Count Again

Probability Level 1

The total number of multiples of 2 that are less than or equal to 100 is $100\div 2 = 50$ .
The total number of multiples of 5 that are less than or equal to 100 is $100\div 5 = 20$ .

Is it true that the total number of multiples of 2 and/or multiples of 5 that are less than or equal to 100 is $50 + 20 = 70$ ?

No, it is not true Yes, it is true

2 solutions

Ralph James
Jun 17, 2016

Some of these multiples will overlap, as a number can be both multiples of $2$ and $5$ (ex: $10$ ). Therefore, simply performing $50+20$ results in overcounting. Since there are $10$ multiples of both $5$ AND $2$ less than or equal $100$ (the multiples of $10$ ), we have to subtract $10$ and get the total number of $60$ .

I think there are 10 multiples of 10 from 1 to 100, and not 9. Answer should be 60

Prince Loomba - 4 years, 11 months ago

Thank you. I have edited the solution accordingly.

Ralph James - 4 years, 11 months ago

No problem. Such mistakes happen quite frequently

Prince Loomba - 4 years, 11 months ago

Prince Loomba
Jun 21, 2016

According to set theory, n (A union B)=nA+nB-n(A intersection B). So multiples of 5 and or 2 are multiples of 5+ multiples of 2-multiples of 10, that is 50+20-10 or 60.

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