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# (1-1/10)(1-1/11)(1-1/12)…(1-1/100) =?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7115
GMAT 1: 760 Q51 V42
GPA: 3.82

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17 Oct 2018, 00:41
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Difficulty:

15% (low)

Question Stats:

83% (01:15) correct 17% (01:23) wrong based on 39 sessions

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[Math Revolution GMAT math practice question]

$$(1-\frac{1}{10})(1-\frac{1}{11})(1-\frac{1}{12})…(1-\frac{1}{100}) =?$$

$$A. \frac{1}{10}$$
$$B. \frac{9}{10}$$
$$C. \frac{9}{100}$$
$$D. \frac{1}{100}$$
$$E. \frac{9}{50}$$

_________________
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" Director Joined: 18 Jul 2018 Posts: 762 Location: India Concentration: Finance, Marketing WE: Engineering (Energy and Utilities) Re: (1-1/10)(1-1/11)(1-1/12)…(1-1/100) =? [#permalink] ### Show Tags 17 Oct 2018, 00:49 1 The question can be reduced to $$\frac{9}{10}*\frac{10}{11}*\frac{11}{12}$$.....$$\frac{98}{99}*\frac{99}{100}$$. All the terms will be canceled except 9/100. C is the answer. _________________ Press +1 Kudo If my post helps! Manager Joined: 09 Jun 2014 Posts: 236 Location: India Concentration: General Management, Operations Schools: Tuck '19 Re: (1-1/10)(1-1/11)(1-1/12)…(1-1/100) =? [#permalink] ### Show Tags 17 Oct 2018, 01:17 MathRevolution wrote: [Math Revolution GMAT math practice question] $$(1-\frac{1}{10})(1-\frac{1}{11})(1-\frac{1}{12})…(1-\frac{1}{100}) =?$$ $$A. \frac{1}{10}$$ $$B. \frac{9}{10}$$ $$C. \frac{9}{100}$$ $$D. \frac{1}{100}$$ $$E. \frac{9}{50}$$ So we are asked to find (1-\frac{1}{10})(1-\frac{1}{11})(1-\frac{1}{12})…(1-\frac{1}{100}) =9/10 * 10/11* 11/12 *...will go on till 99/100 = 9/10 * 10/11* 11/12 *...will go on till99/100 =9/100 Press Kudos if helps!! Manager Joined: 09 Jun 2014 Posts: 236 Location: India Concentration: General Management, Operations Schools: Tuck '19 Re: (1-1/10)(1-1/11)(1-1/12)…(1-1/100) =? [#permalink] ### Show Tags 17 Oct 2018, 01:18 MathRevolution wrote: [Math Revolution GMAT math practice question] $$A. \frac{1}{10}$$ $$B. \frac{9}{10}$$ $$C. \frac{9}{100}$$ $$D. \frac{1}{100}$$ $$E. \frac{9}{50}$$ So we are asked to find $$(1-\frac{1}{10})(1-\frac{1}{11})(1-\frac{1}{12})…(1-\frac{1}{100}) =?$$ =9/10 * 10/11* 11/12 *...will go on till 99/100 = 9/10 * 10/11* 11/12 *...will go on till99/100 =9/100 Press Kudos if helps!! Intern Joined: 09 Jun 2018 Posts: 8 (1-1/10)(1-1/11)(1-1/12)…(1-1/100) =? [#permalink] ### Show Tags 17 Oct 2018, 01:24 1 Product will yield the following: 9/10 * 10/11 * 11/12 * ... * 99/100 So, for the numerator we have: 99!/8! and for the denominator we have: 100!/9! numerator/denominator = (99!/8!)/(100!/9!) = (99!*9!)/(100!*8!) simplifying we get 9/100 ANSWER C Manager Joined: 09 Jun 2014 Posts: 236 Location: India Concentration: General Management, Operations Schools: Tuck '19 Re: (1-1/10)(1-1/11)(1-1/12)…(1-1/100) =? [#permalink] ### Show Tags 17 Oct 2018, 01:28 MarcoAD wrote: Product will yield the following: 9/10 * 10/11 * 11/12 * ... * 99/100 So, for the numerator we have: 99!/8! and for the denominator we have: 100!/9! numerator/denominator = (99!/8!)/(100!/9!) = (99!*9!)/(100!*8!) simplifying we get 9/100 ANSWER C This is a nice approach.. Imagining in terms of factorial ..Makes life simpler Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 5435 Location: United States (CA) Re: (1-1/10)(1-1/11)(1-1/12)…(1-1/100) =? [#permalink] ### Show Tags 17 Oct 2018, 19:09 MathRevolution wrote: [Math Revolution GMAT math practice question] $$(1-\frac{1}{10})(1-\frac{1}{11})(1-\frac{1}{12})…(1-\frac{1}{100}) =?$$ $$A. \frac{1}{10}$$ $$B. \frac{9}{10}$$ $$C. \frac{9}{100}$$ $$D. \frac{1}{100}$$ $$E. \frac{9}{50}$$ Starting with the first 4 factors we have: (1-1/10)(1-1/11)(1-1/12)(1 - 1/13) (9/10)(10/11)(11/12)(12/13) = 9/13 So we see only the first numerator and last denominator remain; thus, the product is 9/100. Answer: C _________________ # Scott Woodbury-Stewart Founder and CEO Scott@TargetTestPrep.com 122 Reviews 5-star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7115 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: (1-1/10)(1-1/11)(1-1/12)…(1-1/100) =? [#permalink] ### Show Tags 19 Oct 2018, 01:05 => $$(1-\frac{1}{10})(1-\frac{1}{11})(1-\frac{1}{12})…(1-\frac{1}{100}) = (\frac{9}{10})(\frac{10}{11})(\frac{11}{12})…(\frac{99}{100}) = \frac{9}{100}.$$ Therefore, C is the answer. Answer: 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$149 for 3 month Online Course"
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Re: (1-1/10)(1-1/11)(1-1/12)…(1-1/100) =?   [#permalink] 19 Oct 2018, 01:05
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