IMC 2020 Q2
2. Which one of these is a multiple of 24?
- A 200
- B 300
- C 400
- D 500
- E 600
Intermediate Mathematical Challenge 2020, Question 2. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 600
The correct answer is a multiple of both 3 and 8, as 24 = 3 × 8. Although 100 is a multiple of 4, it is not a multiple of 8. Therefore even multiples of 100 are multiples of 8, but odd multiples are not. This leaves 200, 400 and 600, but of these only 600 is also a multiple of 3.
Hence the only option which is a multiple of 24 is 600.
Solution © UK Mathematics Trust, from the IMC 2020 solutions. Longer versions with investigations: Solutions and investigations (PDF).