General quant factorials doubt

bblast wrote:How to determine whether a factorial added to an integer is prime or non prime ?

If I take a small factorial :

1>(4! + 3) is non prime at first sight, as we can factor out a 3 from this expression.

On the other hand :

2>My doubt is when we cant factor out anything common from the factorial and integer :
(4! + 11) = 35 is non prime
while (4! + 7) = 31 is prime.

So how to determine whether (81! + 82) or any other factorial combined with a huge number is prime or not ?

Hi bblast!

Great question but sadly, one that has no good answer. If you are adding a number to a factorial and they share NO common factors - there is NO way to tell if the result will be prime!

Sadly/interestingly, primes are elusive little buggers (the reason they are often used in cryptology) - hence why there are no formulas or patterns for determining them!!

Good news - the GMAT will not give you a problem that necessitates you actually knowing if the number is prime or not (you will not have to directly answer). AND, even if they did give it to you in a DS, they could only do so with the understanding that you would "know" there was an answer, even if you didn't know what that answer was. Example (totally made up):

Can the positive integer x be written as the product of 2 integers, both greater than 1?

1) x=2k+1 where k is a positive integer

2) x = 26! + 37

The question is just using fancy wording for the real question "is x non-prime". Statement (1) only tells us that x is odd, so NS to determine if x is prime. Statement (2), however, gives us an actual value for x. We have NO CLUE what that value is and couldn't tell you without calculating it whether it was prime - BUT, it is a single number and therefore could only be prime or non-prime, so Sufficient. We don't know which it is, but we know that it is only one (a single number cannot be both).

Hope this helps!



Whit