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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 ## Least number of letters that can be used if there are 15 pla tagged by: jack0997 ##### This topic has 7 expert replies and 0 member replies ## Least number of letters that can be used if there are 15 pla A botanist plans to code each experimental plant used in an experiment with a code that consists of either a single letter or a pair of distinct letters written in an alphabetic order. What is the least number of letters that can be used if there are 15 plants, and each plant is to get a different code? (A) 3 (B) 4 (C) 5 (D) 7 (E) 14 ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 2008 messages Followed by: 31 members Upvotes: 470 jack0997 wrote: A botanist plans to code each experimental plant used in an experiment with a code that consists of either a single letter or a pair of distinct letters written in an alphabetic order. What is the least number of letters that can be used if there are 15 plants, and each plant is to get a different code? (A) 3 (B) 4 (C) 5 (D) 7 (E) 14 Hi jack, Let the number of letters to be used be n. The number of plants that can be identified using a single letter = nC1 = n. The number of plants that can be identified using two distinct letters = nC2 = [n.(n - 1)] / (1.2) (since the letters are to kept in alphabetic order, we must not order them or apply nP2.) Thus, total number of plants that can be identified if we attempt to have all the 15 codes that are either one-letter code or two-letter codes = n + n (n - 1)/2 Since we need to have at least 15 identifications, we have: n + n (n - 1)/2 â‰¥ 15 => [2n+n(n-1)]/2 â‰¥ 15 => n(2+(n-1)) â‰¥ 30 => n(n+1) â‰¥ 30 Working with the options and starting with the least value of n, we see that n = 5 satisfies the above inequality. The correct answer: C Hope this helps! Relevant book: Manhattan Review GMAT Combinatorics and Probability Guide -Jay _________________ Manhattan Review GMAT Prep Locations: New York | Prague | Johannesburg | Lisbon | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. Last edited by Jay@ManhattanReview on Fri Feb 24, 2017 4:54 am; edited 1 time in total ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15383 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 jack0997 wrote: A botanist plans to code each experimental plant used in an experiment with a code that consists of either a single letter or a pair of distinct letters written in an alphabetic order. What is the least number of letters that can be used if there are 15 plants, and each plant is to get a different code? (A) 3 (B) 4 (C) 5 (D) 7 (E) 14 We can PLUG IN THE ANSWERS, which represent the least number of letters required to make 15 codes. Start with the smallest answer choice. A: 3 The following codes are possible for letters A, B and C: A, B, C, AB, AC, BC. 6 codes. Since the number of codes is too small, eliminate A. B: 4 The following codes are possible for letters A, B, C and D: A, B, C, D, AB, AC, AD, BC, BD, CD. 10 codes. Since the number of codes is too small, eliminate B. C: 5 The following codes are possible for letters A, B, C, D and E: A, B, C, D, E, AB, AC, AD, AE, BC, BD, BE, CD, CE, DE. 15 codes. Success! The correct answer is C. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Last edited by GMATGuruNY on Fri Feb 24, 2017 4:55 am; edited 1 time in total Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 2008 messages Followed by: 31 members Upvotes: 470 Oops. I made a mistake. I hurriedly read the question and interpreted 'either a single letter or a pair of distinct letters' as 'either a single letter or a string of distinct letters.' Mitch cannot be wrong. Corrected my post. -Jay _________________ Manhattan Review GMAT Prep Locations: New York | Prague | Johannesburg | Lisbon | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13038 messages Followed by: 1251 members Upvotes: 5254 GMAT Score: 770 Here's a similar (official) GMAT question to practice with: http://www.beatthegmat.com/distribution-centers-t263732.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 Legendary Member Joined 14 Jan 2015 Posted: 2666 messages Followed by: 125 members Upvotes: 1153 GMAT Score: 770 And if Brent has merely whetted your appetite for still more combination problems, see here: http://www.beatthegmat.com/word-problem-t114724.html _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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Jay@ManhattanReview wrote:
Mitch cannot be wrong.
I'm going to frame this post and mount it on the wall so that it is visible to my family at all times.

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### GMAT/MBA Expert

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GMATGuruNY wrote:
Jay@ManhattanReview wrote:
Mitch cannot be wrong.
I'm going to frame this post and mount it on the wall so that it is visible to my family at all times.
That's a nice decision you've taken. At least this way you can win an argument with your wife.

-Jay
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