The average of 15 numbers is 80. The average of the first 6 numbers is 72. The average of the next 6 numbers is 25% more than the…

Question

The average of 15 numbers is 80. The average of the first 6 numbers is 72. The average of the next 6 numbers is 25% more than the average of the first 6 numbers. The 13th number is 8 more than the 15th number, and the 14th number is 10 less than the 15th number. What is the average of the 13th and 14th numbers?

1. A. 70.89
2. B. 85
3. C. 75.67 (Correct answer)
4. D. 80.65

Correct Answer

Option C — 75.67

Detailed Solution & Explanation

The correct answer is 75.67.

Key Points

• Total of 15 numbers = 15 × 80 = 1200.
• First 6 sum = 6 × 72 = 432.
• Next 6 average = 72 × 1.25 = 90, so sum = 540.
• The last 3 sum = 1200 − 432 − 540 = 228.
• Let the 15th = x: (x+8) + (x−10) + x = 228 → 3x − 2 = 228 → x ≈ 76.67. Then 13th ≈ 84.67 and 14th ≈ 66.67, so their average = (84.67 + 66.67)/2 ≈ 75.67.
• Break a multi-group average into running sums, then set up one equation in the unknown term.