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Inclusion Exclusion

How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?

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Takeaway Time

Pizza, Indian or Chinese takeaway. Each teenager from a class only likes two of these, but can you work which two?

One or Both

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2


A maths exam contained only two questions. Problem one was solved by 70% of the pupils. Problem two was solved by 60% of them. Every pupil solved at least one of the problems. Nine pupils solved both problems. How many pupils took the exam?

In the following year the maths exam contained two percentage problems. This time each problem was solved by 72% of the pupils and every pupil got at least one problem right again. What can you say about the number of pupils in the class?

Can you make a problem like this of your own?