Arithmethic Mean
Algebra
Level
2
Josie want to calculate the Arithmetic Mean of the first 15 positive integers. First she summed all numbers, but she forgot to sum 2 consecutive numbers. After dividing the total sum by 15, the answer was 7. What is the product of the 2 numbers that she forgot to sum?
The answer is 56.
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1 solution
The sum of the first 15 positive integers is 1 2 0 . The total found by Josie was 1 5 ⋅ 7 = 1 0 5 . Then the two consecutive numbers must sum to 1 5 , so they are 7 and 8 . Therefore, the answer is 5 6 .