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Problem 459

Combinatorics Difficulty 2.8 Multiple choice CEMC Gauss (Grade 8) · Canada · 2012

In downtown Gaussville, there are three buildings with different heights: The Euclid (E), The Newton (N) and The Galileo (G). Only one of the statements below is true.

The Newton is not the shortest.
The Euclid is the tallest.
The Galileo is not the tallest.

Ordered from shortest to tallest in height, the buildings are

Pick one

Official 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 $\frac{190}{100}=1.9$ .

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