Numerical answer
The average of 11 numbers is 60. The average of the first six numbers is 58 and the average of the last six numbers is 65. What is the sixth number?
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Answer: 78
The sixth number is counted in both the 'first six' and the 'last six'.
Sum of first six = 6 × 58 = 348; sum of last six = 6 × 65 = 390; sum of all eleven = 11 × 60 = 660.
348 + 390 = 738 counts every number once and the sixth number twice, so the sixth number = 738 − 660 = 78.
Sum of first six = 6 × 58 = 348; sum of last six = 6 × 65 = 390; sum of all eleven = 11 × 60 = 660.
348 + 390 = 738 counts every number once and the sixth number twice, so the sixth number = 738 − 660 = 78.
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