GK 2017 Q8
8. Adam the Ant started at the left-hand end of a pole and crawled \(\tfrac{2}{3}\) of its length. Benny the Beetle started at the right-hand end of the same pole and crawled \(\tfrac{3}{4}\) of its length. What fraction of the length of the pole are Adam and Benny now apart?
- A \(\dfrac{3}{8}\)
- B \(\dfrac{1}{12}\)
- C \(\dfrac{5}{7}\)
- D \(\dfrac{1}{2}\)
- E \(\dfrac{5}{12}\)
Grey Kangaroo 2017, Question 8. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E \(\dfrac{5}{12}\)
Adam the Ant has crawled \(\tfrac{2}{3}\) of the length of the pole and so is \(\tfrac{1}{3}\) of the length of the pole from the right-hand end. Benny the Beetle has crawled \(\tfrac{3}{4}\) of the length of the pole and so is \(\tfrac{1}{4}\) of the length of the pole from the left-hand end. Hence the fraction of the length of the pole that Adam and Benny are apart is \(\left(1 - \tfrac{1}{3} - \tfrac{1}{4}\right) = \tfrac{5}{12}\).
Solution © UK Mathematics Trust, from the GK 2017 solutions.