Discussion
The average age of 7 family members is 75 years, but the average age of 6 of them is 74 years. What is the age of the 7th family member ?
Answer: B
The seventh member is 81 years old.
Work with totals rather than averages:
\[ \begin{aligned} \text{total of 7} &= 7 \times 75 = 525 \\ \text{total of 6} &= 6 \times 74 = 444 \\ \text{7th member} &= 525 - 444 = 81 \end{aligned} \]
75 is just the overall average, and 80 or 70 do not come from the totals.
A shortcut: adding the seventh member raises the average of the other six from 74 to 75, so he must be \(74 + 7 \times 1 = 81\) years old.
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