Maths Olympiad Prep

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Algebra Difficulty 4.9 AIME Find the answer

Let ZZ be as in problem 15. Let XX be the greatest integer such that XZ5|X Z| \leq 5. Find XX.

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Problems 13-15 go together. See below.

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.