The "prime sum" of an integer n greater than 1 is

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swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Fri Apr 20, 2018 8:13 am

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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

The OA is C.

Please, can anyone explain this PS question? I can't get the correct answer. Thanks.

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Source: Beat The GMAT — Problem Solving | Fri Apr 20, 2018 8:13 am

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The "prime sum" of an integer n greater than 1 is

by Brent@GMATPrepNow » Fri Apr 20, 2018 12:17 pm

swerve wrote: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

This question requires us to find the prime factorization of the answer choices
A. 440 = (2)(2)(2)(5)(11).
PRIME SUM = 2 + 2 + 2 + 5 + 11 = 22

B. 512 = (2)(2)(2)(2)(2)(2)(2)(2)(2)
PRIME SUM = 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 18

C. 620 = (2)(2)(5)(31)
PRIME SUM = 2 + 2 + 5 + 31 = 40

STOP right there.
We've found the number that has a prime sum that's greater than 35.

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8137; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Apr 25, 2018 3:47 pm

swerve wrote: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

Scanning our answer choices we want to find the number that contains a large prime factor. Thus, considering answer choice C, we have:

620 = 62 x 10 = 31 x 2 x 2 x 5

The sum is 31 + 5 + 2 + 2 = 40.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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