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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Nine identical chips are numbered from 1 to 9 (one different tagged by: fskilnik@GMATH ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## Nine identical chips are numbered from 1 to 9 (one different ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult GMATH practice exercise (Quant Class 18) Nine identical chips are numbered from 1 to 9 (one different number per chip) and placed in a box. There are N ways in which all the chips are taken out from the box, one at a time and without repositions, in a sequence of alternating odd and even numbers. The value of N is: (A) less than 1400 (B) between 1400 and 2000 (C) between 2000 and 2600 (D) between 2600 and 3200 (E) greater than 3200 Answer: ____(D)__ _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12982 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 fskilnik@GMATH wrote: GMATH practice exercise (Quant Class 18) Nine identical chips are numbered from 1 to 9 (one different number per chip) and placed in a box. There are N ways in which all the chips are taken out from the box, one at a time and without repositions, in a sequence of alternating odd and even numbers. The value of N is: (A) less than 1400 (B) between 1400 and 2000 (C) between 2000 and 2600 (D) between 2600 and 3200 (E) greater than 3200 Answer: ____(D)__ ODDS: 1, 3, 5, 7, 9 EVENS: 2, 4, 6, 8 Take the task of removing the 9 chips and break it into stages. Stage 1: Select an ODD number to be the 1st selection There are 5 ODDs to choose from. So, we can complete stage 1 in 5 ways Stage 2: Select an EVEN number to be the 2nd selection There are 4 EVENs to choose from. So, we can complete stage 2 in 4 ways Stage 3: Select an ODD number to be the 3rd selection There are 4 ODDs remaining. So, we can complete this stage in 4 ways Stage 4: Select an EVEN number to be the 4th selection There are 3 EVENs remaining. So, we can complete this stage in 3 ways Stage 5: Select an ODD number to be the 5th selection There are 3 ODDs remaining. So, we can complete this stage in 3 ways Stage 6: Select an EVEN number to be the 6th selection There are 2 EVENs remaining. So, we can complete this stage in 2 ways Stage 7: Select an ODD number to be the 7th selection There are 2 ODDs remaining. So, we can complete this stage in 2 ways Stage 8: Select an EVEN number to be the 8th selection There is 1 EVEN number remaining. So, we can complete this stage in 1 way Stage 9: Select an ODD number to be the 9th selection There is 1 ODD number remaining. So, we can complete this stage in 1 way By the Fundamental Counting Principle (FCP), we can complete all 9 stages in (5)(4)(4)(3)(3)(2)(2)(1)(1) ways (= 2880 ways) Answer: D Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch this video: http://www.gmatprepnow.com/module/gmat-counting/video/775 You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat-counting/video/776 Then you can try solving the following questions: EASY - http://www.beatthegmat.com/what-should-be-the-answer-t267256.html - http://www.beatthegmat.com/counting-problem-company-recruitment-t244302.html - http://www.beatthegmat.com/picking-a-5-digit-code-with-an-odd-middle-digit-t273110.html - http://www.beatthegmat.com/permutation-combination-simple-one-t257412.html - http://www.beatthegmat.com/simple-one-t270061.html MEDIUM - http://www.beatthegmat.com/combinatorics-solution-explanation-t273194.html - http://www.beatthegmat.com/arabian-horses-good-one-t150703.html - http://www.beatthegmat.com/sub-sets-probability-t273337.html - http://www.beatthegmat.com/combinatorics-problem-t273180.html - http://www.beatthegmat.com/digits-numbers-t270127.html - http://www.beatthegmat.com/doubt-on-separator-method-t271047.html - http://www.beatthegmat.com/combinatorics-problem-t267079.html DIFFICULT - http://www.beatthegmat.com/wonderful-p-c-ques-t271001.html - http://www.beatthegmat.com/permutation-and-combination-t273915.html - http://www.beatthegmat.com/permutation-t122873.html - http://www.beatthegmat.com/no-two-ladies-sit-together-t275661.html - http://www.beatthegmat.com/combinations-t123249.html Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 fskilnik@GMATH wrote: GMATH practice exercise (Quant Class 18) Nine identical chips are numbered from 1 to 9 (one different number per chip) and placed in a box. There are N ways in which all the chips are taken out from the box, one at a time and without repositions, in a sequence of alternating odd and even numbers. The value of N is: (A) less than 1400 (B) between 1400 and 2000 (C) between 2000 and 2600 (D) between 2600 and 3200 (E) greater than 3200 $$?\,\,\mathop = \limits^{\left( * \right)} \,\,\,\# \,\,\left( {{\text{odd,even,odd,even,odd,even,odd,even,odd}}} \right)\,\,{\text{tuples}}$$ $$\left( * \right)\,\,{\text{must}}\,\,{\text{start}}\,\,{\text{and}}\,\,{\text{finish}}\,\,{\text{with}}\,\,{\text{odd numbers}}\,\,\,\left( {5\,\,{\text{odd}}\,\,{\text{numbers}}\,,\,4\,\,{\text{even}}\,{\text{numbers}}} \right)$$ $$?\,\, = \,\,{P_5} \cdot {P_4} = 5!\,\, \cdot 4!\,\, = \,\underleftrightarrow {\,120 \cdot 24 = 2 \cdot {{12}^2} \cdot 10} = 2880$$ The correct answer is (D). We follow the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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