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

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

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

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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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

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: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

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
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