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

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Manager
Joined: 04 Jan 2008
Posts: 117
If x is a positive integer, is x! + (x + 1) a prime number? [#permalink]

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13 Sep 2008, 02:47
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If x is a positive integer, is x! + (x + 1) a prime number?

(1) x < 10
(2) x is even
VP
Joined: 05 Jul 2008
Posts: 1373

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13 Sep 2008, 13:52
gmatnub wrote:
dancinggeometry wrote:
If x is a positive integer, is x! + (x + 1) a prime number?

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

B

Y= X! + (X+1)

X =1 ; Y =3 Yes

X=2 Y =5 Yes

X=3 Y =10 No

NOT A & D

X is even

X=2 Y = 5 yes

X=4 Y = 29 yes

X=6 Y =727 (not sure but say yes)

X=8 Y= 40329 (No divided by 9)

Not B

combine X = {2,4,6,8} Yes yes yes No

Hence No

SVP
Joined: 17 Jun 2008
Posts: 1504

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15 Sep 2008, 00:29
From stmt1: if x = 1 then x! + (x+1) will be 3 and a prime number.
However, if x = 3 then the expression will equal to 10 and is not a prime number.

Hence, insufficient.

From stmt2: x = 2 then expression will equal to 5 and is a prime number. Howeverm if x = 8, x! will be divisible by 2 and (x+1) will be divisible by 3....and hence not a prime. Insufficient.

Combining the two.....insufficient.

Hence, E.
Intern
Joined: 02 Sep 2008
Posts: 45

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15 Sep 2008, 08:03
Yeah,

X < 10 is ablsolutely insufficient even with B when x is even

it is true with x = 2, x! + ( x + 1 ) = 5. It is prime.

it is false with x = 4. X! + (x + 1) = 20 which is not prime..
Re: Zumit DS 023   [#permalink] 15 Sep 2008, 08:03
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