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The average of 15 numbers is 72. The average of the first 6 numbers is 65. The average of the next 5 numbers is 20% higher than the average of the first 6. The 12th number is 8 less than the 15th, the 13th is 5 greater than the 15th, and the 14th number is 78. What is the average of the 12th and 13th numbers?

1. 73.5
2. 80
3. 78
4. 76.5

Correct answer: 73.5

Solution

Total sum of 15 numbers is \(15\times72=1080\). Sum of first 6 numbers is \(6\times65=390\), and sum of next 5 numbers is \(5\times78=390\). So the first 11 numbers sum to 780, leaving 300 for the last four numbers. Using the relations, the 15th number is 75, so the 12th and 13th are 67 and 80, whose average is 73.5.

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