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 ?
General quant factorials doubt
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- bblast
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Hi bblast!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 ?
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
Whitney Garner
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Math is a lot like love - a simple idea that can easily get complicated
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Math is a lot like love - a simple idea that can easily get complicated
- bblast
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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 !!!
Cheers !!
Quant 47-Striving for 50
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Quant 47-Striving for 50
Verbal 34-Striving for 40
My gmat journey :
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My take on the GMAT RC :
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https://www.youtube.com/watch?v=upz46D7 ... TWBZF14TKW_
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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!!
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!!
- prateek_guy2004
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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....
https://www.beatthegmat.com/motivation-t90253.html
https://www.beatthegmat.com/motivation-t90253.html
- czarczar
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Well said.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!!