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Prime Sum

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Prime Sum

by jms123 » Sun Oct 10, 2010 8:14 am
What's a good way to solve this problem?

The "prime sum" of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example, the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 + 2 + 3 = 7. For which of the following integers is the prime sum greater than 35?

A) 440
B) 512
C) 620
D) 700
E) 750

Correct answer: [spoiler]C
Since 620 = 2 x 2 x 5 x 31, the prime sum of 620 is 2 + 2 + 5 + 31 = 40, which is greater than 35[/spoiler]
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by Rahul@gurome » Sun Oct 10, 2010 5:22 pm
Look at each of the answer choices given, until you get an answer to the question.

(A) 440 = 2^3*5*11, so prime sum of 440 = 2+2+2+5+11 = 24 < 35. So, not possible
(B) 512 = 2^9, so the prime sum = 2*9 = 18 < 35
(C) 620 = 2^2 * 5 * 31, so the prime sum = 2+2+5+31 = 40 > 35, holds true.

[spoiler]The correct answer is (C).[/spoiler]
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