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Problem 327

Number theory Difficulty 2.4 Multiple choice CEMC Gauss (Grade 8) · Canada · 2020

In the addition shown, each of $P$ , $Q$ and $R$ is a digit.

The value of $P+Q+R$ is

Pick one

Official solution

Abdul is 9 years older than Susie, and Binh is 2 years older than Susie, and so Abdul is $9-2=7$ years older than Binh.
For example, if Susie is 10 years old, then Abdul is $9+10=19$ , Binh is $2+10=12$ , and Abdul is $19-12=7$ years older than Binh.

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