Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
It appears that you are browsing the GMAT Club forum unregistered!
Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club
Registration gives you:
Tests
Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.
Applicant Stats
View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more
Books/Downloads
Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Re: A researcher plans to identify each participant in a certain [#permalink]
25 Nov 2013, 03:41
1
This post received KUDOS
Expert's post
honchos wrote:
Bunuel wrote:
sarb wrote:
A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?
A. 4 B. 5 C. 6 D. 7 E. 8
Say there are minimum of \(n\) letters needed, then;
The # of single letter codes possible would be \(n\) itself; The # of pair of distinct letters codes possible would be \(C^2_n\) (in alphabetical order);
Why did you ignored possibility of 3 or 4 alphabets taken together, this will give us 4 letters?
Please read the question carefully: a code consists of either a single letter or a pair of distinct letters written in alphabetical order. _________________
Re: A researcher plans to identify each participant in a certain [#permalink]
25 Nov 2013, 03:51
Expert's post
honchos wrote:
Lets take A B C D A B C D AB AC AD BC BD CD ABC BCA CBA
It is alphabetical and all letter for a particular codes are different.
Please read the question carefully. The stem says that a code can consists of 1 or 2 letters ONLY: a code consists of either a single letter or a pair of distinct letters written in alphabetical order. _________________
Re: A researcher plans to identify each participant in a certain [#permalink]
25 Nov 2013, 08:39
honchos wrote:
Bunuel wrote:
sarb wrote:
A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?
A. 4 B. 5 C. 6 D. 7 E. 8
Say there are minimum of \(n\) letters needed, then;
The # of single letter codes possible would be \(n\) itself; The # of pair of distinct letters codes possible would be \(C^2_n\) (in alphabetical order);
Re: A researcher plans to identify each participant in a certain [#permalink]
29 Nov 2013, 19:18
1
This post received KUDOS
honchos wrote:
Bunuel wrote:
sarb wrote:
A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?
A. 4 B. 5 C. 6 D. 7 E. 8
Say there are minimum of \(n\) letters needed, then;
The # of single letter codes possible would be \(n\) itself; The # of pair of distinct letters codes possible would be \(C^2_n\) (in alphabetical order);
Why did you ignored possibility of 3 or 4 alphabets taken together, this will give us 4 letters?
The question specifically points out that the combinations can be a 1 digit letter or a 2 digit letter. I used a simple combination as stated in other answers to find out.
1. A 2. B 3. BA 4. C 5. CA 6. CB 7. D 8. DA 9. DB 10. DC 11. E 12. EA
STOP. you get the answer as 5 (ABCDE) Also what i have found is that when writing down the combinations with no repeats, it is easier to start with one letter and keep repeating it until you exhausted all the options. this will eliminate confusion. like you start with C and repeat with CA CB and then with D DA DB DC..
Re: A researcher plans to identify each participant in a certain [#permalink]
25 Feb 2014, 07:57
Bunuel wrote:
sarb wrote:
A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?
A. 4 B. 5 C. 6 D. 7 E. 8
Say there are minimum of \(n\) letters needed, then;
The # of single letter codes possible would be \(n\) itself; The # of pair of distinct letters codes possible would be \(C^2_n\) (in alphabetical order);
Re: A researcher plans to identify each participant in a certain [#permalink]
25 Feb 2014, 08:39
Expert's post
amz14 wrote:
Bunuel wrote:
sarb wrote:
A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?
A. 4 B. 5 C. 6 D. 7 E. 8
Say there are minimum of \(n\) letters needed, then;
The # of single letter codes possible would be \(n\) itself; The # of pair of distinct letters codes possible would be \(C^2_n\) (in alphabetical order);
Re: A researcher plans to identify each participant in a certain [#permalink]
13 Mar 2014, 14:03
Bunuel wrote:
sarb wrote:
A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?
A. 4 B. 5 C. 6 D. 7 E. 8
Say there are minimum of \(n\) letters needed, then;
The # of single letter codes possible would be \(n\) itself; The # of pair of distinct letters codes possible would be \(C^2_n\) (in alphabetical order);
Re: A researcher plans to identify each participant in a certain [#permalink]
14 Mar 2014, 01:48
2
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
RebekaMo wrote:
Bunuel wrote:
sarb wrote:
A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?
