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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6823
GMAT 1: 760 Q51 V42
GPA: 3.82
If (x+2)!/x! = 72, then x=  [#permalink]

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Updated on: 23 Nov 2017, 02:31
00:00

Difficulty:

15% (low)

Question Stats:

80% (01:06) correct 20% (01:10) wrong based on 96 sessions

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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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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 23 Nov 2017, 01:23. Last edited by Bunuel on 23 Nov 2017, 02:31, edited 1 time in total. Edited the tags. Intern Joined: 17 Nov 2016 Posts: 10 Re: If (x+2)!/x! = 72, then x= [#permalink] ### Show Tags 23 Nov 2017, 01:34 IMO B I just plugged in values from options So when x=7, it will be 9!/7!=72 Posted from my mobile device Manager Joined: 20 Feb 2017 Posts: 164 Location: India Concentration: Operations, Strategy WE: Engineering (Other) Re: If (x+2)!/x! = 72, then x= [#permalink] ### Show Tags 23 Nov 2017, 01:44 (x+2)! = (x+2)(x+1)x! so (x+2)!/x!=(x+2)(x+1)=72 plug the values X=7 _________________ If you feel the post helped you then do send me the kudos (damn theya re more valuable than$)

Intern
Joined: 26 Oct 2017
Posts: 27
Re: If (x+2)!/x! = 72, then x=  [#permalink]

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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

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
Math Expert
Joined: 02 Sep 2009
Posts: 52342
Re: If (x+2)!/x! = 72, then x=  [#permalink]

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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
_________________
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6823
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If (x+2)!/x! = 72, then x=  [#permalink]

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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 $$x ≥0, x = 7.$$

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Re: If (x+2)!/x! = 72, then x= &nbs [#permalink] 26 Nov 2017, 17:28
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