Library / /110 of 122

, 2020

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

How many four-digit numbers $N$ are there, such that half of the number $N$ is divisible by 2, a third of $N$ is divisible by 3 and a fifth of $N$ is divisible by 5?

(A) $1$ (B) $7$ (C) $9$ (D) $10$ (E) $11$

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.