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# If x is a positive integer, is x! + (x + 1) a prime number?

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Manager
Joined: 07 May 2007
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If x is a positive integer, is x! + (x + 1) a prime number? [#permalink]  16 Jul 2007, 16:19
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If x is a positive integer, is x! + (x + 1) a prime number?

(1) x < 10

(2) x is even
Director
Joined: 12 Jun 2006
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Re: DS - x! + (x + 1) [#permalink]  16 Jul 2007, 16:40
iamba wrote:
If x is a positive integer, is x! + (x + 1) a prime number?

(1) x < 10

(2) x is even

I got E. no real method for me. I just tried different #s
CEO
Joined: 29 Mar 2007
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Re: DS - x! + (x + 1) [#permalink]  16 Jul 2007, 20:17
iamba wrote:
If x is a positive integer, is x! + (x + 1) a prime number?

(1) x < 10

(2) x is even

Same here. Got E in 2min and 30sec.

S1: x is less than 10. so I picked 3. 3!+(4)=10 so no. but 2!+3 is a prime number so this stmnt is insuff.

S2: just tried more numbers and came out insuff.
Director
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Re: DS - x! + (x + 1) [#permalink]  16 Jul 2007, 22:04
iamba wrote:
If x is a positive integer, is x! + (x + 1) a prime number?

(1) x < 10
(2) x is even

Could be B.

if x = 2, x! + (x + 1) = 5 prime
if x = 4, x! + (x + 1) = 29 prime
if x = 6, x! + (x + 1) = 727? probably prime
if x = 8, x! + (x + 1) = 40329? probably prime
if x = 10, x! + (x + 1) = 3628811? probably prime
GMAT Instructor
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Consider 8! + 8 + 1. As both 8! and 8+1 are multiples of 3, so is 8! + 8 + 1. Thus (2) is not sufficient
Director
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'E'.

Stmt2: x! + (x + 1) gives a non prime number if x =8. For x=2,4,6, it gives prime number. So insuff

Taking them together, INSUFF
Manager
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kevincan wrote:
Consider 8! + 8 + 1. As both 8! and 8+1 are multiples of 3, so is 8! + 8 + 1. Thus (2) is not sufficient

Yeah True

Stmt 1 is insuff
Stmt 2, we can plug in values....
2,4,6 are looking primes..... than put in 8
8! + 9 = 3(something + 3)..this is clearly not prime!

E
Senior Manager
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I get C

Stmt1
x <10> x can be 2 so 2!+3 = 5 - prime
But x can be 3 so 3!+4 = 10 - Non prime
So InSuff

Stmt2
x is even.

x can be 2 so 2!+3 = 5 - prime
But x can be 14 so 14! + 15 is not prime

Combine 1 and 2 you will see x! + x + 1 is prime

Oops I missed 8! + 9. I agree with E

Last edited by dahcrap on 17 Jul 2007, 10:06, edited 1 time in total.
Manager
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Quote:
If x is a positive integer, is x! + (x + 1) a prime number?

(1) x < 10
(2) x is even

Quote:
get C

Stmt1
x <10> x can be 2 so 2!+3 = 5 - prime
But x can be 3 so 3!+4 = 10 - Non prime
So InSuff

Stmt2
x is even.

x can be 2 so 2!+3 = 5 - prime
But x can be 14 so 14! + 15 is not prime

Combine 1 and 2 you will see x! + x + 1 is prime

I agree with everyone who said E. As was noted upthread, if you combine the 2 statments, you are left with 2, 4, 6, 8 as possibilities for x. However, after Himalayan did the math, it was noted that using x=8 does not produce a prime number.
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