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General quant factorials doubt

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General quant factorials doubt

by bblast » Mon Aug 29, 2011 12:54 am
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 ?
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by Whitney Garner » Mon Aug 29, 2011 4:43 am
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
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by bblast » Mon Aug 29, 2011 9:27 am
Thanks Whit, I was skeptical before posting this stuff. But after reading ur explanation I got a lot of takeaways from the issue. Thanks a lot !!!
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by saketk » Tue Aug 30, 2011 11:39 am
Hey -- Although you got your answer, I just wanted to say that (81! + 82) is not a prime number :)

81! is an even integer.. 82 is also even.. Even+Even = Even
only 2 is an exception, rest all Even are not prime.

I agree with Whit. GMAT wont actually expect you to solve big numbers. You have to use logic!!
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by prateek_guy2004 » Tue Aug 30, 2011 12:12 pm
I am little unsure about the 2nd statement...Though its yes/no ques and dosent need a yes to be sufficient...
Don't look for the incorrect things that you have done rather look for remedies....

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by czarczar » Wed Aug 31, 2011 12:50 pm
saketk wrote:Hey -- Although you got your answer, I just wanted to say that (81! + 82) is not a prime number :)

81! is an even integer.. 82 is also even.. Even+Even = Even
only 2 is an exception, rest all Even are not prime.

I agree with Whit. GMAT wont actually expect you to solve big numbers. You have to use logic!!
Well said.
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