Question

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?

$40$

$77$

$80$

$83$

$87$

Solution:

Antonette got $0.7\cdot 10=7$ questions right on the first test. Similarly, she got $0.8\cdot 20=16$ and $0.9\cdot 30=27$ problems right on her second and third tests.

Adding these up yields $50$ correct questions. Her score on the combined test would have been $100\cdot \dfrac{50}{60}=83\frac{1}{3}\%$ , closest to $83\%$ .

Thus, D is the correct answer.

2006 AMC 8 Problem 12

Solution:

Problem 12 in Other Years