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# If (n+2)!/n!=90, then n=?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6639
GMAT 1: 760 Q51 V42
GPA: 3.82

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02 Aug 2018, 01:21
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5% (low)

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86% (00:44) correct 14% (00:40) wrong based on 57 sessions

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[Math Revolution GMAT math practice question]

If $$\frac{(n+2)!}{n!}=90$$, then $$n=?$$

$$A. 8$$
$$B. 9$$
$$C. 10$$
$$D. 11$$
$$E. 12$$

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 31 Oct 2013 Posts: 881 Concentration: Accounting, Finance GPA: 3.68 WE: Analyst (Accounting) If (n+2)!/n!=90, then n=? [#permalink] ### Show Tags 02 Aug 2018, 01:25 MathRevolution wrote: [Math Revolution GMAT math practice question] If $$\frac{(n+2)!}{n!}=90$$, then $$n=?$$ $$A. 8$$ $$B. 9$$ $$C. 10$$ $$D. 11$$ $$E. 12$$ Option A: 8 back solve it. $$\frac{10!}{8!}$$ = $$\frac{8! * 9 * 10}{8!}$$ = 90. The best answer is A. Director Status: Learning stage Joined: 01 Oct 2017 Posts: 931 WE: Supply Chain Management (Energy and Utilities) If (n+2)!/n!=90, then n=? [#permalink] ### Show Tags Updated on: 02 Aug 2018, 01:52 MathRevolution wrote: [Math Revolution GMAT math practice question] If $$\frac{(n+2)!}{n!}=90$$, then $$n=?$$ $$A. 8$$ $$B. 9$$ $$C. 10$$ $$D. 11$$ $$E. 12$$ $$\frac{(n+2)!}{n!}=90$$ Or, $$\frac{(n!*(n+1)*(n+2))}{n!}$$=$$90$$ Or, (n+1)(n+2)=9*10 Or, n+1=9 and n+2=10 So, n=8. Ans. (A) _________________ Regards, PKN Rise above the storm, you will find the sunshine Originally posted by PKN on 02 Aug 2018, 01:47. Last edited by PKN on 02 Aug 2018, 01:52, edited 1 time in total. Intern Joined: 24 Jul 2018 Posts: 8 Re: If (n+2)!/n!=90, then n=? [#permalink] ### Show Tags 02 Aug 2018, 01:50 I approached it from what was given: (n+1)(n+2) = 90 The multiplication of two consecutive integers equals 90. => 9 and 10 => n = 8 Posted from my mobile device _________________ "Experts who acknowledge the full extent of their ignorance may expect to be replaced by more confident competitors, who are better able to gain the trust of clients. An unbiased appreciation of uncertainty is a cornerstone of rationality—but it is not what people and organizations want." - Daniel Kahnemen Intern Joined: 17 May 2018 Posts: 43 Re: If (n+2)!/n!=90, then n=? [#permalink] ### Show Tags 02 Aug 2018, 01:54 (n+2)! = 1 x 2 x 3 x ... x n x (n+1) x (n+2) n! = 1 x 2 x 3 x ... x n So (n+2)! / n! = (n+1)(n+2) = 90 Let's try the answers. I will start with B: n = 9. Replacing in (n+1)(n+2) the answer is 110. Too high. So the best answer is A. _________________ ¿Tienes que presentar el GMAT y no sabes por dónde empezar? ¡Visita GMAT para Principiantes y recibe el curso completo gratis! CEO Joined: 11 Sep 2015 Posts: 3237 Location: Canada Re: If (n+2)!/n!=90, then n=? [#permalink] ### Show Tags 02 Aug 2018, 06:20 Top Contributor MathRevolution wrote: [Math Revolution GMAT math practice question] If $$\frac{(n+2)!}{n!}=90$$, then $$n=?$$ $$A. 8$$ $$B. 9$$ $$C. 10$$ $$D. 11$$ $$E. 12$$ (n+2)! = (n+2)(n+1)(n)(n-1)(n-2)....(3)(2)(1) n! = (n)(n-1)(n-2)....(3)(2)(1) Given: (n+2)!/n! = 90 Rewrite as: (n+2)(n+1)(n)(n-1)(n-2)....(3)(2)(1)/(n)(n-1)(n-2)....(3)(2)(1) = 90 Simplify: (n+2)(n+1) = 90 At this point, we can simply test the answer choices. A) n = 8 Take (n+2)(n+1) = 90 and replace n with 8 to get: (8+2)(8+1) = 90 It works!! Answer: A Alternatively, we can start with (n+2)(n+1) = 90 Expand to get: n² + 3n + 2 = 90 Subtract 90 from both sides to get: n² + 3n - 88 = 0 Factor: (n + 11)(n - 8) = 0 So, EITHER n = -11 OR n = 8 Since we can't have negative factorials, it must be the case that n = 8 Answer: A Cheers, Brent _________________ Test confidently with gmatprepnow.com Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6639 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If (n+2)!/n!=90, then n=? [#permalink] ### Show Tags 05 Aug 2018, 18:05 => $$\frac{(n+2)!}{n!}= (n+2)(n+1) = 90 = 10*9.$$ Thus, $$n + 2 = 10$$ or $$n = 8.$$ Therefore, the answer is A. Answer : A _________________ 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$99 for 3 month Online Course"
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Re: If (n+2)!/n!=90, then n=? &nbs [#permalink] 05 Aug 2018, 18:05
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