IMC 2015 Q3
3. What is a half of a third, plus a third of a quarter, plus a quarter of a fifth?
- A \(\dfrac{1}{1440}\)
- B \(\dfrac{3}{38}\)
- C \(\dfrac{1}{30}\)
- D \(\dfrac{1}{3}\)
- E \(\dfrac{3}{10}\)
Intermediate Mathematical Challenge 2015, Question 3. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E \(\dfrac{3}{10}\)
Half of a third, plus a third of a quarter, plus a quarter of a fifth equals
\(\dfrac{1}{6} + \dfrac{1}{12} + \dfrac{1}{20} = \dfrac{10 + 5 + 3}{60} = \dfrac{18}{60} = \dfrac{3}{10}\).
Solution © UK Mathematics Trust, from the IMC 2015 solutions. Longer versions with investigations: Solutions and investigations (PDF).