Question

The average of 6 numbers is 30. If the average of the first four is 25 and that of the last three is 35, the fourth number is
A.25
B.30
C.35
D.40

Answer 1

Hint: For finding the average \[{4^{th}}\] number, we will first find the total sum of all the 6 numbers using the average. Then we will find the sum of the first 4 numbers using their average and then the sum of last three numbers using the average of the last 3 numbers that is given. Then as the \[{4^{th}}\] number will be common in the sum of first 4 and last 3 numbers, when we add both these sums we will get a number in which the \[{4^{th}}\] number was added twice. So to find that \[{4^{th}}\] number we will subtract the sum of all 6 numbers from this new sum we have got.

Complete step-by-step answer:
First of all the average of 6 numbers is given as 30. Thus the total sum of these 6 numbers will be given as \[30 \times 6 = 180\].
Now it is also given in the question, that the average of the first 4 numbers is 25, so the sum total of the first 4 numbers will be \[25 \times 4 = 100\].
The third condition is given that the average of the last 3 numbers is 35, so their sum total will be \[35 \times 3 = 105\].
Now if we add both these sums, we will get \[100 + 105 = 205\]. Here we must notice that in the first 4 numbers and the last 3 numbers the \[{4^{th}}\] number will be common, thus it gets added twice. So if we subtract the sum of 6 numbers from this new sum, we will get to know which that \[{4^{th}}\] number is.
Thus, on subtracting we get \[205 - 180 = 25\].
Hence, 25 was the \[{4^{th}}\] number which got added twice.
Hence, option (A) is the correct option.

Note: This question is simply based on logical reasoning. There are certain clues which ease the question. One of them is that there are ‘6 numbers’, then it is given the ‘average of first 4 numbers’ and then ‘average of last 3 numbers’. If we realize 3 and 4 add up to give 7 thus indicating that there is a common number and we have to go by that approach.