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If (x+2)!/x! = 72, then x=

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Math Revolution GMAT Instructor
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If (x+2)!/x! = 72, then x=  [#permalink]

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New post Updated on: 23 Nov 2017, 02:31
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A
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[GMAT math practice question]

If \(\frac{(x+2)!}{x!} = 72\), then \(x=\)?

A. \(6\)
B. \(7\)
C. \(8\)
D. \(9\)
E. \(10\)

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Originally posted by MathRevolution on 23 Nov 2017, 01:23.
Last edited by Bunuel on 23 Nov 2017, 02:31, edited 1 time in total.
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Re: If (x+2)!/x! = 72, then x=  [#permalink]

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New post 23 Nov 2017, 01:34
IMO B

I just plugged in values from options

So when x=7, it will be 9!/7!=72

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Re: If (x+2)!/x! = 72, then x=  [#permalink]

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New post 23 Nov 2017, 01:44
(x+2)! = (x+2)(x+1)x!
so (x+2)!/x!=(x+2)(x+1)=72
plug the values X=7
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Re: If (x+2)!/x! = 72, then x=  [#permalink]

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New post 23 Nov 2017, 01:45
Imo B

(x+2)(x+1)(x)!/x!

(x+2)(x+1)=72

Plug in the values and B gives the answer

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Re: If (x+2)!/x! = 72, then x=  [#permalink]

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New post 23 Nov 2017, 02:31
MathRevolution wrote:
[GMAT math practice question]

If \(\frac{(x+2)!}{x!} = 72\), then \(x=\)?

A. \(6\)
B. \(7\)
C. \(8\)
D. \(9\)
E. \(10\)


This is a variation of the following problems:
https://gmatclub.com/forum/if-n-2-n-156-n-230625.html
https://gmatclub.com/forum/if-n-2-n-132-n-224311.html
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Re: If (x+2)!/x! = 72, then x=  [#permalink]

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New post 26 Nov 2017, 17:28
=>

Now,
\(72= \frac{(x+2)!}{x!} = \frac{[x!*(x+1)*(x+2)]}{x!} =(x+1)(x+2)\).

So,
\(x^2 + 3x + 2 = 72\)
\(x^2 +3x – 70 = 0\)
\((x-7)(x+10) = 0\)
\(x = 7 or x = -10.\)
Since factorials are only defined for \(x ≥0, x = 7.\)

Therefore, the answer is B.
Answer: B
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Re: If (x+2)!/x! = 72, then x= &nbs [#permalink] 26 Nov 2017, 17:28
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