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The average of a group of 9 numbers is 45. If the first five numbers have an average of 42 and the last five numbers have an average of 49, what is the fifth number?

1. 48
2. 50
3. 52
4. 54

Correct answer: 50

Solution

Total of 9 numbers = \(9\times45=405\). Sum of first five = \(5\times42=210\), and sum of last five = \(5\times49=245\). Their sum counts the fifth number twice, so fifth number = \(210+245-405=50\).

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