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If x is a positive integer greater than 1, is x! + x + 1 a p
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08 Jul 2014, 06:07
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62% (00:49) correct 38% (00:44) wrong based on 452 sessions
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If x is a positive integer greater than 1, is x! + x + 1 a prime number? (1) x < 10 (2) x is odd OE (1) INSUFFICIENT If x = 2: 2! + (2 + 1) = 5, which is prime. If x = 3: 3! + (3 + 1) = 6 + (3 + 1) = 10, which is not prime.
(2) SUFFICIENT: If x = 3: 3! + (3 + 1) = 10, which is not prime. If x = 5: 5! + (5 + 1) = (5 × 4 × 3 × 2 × 1) + 6. This expression must be divisible by 3, since both of its terms are divisible by 3. Furthermore it must be even, because both terms are even. Therefore, it is not a prime number.
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Re: If x is a positive integer greater than 1, is x! + x + 1 a p
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08 Jul 2014, 06:55
goodyear2013 wrote: If x is a positive integer greater than 1, is x! + x + 1 a prime number? (1) x < 10 (2) x is odd OE (1) INSUFFICIENT If x = 2: 2! + (2 + 1) = 5, which is prime. If x = 3: 3! + (3 + 1) = 6 + (3 + 1) = 10, which is not prime.
(2) SUFFICIENT: If x = 3: 3! + (3 + 1) = 10, which is not prime. If x = 5: 5! + (5 + 1) = (5 × 4 × 3 × 2 × 1) + 6. This expression must be divisible by 3, since both of its terms are divisible by 3. Furthermore it must be even, because both terms are even. Therefore, it is not a prime number. If x is a positive integer greater than 1, is x! + x + 1 a prime number?(1) x < 10. If x=2, then x! + x + 1 = 5 = prime. If x=3, then x! + x + 1 = 10, not a prime. Not sufficient. (2) x is odd. So, x is an odd integer greater than 1: 3, 5, 7, ... In this case x! + x + 1 = even + odd + odd = even > 2, not a prime. Sufficient. Answer: B.
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Re: If x is a positive integer greater than 1, is x! + x + 1 a p
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09 Jul 2014, 00:19
Let X<10, then for the x=2 x! + x + 1 = 5 = prime number & for the x=3 x! + x + 1 = 10, not a prime number So it is not possible if x is a positive integer greater than 1, is x! + x + 1 a prime number..



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Re: If x is a positive integer greater than 1, is x! + x + 1 a p
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01 Oct 2014, 05:27
Bunuel wrote: goodyear2013 wrote: If x is a positive integer greater than 1, is x! + x + 1 a prime number? (1) x < 10 (2) x is odd OE (1) INSUFFICIENT If x = 2: 2! + (2 + 1) = 5, which is prime. If x = 3: 3! + (3 + 1) = 6 + (3 + 1) = 10, which is not prime.
(2) SUFFICIENT: If x = 3: 3! + (3 + 1) = 10, which is not prime. If x = 5: 5! + (5 + 1) = (5 × 4 × 3 × 2 × 1) + 6. This expression must be divisible by 3, since both of its terms are divisible by 3. Furthermore it must be even, because both terms are even. Therefore, it is not a prime number. If x is a positive integer greater than 1, is x! + x + 1 a prime number?(1) x < 10. If x=2, then x! + x + 1 = 5 = prime. If x=3, then x! + x + 1 = 10, not a prime. Not sufficient. (2) x is odd. So, x is an odd integer greater than 1: 3, 5, 7, ... In this case x! + x + 1 = even + odd + odd = even > 2, not a prime. Sufficient. Answer: B. Is there any other way , apart from testing number. I solved it correctly but took more than 2 min.
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Re: If x is a positive integer greater than 1, is x! + x + 1 a p
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13 Apr 2016, 06:45
(1) x < 10.
If x=2, then f(x)= 5 => prime If x=3, then f(x) = 10 => not prime
Not suff.
(2) x is odd.
x! + x + 1 = x(x1)(x2)(x3)...(xn) + x + 1 (with n always is even)
=> x[1 + (x1)(x2)(x3)...(xn)] + 1
We have (x1) always even, (x2) odd, (x3) even, ... (xn)odd => (x1)(x2)(x3)...(xn) = even
=> [1 + (x1)(x2)(x3)...(xn)] = odd (1+ even) => x[1 + (x1)(x2)(x3)...(xn)] = odd (odd * odd) => x[1 + (x1)(x2)(x3)...(xn)] + 1 = even (odd + 1)
=> suff.
I just write in detail, it would be very quick to infer that.



