IMC 2014 Q17
17. How many weeks are there in 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 minutes?
- A 1
- B 2
- C 3
- D 4
- E 5
Intermediate Mathematical Challenge 2014, Question 17. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 4
The number of minutes in one week is 7 × 24 × 60, which may be written as 7 × (6 × 4) × (5 × 3 × 2 × 2) = (7 × 6 × 5 × 4 × 3 × 2) × 2. So the number of weeks in 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 minutes is 8 ÷ 2 = 4.
Solution © UK Mathematics Trust, from the IMC 2014 solutions. Longer versions with investigations: Solutions and investigations (PDF).