GK 2015 Q16
16. Miss Spelling, the English teacher, asked five of her students how many of the five of them had done their homework the day before. Daniel said none, Ellen said only one, Cara said exactly two, Zain said exactly three and Marcus said exactly four. Miss Spelling knew that the students who had not done their homework were not telling the truth but those who had done their homework were telling the truth. How many of these students had done their homework the day before?
- A 0
- B 1
- C 2
- D 3
- E 5
Grey Kangaroo 2015, Question 16. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 1
All the students have given different answers to the questions so only one, at most, can be telling the truth. Suppose no student is telling the truth; but then Daniel is telling the truth, contradicting this. Hence exactly one student, Ellen, is telling the truth and so only one student had done their homework.
Solution © UK Mathematics Trust, from the GK 2015 solutions.