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The sum of all integers from 1 to 520 that are multiples of 4 or 5?

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The sum of all integers from 1 to 520 that are multiples of 4 or 5?

(a) 187

(b) 208

(c) 421

(d) 52

The question was posed to me in a job interview.

My query is from Discrete Probability topic in portion Discrete Probability of Discrete Mathematics

1 Answer

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Best answer
Right option is (b) 208

Best explanation: PIE is used to count the elements of a set and stated as the sum of elements in A or B is equal to the sum of elements in A plus the sum of elements in B minus the sum of elements in A and B. Let A be the set of multiples of 4 and B be the set of multiples of 5, then A ⋂ B is the set of multiples of 20, and hence

\(\frac{520}{4} + \frac{520}{5} – \frac{520}{20}\) = 208.

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