Library / CEMC Gauss (Grade 7) /289 of 462

CEMC Gauss (Grade 7), 2012

Algebra Difficulty 1.8 Junior Find the answer Canada

A quiz has three questions, with each question worth one mark. If 20% of the students got 0 questions correct, 5% got 1 question correct, 40% got 2 questions correct, and 35% got all 3 questions correct, then the overall class mean (average) mark was

Pick one

Solution

Without changing the overall class mean, we may consider that the class has 100 students.

That is, 20 students got 0 questions correct, 5 students got 1 question correct, 40 students got 2 questions correct, and 35 students got 3 questions correct.
The combined number of marks achieved by all 100 students in the class is then, $(20\times0)+(5\times1)+(40\times2)+(35\times3)=0+5+80+105=190.$ Since the 100 students earned a total of 190 marks, then the overall class average was $\frac{190}{100}=1.9$ .

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.