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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 If all of the telephone extensions in a certain company must tagged by: BTGmoderatorLU This topic has 3 expert replies and 1 member reply Top Member If all of the telephone extensions in a certain company must Timer 00:00 Your Answer A B C D E Global Stats Difficult Source: Princeton Review If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2, 3, and 6, what is the greatest number of four-digit extensions that the company can have? A. 4 B. 6 C. 12 D. 16 E. 24 The OA is C. GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12433 messages Followed by: 1244 members Upvotes: 5254 GMAT Score: 770 BTGmoderatorLU wrote: Source: Princeton Review If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2, 3, and 6, what is the greatest number of four-digit extensions that the company can have? A. 4 B. 6 C. 12 D. 16 E. 24 The OA is C. Take the task of arranging the 4 digits and break it into stages. Weâ€™ll begin with the most restrictive stage. Stage 1: Select the digit in the units position Since the 4-digit extension must be EVEN, the unit digit must be either 2 or 6 So, we can complete stage 1 in 2 ways Stage 2: Select the tens digit There are 3 remaining digits from which to choose, so we can complete this stage in 3 ways. Stage 3: Select the hundreds digit There are 2 digits remaining, so we can complete this stage in 2 ways. Stage 4: Select the thousands digit There 1 digit remaining, so we can complete this stage in 1 way. By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus create an even extension) in (2)(3)(2)(1) ways (= 12 ways) Answer: C Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free 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 our video course along with Sign up for our free Question of the Day emails And check out all of our 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 08 Dec 2008 Posted: 12433 messages Followed by: 1244 members Upvotes: 5254 GMAT Score: 770 BTGmoderatorLU wrote: Source: Princeton Review If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2, 3, and 6, what is the greatest number of four-digit extensions that the company can have? A. 4 B. 6 C. 12 D. 16 E. 24 The OA is C. NOTE: Always SCAN the answer choices before performing any calculations. Here, we notice that the answer choices are pretty small, so if we don't come up a full solution, we should consider LISTING AND COUNTING We get the following extensions: 1236 1326 1362 1632 2136 2316 3126 3162 3216 3612 6132 6312 TOTAL = 12 Answer: C Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our 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! Top Member Newbie | Next Rank: 10 Posts Joined 06 Dec 2018 Posted: 7 messages To use all 1/2/3/6 in a 4-digit number, this means no number can be used twice. Thus if we consider _ _ _ _, the last digit must either be 2 or 6. For the first three digits: the first digit we have 3 choices, 2 for the second, 1 for the third. Thus, 3*2*1. We can do this twice (with 2 or 6 as ending, yielding 12. GMAT/MBA Expert GMAT Instructor Joined 04 Dec 2012 Posted: 1981 messages Followed by: 236 members Upvotes: 1443 Here is yet another solution: Most of the time when we're arranging n things (people in a line, letter combinations, etc) with a diminishing pool (i.e. we can't use the same item twice), the number of arrangements is simply n!. If we could arrange these 4 numbers into extensions without any restrictions, we'd have 4 options for the 1st number, 3 for the 2nd, 2 for the 3rd, 1 for the 4th: 4*3*2*1 = 4! = 24. These passcodes have to be even, though. Two of our digits are even (2 and 6) and two are odd (1 and 3). It thus stands to reason that HALF of the 24 combinations we came up with will end with an odd digit, and half with an even. If we only want the even results, we simply divide by 2: 24/2 = 12. _________________ Ceilidh Erickson Manhattan Prep GMAT & GRE instructor EdM in Mind, Brain, and Education Harvard Graduate School of Education Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience. Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry! Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week. • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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