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Re: If x is a positive integer greater than 1, is x! + x + 1 a p
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29 Sep 2016, 05:47
goodyear2013 wrote: If x is a positive integer greater than 1, is x! + x + 1 a prime number?
(1) x < 10
(2) x is odd
I got to B in ~1 minute.. 1. x<10 > 1<x<10 suppose x=2. 2+2+1 = 5 suppose x=3 3! = 6. 6+3+1 = 10  not prime. 2 outcomes  insufficient. 2. x is odd. since x can't be 1, x! of any odd number will always be even. since x is odd, x+1 will always be even now..x!(even) + x+1(even) = even. even number can't be a prime number.



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Re: If x is a positive integer greater than 1, is x! + x + 1 a p
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08 Apr 2017, 03:49
definitely no. this is why option b ? please help anyone



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If x is a positive integer greater than 1, is x! + x + 1 a p
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08 Apr 2017, 03:59



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Re: If x is a positive integer greater than 1, is x! + x + 1 a p
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08 Apr 2017, 04:08



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Re: If x is a positive integer greater than 1, is x! + x + 1 a p
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28 May 2017, 15:32
him1985 wrote: Bunuel wrote: goodyear2013 wrote: If x is a positive integer greater than 1, is x! + x + 1 a prime number? (1) x < 10 (2) x is odd OE (1) INSUFFICIENT If x = 2: 2! + (2 + 1) = 5, which is prime. If x = 3: 3! + (3 + 1) = 6 + (3 + 1) = 10, which is not prime.
(2) SUFFICIENT: If x = 3: 3! + (3 + 1) = 10, which is not prime. If x = 5: 5! + (5 + 1) = (5 × 4 × 3 × 2 × 1) + 6. This expression must be divisible by 3, since both of its terms are divisible by 3. Furthermore it must be even, because both terms are even. Therefore, it is not a prime number. If x is a positive integer greater than 1, is x! + x + 1 a prime number?(1) x < 10. If x=2, then x! + x + 1 = 5 = prime. If x=3, then x! + x + 1 = 10, not a prime. Not sufficient. (2) x is odd. So, x is an odd integer greater than 1: 3, 5, 7, ... In this case x! + x + 1 = even + odd + odd = even > 2, not a prime. Sufficient. Answer: B. Is there any other way , apart from testing number. I solved it correctly but took more than 2 min. The main takeaways from this question is this: 2 is the ONLY number (apart from 1) that, when expressed as a factorial, will give you a prime # (when you add "x" and "1"). Why, you ask? B/c any number > 2 will include "2" in its prime factorization. Meaning, if you have 3! = 3x2; or 5! = 5x4x3x2. ALSO, any number multiplied by an even will be EVEN. and the ONLY EVEN PRIME = 2. Therefore, (1) = insufficient b/c x<10 includes 2 (prime) as well as 3, 4, 5, 6, 7, 8, 9 (which are all NOT prime). (2) is sufficient b/c we know "1" cannot be included here, so the only numbers to play with are: 3, 5, 7, 9  which are all NOT prime. This is sufficient b/c we can safely say "x! + x + 1 is NOT PRIME" under these conditions



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Re: If x is a positive integer greater than 1, is x! + x + 1 a p
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23 Dec 2018, 09:34
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