2006 AMC 8 Problems/Problem 12

Problem

Antonette gets $70 \%$ on a 10-problem test, $80 \%$ on a 20-problem test and $90 \%$ on a 30-problem test. If the three tests are combined into one 60-problem test, which percent is closest to her overall score?

$\textbf{(A)}\ 40\qquad\textbf{(B)}\ 77\qquad\textbf{(C)}\ 80\qquad\textbf{(D)}\ 83\qquad\textbf{(E)}\ 87$

Solution

$70 \% \cdot 10=7$

$80 \% \cdot 20=16$

$90 \% \cdot 30=27$

Adding them up gets $7+16+27=50$ . The overall percentage correct would be $\frac{50}{60}=\frac{5}{6}=5 \cdot 16.\overline{6}=83.\overline{3} \approx \boxed{\textbf{(D)}\ 83}$ .

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2006 AMC 8 Problems/Problem 12

Problem

Solution