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Factorials - Data Sufficiency problem

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Junior | Next Rank: 30 Posts
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by Edthesock » Tue Jan 20, 2009 5:15 pm
If x is a positive integer, is x! + (x + 1) a prime number?

(1) x < 10

(2) x is even


The only way I was able to solve this was to do every factorial up to 9 and see if any of them were prime/not prime after adding x+1. Obviously, this is inefficient and certainly not how it is to be solved... any help?

Answer is E, neither answer is sufficient
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by Neo2000 » Tue Jan 20, 2009 5:33 pm
Consider the first statement

For X = 2, yes the number is prime but for X = 3 no, the number is not prime. Therefore insufficient

Consider both statements together
X = 2 or 4 or 6 or 8
For X = 2, yes for X = 8 the number is not prime. Insufficient

Consider 2nd statement alone
From above we know that for X =2 it is prime but for X = 8 it is not prime.

Hence E
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