Maths Olympiad Prep

Library / UKMT Senior Mathematical Challenge /180 of 212

UKMT Senior Mathematical Challenge, 2020

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

The letters pp, qq, rr, ss and tt represent different positive single-digit numbers such that p−q=rp - q = r and r−s=tr - s = t. How many different values could tt have?

(A) 66 (B) 55 (C) 44 (D) 33 (E) 22

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.