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You can find the sum by taking the average of the highest and lowest numbers that satisfy your criteria multiplied by how many numbers there are. Find out how many numbers there are by subtracting the highest number that satisfies your condition minus the lowest number that satisfies your condiction, divide by the interval (here that's 30), then add 1.

600 - 300 = 300; 300 / 30 = 10, 10 +1 = 11

Now the average of 600 and 300 is 450. so 450 * 11 = 4950. Notice also that 11 is prime and the question calls for the largest prime number. Because we already used 11, we know C is possible, and 13 and 17 are not factors.

4950 / 13 = 380 and 10/13 - not a factor

4950 / 17 = 291 and 3/17 = not a factor.

So C is the answer.

For methods on finding divisibility by the primes up to 50, check out this link

even integers of 15 can only be multiples of 30. so find all the multiples of 30 in 300-600. then you can factor out and find that the total is 4950 and there is a factor of 11 in there which makes it largest prime. factor.
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Re: If integer k is equal to the sum of all even multiples of 15 [#permalink]

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