Primes ... Prime sum of an integer ...

Expert replies

II: Master | Next Rank: 500 Posts; Posts: 400; Joined: Mon Dec 10, 2007 1:35 pm; Location: London, UK; Thanked: 19 times; GMAT Score:680

by II » Tue Aug 12, 2008 3:20 pm

Answer choices:

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

I am interested in finding out the shortcuts which will enable me to answer this question more quickly.
I suppose one approach is to go through each answer choice, find all the prime factors and then simply add them. However under the 2 min time constraint with the added pressure of the GMAT exam ... this could cause problems.
Are there any shortcuts ... other approaches people would use on this one.

Thanks.

Attachments

Like this post

Source: Beat The GMAT — Problem Solving | Tue Aug 12, 2008 3:20 pm

sudhir3127: Legendary Member; Posts: 829; Joined: Mon Jul 07, 2008 10:09 pmFollowed by: 3 members; Location: INDIA; Thanked: 84 times

by sudhir3127 » Tue Aug 12, 2008 8:59 pm

even i am interested to know if any such formula exists.. though i got to the answer in 10 seconds ..

we can clearly see that 620 is the only number which has a bigger prime 31.

the momemt u see the number we must realise it ..
but a formula will help though....

Like this post

GMAT/MBA Expert

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Wed Aug 13, 2008 5:37 am

sudhir3127 wrote:even i am interested to know if any such formula exists.. though i got to the answer in 10 seconds ..

we can clearly see that 620 is the only number which has a bigger prime 31.

the momemt u see the number we must realise it ..
but a formula will help though....

Sudhir asked if I could add a comment here- there couldn't possibly be a formula for finding a prime sum- the best you could have is an inequality that gives a maximum and minimum 'prime sum' for numbers of different sizes. For example, the prime sum of x will never be larger than x, since by multiplying primes, you'll always get a result larger than or equal to what you get by adding them. And, except in the case of 4 = 2^2, if a number is equal to its prime sum, the number is prime. However, since it's very unlikely you'll ever again see a question specifically about 'prime sums', it would not be worthwhile learning these sorts of facts.

As for the problem above, I'd do it exactly as Sudhir has done- you want to find a number with a large prime divisor, and 620 is the only candidate. I do think it should be possible to do this question quite quickly, even if you don't notice immediately that 620 is divisible by 31. If you can understand that the question is asking you to prime factorize each number and add the prime divisors, the only remaining task is getting the prime factorizations, something any GMAT test-taker should be fast with.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

Like this post

II: Master | Next Rank: 500 Posts; Posts: 400; Joined: Mon Dec 10, 2007 1:35 pm; Location: London, UK; Thanked: 19 times; GMAT Score:680

by II » Thu Aug 14, 2008 12:11 am

thanks for the comments guys.

My original approach was to work through the answer choices, listing the prime factors of each number and then adding them (finding the prime sum).
However, it would be much quicker to identify a number which has the largest prime factor and work with that first to see if the prime sum is higher than 35 ... which in this case would be 620.
But if you could not see this straight away, then list out the prime factors for each answer choice ... starting with the "easy" numbers, such as "512" (which is 2 to the power of 9), "700", and then look through to see which one has the largest prime factors.

Thanks.
II

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review