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The average of 13 numbers is 75. If the average of the first six numbers is 69 and the average of the last six numbers is 80, what is the 7th number?

1. 81
2. 82
3. 83
4. 84

Correct answer: 81

Solution

The sum of all 13 numbers is 1375 = 975. The sum of the first six is 669 = 414 and the sum of the last six is 680 = 480. Since these two groups cover 12 numbers and together include the 7th number once each, the 7th number is 414 + 480 - 975 = 81.

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