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# If (n+2)!/n!=132, n=?

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Math Revolution GMAT Instructor
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Updated on: 10 May 2017, 23:59
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78% (01:15) correct 22% (01:32) wrong based on 226 sessions

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If $$\frac{(n+2)!}{n!}= 132$$, n=?

A. 2/131
B. 9
C. 10
D. 11
E. 12

*An answer will be posted in 2 days

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"Only $79 for 1 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 25 Aug 2016, 18:29. Last edited by Bunuel on 10 May 2017, 23:59, edited 1 time in total. Edited the question and the tags. Current Student Joined: 12 Aug 2015 Posts: 2609 Schools: Boston U '20 (M) GRE 1: Q169 V154 Re: If (n+2)!/n!=132, n=? [#permalink] ### Show Tags Updated on: 25 Aug 2016, 20:14 1 Hi MathRevolution Firstly this Ain't a probability Question Kindly change that Here is my approach => (n+2)(n+1)*n!/n!=132=> (n+2)*(n+1)=132 Checking the values => n must be 10 => 12 *11=132 SMASH THAT C Regards STONE COLD _________________ Originally posted by stonecold on 25 Aug 2016, 20:10. Last edited by stonecold on 25 Aug 2016, 20:14, edited 1 time in total. Senior Manager Joined: 23 Apr 2015 Posts: 295 Location: United States Concentration: General Management, International Business WE: Engineering (Consulting) Re: If (n+2)!/n!=132, n=? [#permalink] ### Show Tags 25 Aug 2016, 20:11 1 1 MathRevolution wrote: If (n+2)!/n!=132, n=? A. 2/131 B. 9 C. 10 D. 11 E. 12 *An answer will be posted in 2 days $$\frac{(n+2)!}{n!}$$ can be written as $$\frac{(n+2)(n+1)n!}{n!}$$ This gives $$(n+2)(n+1) = 132 = 11*12$$ Out of the choices given C) 10, would be the right value to solve. Answer is C CEO Joined: 12 Sep 2015 Posts: 3848 Location: Canada Re: If (n+2)!/n!=132, n=? [#permalink] ### Show Tags 26 Aug 2016, 05:51 1 Top Contributor 1 MathRevolution wrote: If (n+2)!/n!=132, n=? A. 2/131 B. 9 C. 10 D. 11 E. 12 *An answer will be posted in 2 days (n+2)!/n! = 132 Rewrite as: [(n+2)(n+1)(n)(n-1)(n-2)....(3)(2)(1)]/[(n)(n-1)(n-2)....(3)(2)(1)] = 132 Cancel out terms: (n+2)(n+1) = 132 From here, we might just TEST the answer choices. Since (12)(11) = 132, we can see that n = 10 Answer: Alternatively, we can take (n+2)(n+1) = 132 and expand it to get: n² + 3n + 2 = 132 Subtract 132 from both sides to get: n² + 3n - 130 = 0 Factor to get: (n + 13)(n - 10) = 0 So, n = -13 or n = 10 Since n cannot be negative in a factorial, n must equal 10 Answer: RELATED VIDEOS ADDITIONAL PRACTICE _________________ Test confidently with gmatprepnow.com Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7605 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If (n+2)!/n!=132, n=? [#permalink] ### Show Tags 30 Aug 2016, 20:03 (n+2)!/n!=(n+2)(n+1)n!/n!=(n+2)(n+1)=132, n^2+3n-130=0, (n+12)(n-10)=0. Hence, the correct answer is C. _________________ 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$79 for 1 month Online Course"
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11 May 2017, 02:06

Once you get to (n+2)*(n+1)=132 (or further n² + 3n + 2 = 132)

It's important to develop a "feel" for such equations. I'd just immediately look at the biggest term n² , we need an n that's at least close to 132 when squared, so 10^2 = 100 seems like a good starting point. If you just mentally plug that into either of those equations, you would realized you've hit jackpot. So definitely no factorization of quadratic or going through all the options required.
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11 May 2017, 02:35
MathRevolution wrote:
If $$\frac{(n+2)!}{n!}= 132$$, n=?

A. 2/131
B. 9
C. 10
D. 11
E. 12

*An answer will be posted in 2 days

$$\frac{(n+2)!}{n!}= 132$$
-> (n+2)(n+1) = 132 = 12 x 11
-> n+1 = 11
-> n = 10

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17 Jul 2018, 16:42
MathRevolution wrote:
If $$\frac{(n+2)!}{n!}= 132$$, n=?

A. 2/131
B. 9
C. 10
D. 11
E. 12

(n+2)!/n! = 132

(n+2)(n+1)n!/n! = 132

(n+2)(n+1) = 132

n^2 + 3n + 2 = 132

n^2 + 3n - 130 = 0

(n - 10)(n + 13) = 0

n = 10 or n = -13

Since the factorial of a negative number is undefined, n can’t be -13, so n = 10.

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Re: If (n+2)!/n!=132, n=?   [#permalink] 17 Jul 2018, 16:42
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