GK 2015 Q7
7. In a class, no two boys were born on the same day of the week and no two girls were born in the same month. Were another child to join the class, this would no longer be true. How many children are there in the class?
- A 18
- B 19
- C 20
- D 24
- E 25
Grey Kangaroo 2015, Question 7. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 19
Suppose another child were to join the class. The question tells us that then one of the two conditions would no longer be true. For this to happen, there must be no day of the week available for a new boy to have been born on and no month of the year available for a new girl to have been born in. Hence there must be 7 boys and 12 girls currently in the class and so there are 19 children in total in the class.
Solution © UK Mathematics Trust, from the GK 2015 solutions.