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If x is a positive integer, is x! + (x + 1) a prime number? [#permalink]
 16 Jul 2007, 17:19
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If x is a positive integer, is x! + (x + 1) a prime number?
(1) x < 10
(2) x is even
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Director
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Re: DS - x! + (x + 1) [#permalink]
16 Jul 2007, 17:40
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
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CEO
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Re: DS - x! + (x + 1) [#permalink]
16 Jul 2007, 21:17
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.
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Director
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Re: DS - x! + (x + 1) [#permalink]
16 Jul 2007, 23:04
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
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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
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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
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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
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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, 11:06, edited 1 time in total.
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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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