The average of 17 numbers is 90. The average of the first 7 numbers is 85. The average of the next 7 numbers is 20% more than the average of the first 7 numbers. The 15th number is 6 more than the 17th number, and the 16th number is 4 less than the 17th number. What is the average of the 15th and 16th numbers?
Show answer & explanation
Correct answer: C
Explanation
Answer: 74
Solution:
Total sum of 17 numbers = 17 × 90 = 1530
Sum of first 7 numbers = 7 × 85 = 595
Average of next 7 numbers = 85 + 20% of 85 = 85 × 1.2 = 102
Sum of next 7 numbers = 7 × 102 = 714
Sum of first 14 numbers = 595 + 714 = 1309
Sum of 15th, 16th, and 17th numbers = 1530 − 1309 = 221
Let 17th number = x
- 15th number = x + 6
- 16th number = x − 4
So: (x + 6) + (x − 4) + x = 221
3x + 2 = 221
3x = 219
x = 73
Therefore:
- 15th number = 73 + 6 = 79
- 16th number = 73 − 4 = 69
Average of 15th and 16th numbers = (79 + 69)/2 = 148/2 = 74