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?
(A) 5
(B) 7
(C) 11
(D) 13
(E) 17
(A) 5
(B) 7
(C) 11
(D) 13
(E) 17
the smallest even multiple of 15 between 295 and 615 is 300.
the largest even multiple of 15 between 295 and 615 is 600.
the distance between every even multiple of 15 is 30.
between 300 and 600, inclusive, there are (600 - 300)/30 + 1 = 11 even multiples of 30.
k = (11/2)*(300 + 600)
k = 5.5*100*9
k = 55*10*9
k = 11*5*5*2*3*3
therefore, the largest prime factor of k is 11.
choose c.
-BM-
