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

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.