IMC 2018 Q9
9. Which integer \(n\) satisfies \(\dfrac{3}{10} < \dfrac{n}{20} < \dfrac{2}{5}\)?
- A 3
- B 4
- C 5
- D 6
- E 7
Intermediate Mathematical Challenge 2018, Question 9. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 7
We are given that \(\dfrac{3}{10} < \dfrac{n}{20} < \dfrac{2}{5}\). Therefore \(\dfrac{6}{20} < \dfrac{n}{20} < \dfrac{8}{20}\). So, as \(n\) is an integer, \(n = 7\).
Solution © UK Mathematics Trust, from the IMC 2018 solutions. Longer versions with investigations: Solutions and investigations (PDF).