The average of a group of 11 numbers is 61. If the first six numbers have an average of 57 and the last six numbers have an average of 65, what is the sixth number?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 61.
Let the sixth number be x
Total of 11 numbers = 11 × 61 = 671
Sum of first 6 = 6 × 57 = 342
Sum of last 6 = 6 × 65 = 390
Both sums include the 6th number once
So,
342 + 390 − x = 671
⇒ 732 − x = 671
⇒ x = 61