A. 4 B. 5 C. 6 D. 7 E. 8
Say there are minimum of \(n\) letters needed, then;
The # of single letter codes possible would be \(n\) itself; The # of pair of distinct letters codes possible would be \(C^2_n\) (in alphabetical order);
Re: A researcher plans to identify each participant in a certain [#permalink]
06 Apr 2014, 11:38
Bunuel wrote:
sarb wrote:
A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?
A. 4 B. 5 C. 6 D. 7 E. 8
Say there are minimum of \(n\) letters needed, then;
The # of single letter codes possible would be \(n\) itself; The # of pair of distinct letters codes possible would be \(C^2_n\) (in alphabetical order);
Probability and Combinatorics are my weakest subjects by far, so please ignore the rudimentary question.
When we say \(C^2_n+n\geq{12}\) that means that we are going to find a combination of 2 letters out of a group of n letters which in turn would yield "x" amount of options. Correct? If so, why are we adding the n following that equation and more importantly, how does that equation yield 5? When I factor it out, i get n(n+1) >= 24. That yields -1 and 0. Why am I so off here?
My question would be - what does this formula mean and how do you solve it? \(C^2_n+n\geq{12}\)
Also, the question is saying that they need to be in alphabetical order, doesn't that mean that order DOES matter? How does that affect the above equation.
P.S: For what it's worth, I've read the Combinatorics and Probability strategy guide(Manhattan Gmat) and understand the content of the guide but these two topics still elude me. I'm open to learning from another venue if helpful?
Re: A researcher plans to identify each participant in a certain [#permalink]
06 Apr 2014, 12:09
Expert's post
russ9 wrote:
Bunuel wrote:
sarb wrote:
A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?
A. 4 B. 5 C. 6 D. 7 E. 8
Say there are minimum of \(n\) letters needed, then;
The # of single letter codes possible would be \(n\) itself; The # of pair of distinct letters codes possible would be \(C^2_n\) (in alphabetical order);
Probability and Combinatorics are my weakest subjects by far, so please ignore the rudimentary question.
When we say \(C^2_n+n\geq{12}\) that means that a combination of 2 letters out of a group of n letters should yield "x" amount of options. Correct? If so, why are we adding the n following that equation and more importantly, how does that equation yield 5? When I factor it out, i get n(n+1) >= 24. That yields -1 and 0. Why am I so off here?
Also, the question is saying that they need to be in alphabetical order, doesn't that mean that order DOES matter? How does that affect the above equation.
P.S: For what it's worth, I've read the Combinatorics and Probability strategy guide and understand the content of the guide but these two topics still elude me. I'm open to learning from another venue if helpful?
The first advice would be, and I cannot stress this enough, to read the whole thread and follow the links to similar problems.
As for your questions:
Why we are adding n.
The question says that the code can consists of 1 or 2 letters. Now, if we have n letters how many codes we can make?
The # of single letter codes possible would be n itself; The # of pair of distinct letters codes possible would be \(C^2_n\).
So, out of n letters we can make \(n+C^2_n\) codes: n one-letter codes and \(C^2_n\) two-letter codes.
How the equation yields 5
By trial and error: If n=4, then n(n+1)=20<24; If n=5, then n(n+1)=30>24.
Hence, \(n_{min}=5\).
Notice that we have \(n(n+1)\geq{24}\) NOT \(n(n+1)\geq{0}\).
Re: A researcher plans to identify each participant in a certain [#permalink]
06 Apr 2014, 12:48
Hi Bunuel,
Thanks for the clarification. I was having a hard time grasping the equation itself but I followed a link to the mathbook topic and that does a good job of explaining why the equation is the way it is.
What I do question is the arrangement of the letters. I did go to the two links you posted and it's still a little unclear. How does the 2Cn equation know to not double count BA and AB. Wouldn't we have to go to the permutation equation for that?
