Competition problem — Algebra — Maths Olympiad Prep

Library / /15 of 520

Algebra Difficulty 1.7 Junior Find the answer

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?

Pick one

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 $\frac{50}{60}=\frac{5}{6}=5 \cdot 16.\overline{6}=83.\overline{3} \approx \boxed{\textbf{(D)}\ 83}$ .

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.