14. A lot of goals were scored in a hockey match I watched recently. In the first half, six goals were scored and the away team was leading at half-time. In the second half, the home team scored three goals and won the game. How many goals did the home team score altogether?
A 3
B 4
C 5
D 6
E 9
Solution
C

Since six goals were scored in the first half and the away side was leading at half-time, the possible half-time scores were $0-6,1-5$, and $2-4$. However, we are also told that the home team scored three goals in the second half and won the game. Hence the home team cannot have been more than two goals behind at half-time. Therefore the score at half-time was 2 - 4 . Hence the number of goals the home team scored in total was $2+3=5$.