Track / Stage 2 / 69 of 320 #389 of 2604

Problem 389

Combinatorics Difficulty 2.0 Find the answer UKMT Junior Kangaroo · United Kingdom · 2023

There are $66$ cats in my street. I don't like $21$ of them because they catch mice. Of the rest, $32$ have stripes and $27$ have one black ear. The number of cats with both stripes and one black ear is as small as it could possibly be. How many cats have both stripes and one black ear? (A) $5$ (B) $8$ (C) $11$ (D) $13$ (E) $14$

The source for this one didn't record the answer, so there is nothing to check what you type against. Work it on paper and mark yourself against the solution below.

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

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