Arithmatic Mean Question Answers

CAT Sample Questions in Math - Averages

Question 4 the day : April 13, 2004
The question for the day is from the topic averages. It is a question based on the concept of simple average

Question
The average of 5 quantities is 6. The average of 3 of them is 8. What is the average of the remaining two numbers?

1. 6.5
2. 4
3. 3
4. 3.5

Correct choice is (3) and the Correct Answer is 3

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Explanatory Answer

The average of 5 quantities is 6.
Therefore, the sum of the 5 quantities is 5 * 6 = 30.

The average of three of these 5 quantities is 8.
Therefore, the sum of these three quantities = 3 * 8 = 24

The sum of the remaining two quantities = 30 - 24 = 6.
Average of these two quantities = = 3.

Note:

From the answer choices, you can eliminate choice (1) and choice (2) even without solving the question.

As the average of the 5 quantities is 6 and the average of three of these five is 8, the average of the remaining two should be a value that is less than 6. So choice (1) which is more than 6 can be eliminated.

If there were a total of four quantities and the overall average was 6 and the average of 2 of the four were 8, then the average of the remaining two would have been 4. i.e., the simple average of 4 and 8 is 6. However, we have unequal number of quantities. Hence, choice (2) can be eliminated.