6. There are fewer than 30 students in the A-level mathematics class. One half of them play the piano, one quarter play hockey and one seventh are in the school play.
How many of the students play hockey?
A 3
B 4
C 5
D 6
E 7
Solution
E

Because one half of the students play the piano, the number of students is a multiple of 2 .
Because one quarter of the students play hockey, the number of students is a multiple of 4 .
Because one seventh of the students are in the school play, the number of students is a multiple of 7 .

Therefore the number of students is a multiple of 2, 4 and 7 . Hence the number of students is a multiple of 28 .
Because there are fewer than 30 students in the class, it follows that there are 28 students in the class.
Therefore, because one quarter of the 28 students play hockey, the number of students who play hockey is 7.