This is Zi Heng Lim's solution:
| 70% + 60% |
= 130% |
| 130% - 100% |
= 30% |
|
|
| 30% |
= 9 pupils |
| 100% |
= 9/30 * 100 |
|
= 30 pupils. |
30 pupils took the exam.
Andrei Lazanu, age 12, School 205, Bucharest, Romania solved
this problem using a Venn diagram.
Let A be the set of solvers of the first problem, and B the set of solvers of
the second problem and the number in set A be written
n(A) etc. Their
intersection has 9 elements:
Their union contains all students. It is evident that:
If x is the number of students participating in the exam, then A has 70 per
cent of x elements, B has 60 per cent of x elements, and relation (2) can be
re-written as
or x=30. So, 30 pupils
came to the exam, 21 solved the first problem and 18 the second one.
Prateek Mehrotra, James Wakefield, Alan Rowan, Jenny Cook and
Robert Haynes also sent in good solutions.