Library / CEMC Gauss (Grade 8) /362 of 525

CEMC Gauss (Grade 8), 1999

Number theory Difficulty 2.0 Junior Find the answer Canada

Kalyn writes down all of the integers from $1$ to $1000$ that have $4$ as the sum of their digits. If $\frac{a}{b}$ (in lowest terms) is the fraction of these numbers that are prime, then $a+b$ is

(A) $5$ (B) $4$ (C) $15$ (D) $26$ (E) $19$

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: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.