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# Counting

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The positive integers from 1 to 150 inclusive are placed in a 10 by 15 grid so that each cell contains exactly one integer. Then the multiples of 3 are given a red mark, the multiples of 5 are given a blue mark, and the multiples of 7 are given a green mark. How many cells have more than 0 marks?

Dec 11, 2021

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The positive integers from 1 to 150 inclusive are placed in a 10 by 15 grid so that each cell contains exactly one integer. Then the multiples of 3 are given a red mark, the multiples of 5 are given a blue mark, and the multiples of 7 are given a green mark. How many cells have more than 0 marks?

Here is how to start it.

Draw a Venn diagram

The bit that overlaps the most has the number of multiples of all of them in it.

3*5*7=105   There is only one multiple of 105 in that set of numbers.

Now work out from there.

How many multiples of 3 and 5 are there?   3*5=15       150/15=10      10-1=9

So where are you going to put the 9?

Dec 11, 2021