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Problem 115

Algebra Difficulty 1.3 Multiple choice CEMC Gauss (Grade 7) · Canada · 2017

The sum of three consecutive integers is 153. The largest of these three integers is

Pick one

Official solution

The mean (average) of three integers whose sum is 153 is $\frac{153}{3}=51$ .

The mean of three consecutive integers equals the middle of the three integers.

That is, 51 is the middle integer of three consecutive integers and so the largest of these integers is 52.

(We may check that $50+51+52=153$ .)

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