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Problem 59

Number theory Difficulty 1.1 Multiple choice CEMC Gauss (Grade 7) · Canada · 2017

When two integers between 1 and 10 are multiplied, the result is 14. What is the sum of these two integers?

Pick one

Official solution

There are only two different products of two positive integers whose result is 14.

These are $2\times7$ and $1\times14$ .

Since the two integers must be between 1 and 10, then the product must be $2\times7$ .

The sum of these two integers is $2+7=9$ .

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