Prime Sum

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money9111: Legendary Member; Posts: 2109; Joined: Sun Apr 19, 2009 10:25 pmFollowed by: 79 members; Location: New Jersey; Thanked: 109 times; GMAT Score:640

by money9111 » Mon Feb 01, 2010 8:32 pm

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=2x2x3 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

i began this one trying to find the prime factors of each number.

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Source: Beat The GMAT — Problem Solving | Mon Feb 01, 2010 8:32 pm

money9111: Legendary Member; Posts: 2109; Joined: Sun Apr 19, 2009 10:25 pmFollowed by: 79 members; Location: New Jersey; Thanked: 109 times; GMAT Score:640

by money9111 » Mon Feb 01, 2010 8:41 pm

OA C

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Mon Feb 01, 2010 8:49 pm

we need to check div by aprime no. near to 35 , which are 29,31,37

a)440
the highest prime no it is div by is 11 occurring ones , infact its 11*4*5*2 prime sum=22

b)512 is 2^9 ps=18
c)620=31*2*5*10
prime sum >35
hence c

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