IMC 2009 Q10
10. Fussy Fiona wants to buy a new house but she doesn't like house numbers that are divisible by 3 or by 5. If all the houses numbered between 100 and 150 inclusive are for sale, how many houses can she choose from?
- A 24
- B 25
- C 26
- D 27
- E 28
Intermediate Mathematical Challenge 2009, Question 10. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 27
There are 51 houses numbered from 100 to 150 inclusive. Of these, 17 are multiples of 3, 11 are multiples of 5 and 4 are multiples of both 3 and 5.
So the number of houses Fiona can choose from is 51 − (17 + 11 − 4) = 27.
Solution © UK Mathematics Trust, from the IMC 2009 solutions.