in a room with an average age of 20. The weighted average age of all the people in the room is as follows:

(5 x 40) + (3 x 20)/(5 + 3) = (200 + 60)/8 = 260/8 = 32.5 years old

Notice that the weighted average of the ages of all people in the room is closer to 40 (the average age of the 5 women) than it is to 20 (the average age of the 3 men). The reason for this is that there are a greater number of women than there are men.

Let’s apply this principle to the above problem.

We are given that the combined average score for the morning and afternoon class is 84. We need to determine which class had more students.

Statement One Alone:

The average score for the students in the morning class was 80.

Since we do not have any information regarding the average score of the afternoon class, we do not have enough information to answer the question. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The average score for the students in the afternoon class was 86.

Since we do not have any information regarding the average score of the morning class, we do not have enough information to answer the question. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using the information from statements one and two, we see that the average score of the morning class was 80 and that the average score from the afternoon class was 86. Using the example provided above, we know that since the average score from the afternoon class is closer to the combined (i.e., weighted) average of 84, there are more students in the afternoon class.

Answer: C

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