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# For which of the following values of x is the equation

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SVP
Joined: 21 Jul 2006
Posts: 1512

Kudos [?]: 1005 [0], given: 1

For which of the following values of x is the equation [#permalink]

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08 Dec 2007, 09:19
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For which of the following values of x is the equation (x+4)!/x! = (x+1)!

a) 6
b) 7
c) 8
d) 9
e) 10

Kudos [?]: 1005 [0], given: 1

SVP
Joined: 29 Aug 2007
Posts: 2472

Kudos [?]: 842 [0], given: 19

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08 Dec 2007, 11:34
tarek99 wrote:
For which of the following values of x is the equation (x+4)!/x! = (x+1)!

a) 6
b) 7
c) 8
d) 9
e) 10

(x+4)! / x! = (x+1)!
(x+4) (x+3) (x+2) (x+1) (x!) / (x!) = (x+1) (x!)
(x+4) (x+3) (x+2) = (x!)

plugg it: got 6.

Kudos [?]: 842 [0], given: 19

Director
Joined: 12 Jul 2007
Posts: 857

Kudos [?]: 330 [0], given: 0

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08 Dec 2007, 11:40
GMAT TIGER wrote:
tarek99 wrote:
For which of the following values of x is the equation (x+4)!/x! = (x+1)!

a) 6
b) 7
c) 8
d) 9
e) 10

(x+4)! / x! = (x+1)!
(x+4) (x+3) (x+2) (x+1) (x!) / (x!) = (x+1) (x!)
(x+4) (x+3) (x+2) = (x!)

plugg it: got 6.

yup, and you can simplify it out when plugging it in as well.

using 6:

10*9*8 = 6*5*4*3*2
9*8 = 6*4*3
3*2 = 6

checks out

Kudos [?]: 330 [0], given: 0

SVP
Joined: 21 Jul 2006
Posts: 1512

Kudos [?]: 1005 [0], given: 1

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08 Dec 2007, 13:13
You guys are right and the OA is A. however, i need to correct your calculation here:

"yup, and you can simplify it out when plugging it in as well.

using 6:

10*9*8*7 = 7*6*5*4*3*2
7 = 7 "

you're approach is correct, however, you forgot the 7, which i've added and have highlighted for you.

Kudos [?]: 1005 [0], given: 1

Director
Joined: 12 Jul 2007
Posts: 857

Kudos [?]: 330 [0], given: 0

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08 Dec 2007, 13:16
tarek99 wrote:
You guys are right and the OA is A. however, i need to correct your calculation here:

"yup, and you can simplify it out when plugging it in as well.

using 6:

10*9*8*7 = 7*6*5*4*3*2
9*8*7 = 7*6*4*3
7 = 7 "

you're approach is correct, however, you forgot the 7, which i've added and have highlighted for you.

(x+1) appeared on both sides of the equation and can be canceled out before plugging in x. you can leave it in if you want, it's just unnecessary

Kudos [?]: 330 [0], given: 0

08 Dec 2007, 13:16
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