Library / UKMT Senior Mathematical Challenge /164 of 212

UKMT Senior Mathematical Challenge, 2024

Number theory Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Let $x$ and $y$ be positive integers such that $\frac{1}{x}+\frac{1}{y}=\frac{1}{20}$ . What is the maximum possible value of $y$ ?

(A) $40$ (B) $60$ (C) $240$ (D) $420$ (E) $480$

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

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: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.