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MGMAT 11

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by resilient » Mon May 26, 2008 6:04 pm
If integer k is equal to the sum of all even multiples of 15 between 295 and 615, what is the greatest prime factor of k?


5


7


11


13


17

WHT IS THE EASIEST WAY TO DO THIS?!


QA IS 11
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by aatech » Mon May 26, 2008 6:34 pm
My approach is this.. I am sure there would be some better and faster way of doing this

Even multiples of 15 between 295 and 615 will give 300 as first no and 600 as the last no. The diff between 2 consecutive no in this series will be 30. This gives, total nos in the series = 11.

Sum of n numbers in arithmetic progression is given by
(n/2)[2a+(n-1)d]

So, in this case sum will be (11/2)[600+300]= 11*450=11*5*3*3*5*2

Greatest prime factor = 11 ANS
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