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

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Manager
Joined: 16 Jan 2007
Posts: 73

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

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29 Dec 2007, 02:17
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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 easier way to solve the problem apart from backsolving ?

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Manager
Joined: 15 Nov 2007
Posts: 134

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29 Dec 2007, 02:27
dynamo wrote:
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 easier way to solve the problem apart from backsolving ?

all i can think of, besides backsolving, is watching the intersection of numbers -- since X! in the denominator removes the "edge" the left side has and forces intersection with the right. i'd love to hear someone else's take. what i've said here amounts to backsolving.

Kudos [?]: 57 [0], given: 2

CEO
Joined: 17 Nov 2007
Posts: 3583

Kudos [?]: 4663 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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29 Dec 2007, 04:32
(X+4)!/X! = (X+1)!

(X+4)*(X+3)*(X+2)=X!

X+4,X+3,X+2 - should not be prime numbers.

6: 6,5,4
7: 7,6,5
8: 8,7,6
9: 9,8,7
10: 10,9,8 - BINGO
11: 11,10,9
12: 12,11,10
13: 13,12,11
14: 14,13,12

Maybe for clarity I should write "2: 6,5,4" instead of "6: 6,5,4"

Last edited by walker on 29 Dec 2007, 10:20, edited 3 times in total.

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Manager
Joined: 22 Oct 2006
Posts: 71

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Location: India

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29 Dec 2007, 05:00
I think it is A...x=6
What is OA?

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VP
Joined: 09 Jul 2007
Posts: 1098

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Location: London

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29 Dec 2007, 05:04
A. for me as well if i am not missing any crucial point

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Director
Joined: 09 Aug 2006
Posts: 754

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29 Dec 2007, 08:28
Sorry mate. Could only come up with back solving to give A.

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Manager
Joined: 16 Jan 2007
Posts: 73

Kudos [?]: 27 [0], given: 0

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29 Dec 2007, 08:53
Walker u are right . the Answer is 10.
Thanks everyone.

As per the rule

n^Cr = n^Cn-r , 6,8 and 10 are correct. but not sure how to distinguish between them.

Walker, can you please explain as to why the nos shd not be prome.
Also :- x = 6 so 3!
but how do find the the factorial value for x = 7,8,9 and 10.

Kudos [?]: 27 [0], given: 0

CEO
Joined: 17 Nov 2007
Posts: 3583

Kudos [?]: 4663 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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29 Dec 2007, 10:00
dynamo wrote:
Walker u are right . the Answer is 10.

x+4=10 ==> x=6

dynamo wrote:
but how do find the the factorial value for x = 7,8,9 and 10.

(X+4)*(X+3)*(X+2)=X!

all prime factors of X!=X*(X-1)....1 less then X
therefore, if, for example, (X+2) is prime, X! can not be divided by (X+2)

Kudos [?]: 4663 [0], given: 360

29 Dec 2007, 10:00
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# For which of the following values of X is the equation

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