The mean of 11 numbers is 35. If the mean of the first 6 numbers is 32 and that of the last 6 numbers is 37, find the 6th number.
Answer: B
Total sum of 11 numbers = 11 × 35 = 385.
Sum of the first 6 numbers = 6 × 32 = 192.
Sum of the last 6 numbers = 6 × 37 = 222.
The 6th number is included in both the 'first 6' and 'last 6' groups. So, if we add the sum of the first 6 and the last 6, the 6th number is counted twice.
Sum of (first 6 + last 6) = 192 + 222 = 414.
This sum is equal to (Sum of all 11 numbers) + (6th number).
414 = 385 + (6th number)
6th number = 414 - 385 = 29.