A set of fifteen numbers has an arithmetic mean of 42 . The mean of the first eight numbers is 39 , while the mean of the last eight numbers is 44 . The value of the eighth number is

Correct option is C

Given:
Mean of 15 numbers = 42
Mean of first 8 numbers = 39
Mean of last 8 numbers = 44
Formula Used:
Sum = Mean × Number of observations
Overlapping term = (Sum of first n terms + Sum of last n terms) - Total Sum
Solution:
Calculate the total sum of all 15 numbers.
Total Sum = 15 × 42 = 630
Calculate the sum of the first 8 numbers.
Sum of first 8 = 8 × 39 = 312
Calculate the sum of the last 8 numbers.
Sum of last 8 = 8 × 44 = 352
Since the 8th number is counted twice (once in the first 8 and once in the last 8), we can find its value by adding the two subgroup sums and subtracting the total sum.
Value of 8th number = 312 + 352 - 630
Value of 8th number = 664 - 630 = 34
Final Answer
So the correct answer is (c)