IMC 2019 Q3
3. There are 120 000 red squirrels living in Scotland. This represents 75% of their total UK population.
How many more red squirrels live in Scotland than live in the remainder of the UK?
- A 30 000
- B 40 000
- C 60 000
- D 80 000
- E 90 000
Intermediate Mathematical Challenge 2019, Question 3. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 80 000
First note that three quarters of the UK red squirrels live in Scotland. So one quarter of the UK red squirrels live in the remainder of the UK and the number of such squirrels is therefore one third of the number of red squirrels living in Scotland, which is \(\dfrac{1}{3} \times 120\,000 = 40\,000\).
So the required difference equals 120 000 − 40 000 = 80 000.
Solution © UK Mathematics Trust, from the IMC 2019 solutions. Longer versions with investigations: Solutions and investigations (PDF).