How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
Weekly Problem 27 - 2011
Pizza, Indian or Chinese takeaway. Each teenager from a class only likes two of these, but can you work which two?
This is Zi Heng's solution:
30 pupils took the exam.
Andrei, 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: $$n(A\cap B)=9$$
Their union contains all students. It is evident that: $$n(A\cup
B)=n(A)+n(B)-n(A\cap B)$$ 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 $x=0.7x+0.6x-9$ or $x=30$. So, 30 pupils came to the exam, 21
solved the first problem and 18 the second one.
Prateek , James , Alan , Jenny and Robert also
sent in good solutions. Joseph's solution to the second part of the