Library / CEMC Gauss (Grade 8) /278 of 525

CEMC Gauss (Grade 8), 2024

Number theory Difficulty 1.3 Junior Find the answer Canada

In a drawer, the ratio of the number of spoons to the number of
forks is $1:2$ . The total number of
spoons and forks in the drawer cannot be equal to

Pick one

Solution

The ratio of the number of spoons to the number of forks is $1:2$ , which means that for each spoon in
the drawer, there are $2$ forks in
the drawer.

That is, the spoons and forks in the drawer can be separated into groups
of $3$ ( $1$ spoon and $2$ forks), and thus the total number of
spoons and forks in the drawer must be a multiple of $3$ .

Each of the answers $12$ , $6$ , $18$ , and $3$ is a multiple of $3$ .

The only answer given that is not a multiple of $3$ is $10$ , and so the total number of spoons and
forks in the drawer cannot be $10$ .

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

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