Re: A researcher plans to identify each participant in a certain [#permalink]
06 Apr 2014, 12:58
Expert's post
russ9 wrote:
Hi Bunuel,
Thanks for the clarification. I was having a hard time grasping the equation itself but I followed a link to the mathbook topic and that does a good job of explaining why the equation is the way it is.
What I do question is the arrangement of the letters. I did go to the two links you posted and it's still a little unclear. How does the 2Cn equation know to not double count BA and AB. Wouldn't we have to go to the permutation equation for that?
Apart from that link I can only advice you to check it yourself. How many 2-letter words in alphabetical order are possible from say 3 letters {a, b, c}. _________________
Re: A researcher plans to identify each participant in a certain [#permalink]
15 May 2014, 13:53
Bunuel wrote:
sarb wrote:
A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?
A. 4 B. 5 C. 6 D. 7 E. 8
Say there are minimum of \(n\) letters needed, then;
The # of single letter codes possible would be \(n\) itself; The # of pair of distinct letters codes possible would be \(C^2_n\) (in alphabetical order);
Re: A researcher plans to identify each participant in a certain [#permalink]
16 May 2014, 00:43
Expert's post
bytatia wrote:
Bunuel wrote:
sarb wrote:
A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?
A. 4 B. 5 C. 6 D. 7 E. 8
Say there are minimum of \(n\) letters needed, then;
The # of single letter codes possible would be \(n\) itself; The # of pair of distinct letters codes possible would be \(C^2_n\) (in alphabetical order);
Re: A researcher plans to identify each participant in a certain [#permalink]
17 May 2014, 23:24
Bunuel wrote:
sarb wrote:
A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?
A. 4 B. 5 C. 6 D. 7 E. 8
Say there are minimum of \(n\) letters needed, then;
The # of single letter codes possible would be \(n\) itself; The # of pair of distinct letters codes possible would be \(C^2_n\) (in alphabetical order);
Every time I see your explanation, problem becomes so easy, but when I tried my own, I hardly get the correct. How to improve my understanding on combination and Probability ?
Re: A researcher plans to identify each participant in a certain [#permalink]
18 May 2014, 00:07
Expert's post
1
This post was BOOKMARKED
gauravsaxena21 wrote:
Bunuel wrote:
sarb wrote:
A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?
A. 4 B. 5 C. 6 D. 7 E. 8
Say there are minimum of \(n\) letters needed, then;
The # of single letter codes possible would be \(n\) itself; The # of pair of distinct letters codes possible would be \(C^2_n\) (in alphabetical order);
Every time I see your explanation, problem becomes so easy, but when I tried my own, I hardly get the correct. How to improve my understanding on combination and Probability ?
Re: A researcher plans to identify each participant in a certain [#permalink]
13 Aug 2014, 16:49
Bunuel wrote:
sarb wrote:
A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?
A. 4 B. 5 C. 6 D. 7 E. 8
Say there are minimum of \(n\) letters needed, then;
The # of single letter codes possible would be \(n\) itself; The # of pair of distinct letters codes possible would be \(C^2_n\) (in alphabetical order);
Re: A researcher plans to identify each participant in a certain [#permalink]
13 Aug 2014, 23:54
1
This post received KUDOS
Expert's post
ccyang24 wrote:
Bunuel wrote:
sarb wrote:
A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?
A. 4 B. 5 C. 6 D. 7 E. 8
Say there are minimum of \(n\) letters needed, then;
The # of single letter codes possible would be \(n\) itself; The # of pair of distinct letters codes possible would be \(C^2_n\) (in alphabetical order);
Re: A researcher plans to identify each participant in a certain [#permalink]
02 Sep 2014, 17:53
Bunuel wrote:
sarb wrote:
A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?
A. 4 B. 5 C. 6 D. 7 E. 8
Say there are minimum of \(n\) letters needed, then;
The # of single letter codes possible would be \(n\) itself; The # of pair of distinct letters codes possible would be \(C^2_n\) (in alphabetical order);
The “3 golden nuggets” of MBA admission process With ten years of experience helping prospective students with MBA admissions and career progression, I will be writing this blog through...
You know what’s worse than getting a ding at one of your dreams schools . Yes its getting that horrid wait-listed email . This limbo is frustrating as hell . Somewhere...