CEMC Fermat, 2019

Algebra Difficulty 1.4 Junior Find the answer Canada

The first part of the Genius Quiz has 30 questions and the second part has 50 questions. Alberto answered exactly 70% of the 30 questions in the first part correctly. He answered exactly 40% of the 50 questions in the second part correctly. The percentage of all of the questions on the quiz that Alberto answered correctly is closest to

Pick one

Solution

Alberto answered 70% of 30 questions correctly in the first part.

Thus, Alberto answered $\frac{70}{100} \times 30 = 21$ questions correctly in the first part.

Alberto answered 40% of 50 questions correctly in the second part.

Thus, Alberto answered $\frac{40}{100} \times 50 = 20$ questions correctly in the second part.

Overall, Alberto answered $21+20=41$ of $30+50=80$ questions correctly.

This represents a percentage of $\frac{41}{80}\times 100\% = 51.25\%$ .

Of the given choices, this is closest to 51%.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.