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

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Director
Joined: 17 Oct 2005
Posts: 940
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For which of the following values of x is the equation [#permalink]  30 Oct 2005, 21:04
For which of the following values of x is the equation (x+4)! / x! = (x+1)! true?

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

Is there any way to solve this quickly without doing the long math? thanks
SVP
Joined: 05 Apr 2005
Posts: 1733
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Re: PR Test 2 #19 Factorials [#permalink]  30 Oct 2005, 21:15
i donot have any short cut except trial and error....

A. x= 6

(x+4)! / x! = (x+1)!
(x+4)(x+3)(x+2)(x+1) x! / x! = (x+1)!
(x+4)(x+3)(x+2)(x+1) = (x+1)!
10x9x8x7=7!
720x7=7x6!
720x7=7x120
Manager
Joined: 20 Mar 2005
Posts: 201
Location: Colombia, South America
Followers: 1

Kudos [?]: 6 [0], given: 0

I think the easiest way is just plugging numbers, I started with 6

so 10!/6! is equal to 7!

so 10*9*8*7 should be equal to 7*6*5*4*3*2

simplifying end up to be the same

as 5*2*3*3*2*2*2*7 = 7*3*2*5*2*2*3*2

7*5*3^2*2^4 = 7*5*3^2*2^4
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