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

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

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.
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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....
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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

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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
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