• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
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 4 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: 12921 messages Followed by: 1248 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 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 08 Dec 2008 Posted: 12921 messages Followed by: 1248 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 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! 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: 2069 messages Followed by: 238 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. ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2624 messages Followed by: 18 members Upvotes: 43 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. Since the last digit of the extension must be even, the last digit can be either 6 or 2. If we let 6 be the last digit, then we have 3! = 6 options for the other 3 digits. If we let 2 be the last digit, we also have 6 options. Therefore, we have a total of 12 options. Answer: C _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

### Top First Responders*

1 Ian Stewart 64 first replies
2 Jay@ManhattanReview 53 first replies
3 Brent@GMATPrepNow 52 first replies
4 GMATGuruNY 28 first replies
5 Scott@TargetTestPrep 19 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

200 posts
2 Max@Math Revolution

Math Revolution

93 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

90 posts
4 Ian Stewart

GMATiX Teacher

71 posts
5 Rich.C@EMPOWERgma...

EMPOWERgmat

68 posts
See More Top Beat The GMAT Experts