Maths Olympiad Prep

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Algebra Difficulty 1.4 Junior Find the answer Canada

The sum of the first 100 positive integers (that is, 1+2+3++99+1001+2+3+\cdots+99+100) equals 5050. The sum of the first 100 positive multiples of 10 (that is, 10+20+30++990+100010+20+30+\cdots+990+1000) equals

Pick one

Solution

A translation moves (slides) an object some distance without altering it in any other way.

That is, the object is not rotated, reflected, and its exact size and shape are maintained.

Of the triangles given, the triangle labelled DD is the only triangle whose orientation is identical to that of the shaded triangle.

Thus, DD is the triangle which can be obtained when the shaded triangle is translated.

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