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Problem 201

Number theory Difficulty 1.5 Multiple choice CEMC Gauss (Grade 8) · Canada · 2017

The number of even integers between 1 and 103 is the same as the number of odd integers between 4 and

Pick one

Official solution

Henry was slower than Faiz and thus finished the race behind Faiz.

Ryan was faster than Henry and Faiz and thus finished the race ahead of both of them.

From fastest to slowest, these three runners finished in the order Ryan, Faiz and then Henry.

Toma was faster than Ryan but slower than Omar.

Therefore, from fastest to slowest, the runners finished in the order Omar, Toma, Ryan, Faiz, and Henry.

The student who finished fourth was Faiz.

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