CEMC Fermat, 2026

Algebra Difficulty 1.1 Junior Find the answer Canada

The value of $\dfrac{101^2-101}{100}$ is

Pick one

Solution

Solution 1:

Factoring the numerator and simplifying, we get $\dfrac{101^2-101}{100}=\dfrac{101(101-1)}{100}=\dfrac{101(100)}{100}=101$ .

Solution 2:

Evaluating, we get $\dfrac{101^2-101}{100}=\dfrac{10\,201-101}{100}=\dfrac{10\,100}{100}=101$ .

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.