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If integer k is equal to the sum of all even multiples of 15 between 295 and 615,

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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
Official Answer

1 Answer

flamingo
1

To find the number of terms:
the smallest integer greater than equal to 295 that is divisible by 30, i.e. 300
the greatest integer smaller than equal to 615 that is divisible by 30, i.e. 600

It becomes an evenly spaced set: {300, 330, 360, 390, 420, 450, 480, 510, 540, 570, 600}

Number of terms in an evenly spaced set
(Last term-First term)/(Common Difference)+1

(600 - 300 )/30 + 1 = 11


Average= (First Term+Last Term)/2

Sum=Number of terms*Average

=> 11* ( 300 + 600) / 2 

=> 11 * 450 

=> 11 * 2 * 3^2 * 5^2 


Clearly Highest prime=11

Ans: "C" 

answered Jun 18, 2014 by Guru (5,599 points)
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