• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 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 Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

Least number of letters that can be used if there are 15 pla

This topic has 7 expert replies and 0 member replies

Least number of letters that can be used if there are 15 pla

Post
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

  • +1 Upvote Post
  • Quote
  • Flag
Post
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 ≥ 15

=> [2n+n(n-1)]/2 ≥ 15

=> n(2+(n-1)) ≥ 30

=> n(n+1) ≥ 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

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
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

  • +1 Upvote Post
  • Quote
  • Flag
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.
Post
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.Smile 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.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
Here's a similar (official) GMAT question to practice with: http://www.beatthegmat.com/distribution-centers-t263732.html

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use my video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for free Question of the Day emails
And check out all of these free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’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
Post
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

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

GMAT/MBA Expert

Post
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.

_________________
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

  • +1 Upvote Post
  • Quote
  • Flag
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.
Post
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. Smile

-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.

  • +1 Upvote Post
  • Quote
  • Flag
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors

Top First Responders*

1 Ian Stewart 41 first replies
2 Brent@GMATPrepNow 40 first replies
3 Scott@TargetTestPrep 39 first replies
4 Jay@ManhattanReview 32 first replies
5 GMATGuruNY 26 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

159 posts
2 image description Max@Math Revolution

Math Revolution

92 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

60 posts
4 image description Ian Stewart

GMATiX Teacher

50 posts
5 image description GMATGuruNY

The Princeton Review Teacher

37 posts
See More Top Beat The GMAT Experts