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* Multiples of 3 below 1000 range from 1 x 3 = 3 to 333 x 3 = 999. The average of all these is (3+999)/2 = 501. The total is therefore: 501 x 333 = 166833. * Multiples of 5 below 1000 range from 1 x 5 = 5 to 199 x 5 = 995. The average of all these is (5+995)/2 = 500. The total is therefore: 500 x 199 = 99500. As things stand we have counted the multiples of 15 (which divide by both 3 and 5) twice, so the whole set of them must be subtracted once: * Multiples of 15 below 1000 range from 1 x 15 = 15 to 66 x 15 = 990. The average of all these is (15+990)/2 = 502.5. The total is therefore: 502.5 x 66 = 33165. The grand total is 166833 + 99500 - 33165 = 233168

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Q: Add all the natural numbers below one thousand that are multiples of 3 or 5?
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