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:

A researcher plans to identify each participant in a certain [#permalink]
17 Jun 2012, 03:13

1

This post received KUDOS

31

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

54% (02:10) correct
46% (01:29) wrong based on 978 sessions

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?

Re: A researcher plans to identify each participant in a certain [#permalink]
17 Jun 2012, 03:24

5

This post received KUDOS

Expert's post

17

This post was BOOKMARKED

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 Jun 2012, 03:34

3

This post received KUDOS

Expert's post

8

This post was BOOKMARKED

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?

Re: A researcher plans to identify each participant in a certain [#permalink]
17 Jun 2012, 03:49

2

This post received KUDOS

Expert's post

3

This post was BOOKMARKED

Almost identical question:

John has 12 clients and he wants to use color coding to identify each client. If either a single color or a pair of two different colors can represent a client code, what is the minimum number of colors needed for the coding? Assume that changing the color order within a pair does not produce different codes. A. 24 B. 12 C. 7 D. 6 E. 5

The concept is not that hard. We can use combination or trial and error approach.

Combination approach: Let # of colors needed be \(n\), then it must be true that \(n+C^2_n\geq{12}\) (\(C^2_n\) - # of ways to choose the pair of different colors from \(n\) colors when order doesn't matter) --> \(n+\frac{n(n-1)}{2}\geq{12}\) --> \(2n+n(n-1)\geq{24}\) --> \(n(n+1)\geq{24}\) --> as \(n\) is an integer (it represents # of colors) \(n\geq{5}\) --> \(n_{min}=5\).

Trial and error approach: If the minimum number of colors needed is 4 then there are 4 single color codes possible PLUS \(C^2_4=6\) two-color codes --> 4+6=10<12 --> not enough for 12 codes;

If the minimum number of colors needed is 5 then there are 5 single color codes possible PLUS \(C^2_5=10\) two-color codes --> 5+10=15>12 --> more than enough for 12 codes.

Actually as the least answer choice is 5 then if you tried it first you'd get the correct answer right away.

Re: A researcher plans to identify each participant in a certain [#permalink]
03 Dec 2012, 01:30

Expert's post

1

This post was BOOKMARKED

ronr34 wrote:

Hi Bunnel

won't this \(C^2_n\) just give you all the pairs available? we need them also ordered....

Notice that we are told that letters in the code should be written in alphabetical order. Now, 2Cn gives different pairs of 2 letters possible out of n letters, but since codes should be written in one particular order (alphabetical), then for each pair there will be only one ordering possible, thus the number of codes out of n letters equals to number of pairs out of n letters.

Re: A researcher plans to identify each participant in a certain [#permalink]
23 Dec 2012, 12:22

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]
23 Dec 2012, 23:41

2

This post received KUDOS

Expert's post

eaakbari 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]
24 Dec 2012, 00:28

1

This post received KUDOS

Bunuel wrote:

Practice: try to use the same concept.

Okay here goes,

The # of single letter codes possible would be \(n\) itself; The # of pair of distinct letters codes possible would be (in alphabetical order); \(nC2\) The # of Triples of distinct letters codes possible would be (in alphabetical order); \(nC3\)

Re: A researcher plans to identify each participant in a certain [#permalink]
24 Dec 2012, 00:49

1

This post received KUDOS

Expert's post

eaakbari wrote:

Bunuel wrote:

Practice: try to use the same concept.

Okay here goes,

The # of single letter codes possible would be \(n\) itself; The # of pair of distinct letters codes possible would be (in alphabetical order); \(nC2\) The # of Triples of distinct letters codes possible would be (in alphabetical order); \(nC3\)

Thus

\(nC3 + nC2 + n\)> \(12\)

\(n*(n-1)/2 + n*(n-1)*(n-2)/3*2 + n\)> \(12\)

Simplifying

\(n*(n^2 +5)\)> \(72\)

Only sufficient value of \(n = 4\)

Is it correct?

Correct.

Three letters A, B, and C, are enough for 7<12 codes: A; B; C; AB; AC; BC; ABC.

Four letters A, B, C, and D are enough for 15>12 codes: A; B; C; D; AB; AC; AD; BC; BD; CD; ABC; ABD; ACD; BCD; ABCD. _________________

Re: A researcher plans to identify each participant in a certain [#permalink]
22 Nov 2013, 14:15

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);

I still have a little confuse in your formula \(C^2_n\). I am thinking this should be \(A^2_n\) because the 2-letter code must be in alphabetical order.

Hope to hear from you soon.

Thanks

Last edited by yenpham9 on 22 Nov 2013, 14:22, edited 1 time in total.

Re: A researcher plans to identify each participant in a certain [#permalink]
22 Nov 2013, 14:19

Expert's post

yenpham9 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);

I still have a little confuse in your formula \(C^2_n\). I am thinking this should be \(A^2_n\) because the 2-letter code must be in alphabetical order.

Re: A researcher plans to identify each participant in a certain [#permalink]
22 Nov 2013, 14:21

Expert's post

5

This post was BOOKMARKED

Bunuel wrote:

yenpham9 wrote:

Bunuel wrote:

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);

I still have a little confuse in your formula \(C^2_n\). I am thinking this should be \(A^2_n\) because the 2-letter code must be in alphabetical order.

Re: A researcher plans to identify each participant in a certain [#permalink]
22 Nov 2013, 14:37

Bunuel wrote:

ronr34 wrote:

Hi Bunnel

won't this \(C^2_n\) just give you all the pairs available? we need them also ordered....

Notice that we are told that letters in the code should be written in alphabetical order. Now, 2Cn gives different pairs of 2 letters possible out of n letters, but since codes should be written in one particular order (alphabetical), then for each pair there will be only one ordering possible, thus the number of codes out of n letters equals to number of pairs out of n letters.

Hope it's clear.

Hi Bunuel,

From n letters we choose the number of pairs, the result will be \(C^2_n\) which may include 2 kinds of pairs (AB) and (BA). Still confused .

Re: A researcher plans to identify each participant in a certain [#permalink]
22 Nov 2013, 14:43

Expert's post

yenpham9 wrote:

Bunuel wrote:

ronr34 wrote:

Hi Bunnel

won't this \(C^2_n\) just give you all the pairs available? we need them also ordered....

Notice that we are told that letters in the code should be written in alphabetical order. Now, 2Cn gives different pairs of 2 letters possible out of n letters, but since codes should be written in one particular order (alphabetical), then for each pair there will be only one ordering possible, thus the number of codes out of n letters equals to number of pairs out of n letters.

Hope it's clear.

Hi Bunuel,

From n letters we choose the number of pairs, the result will be \(C^2_n\) which may include 2 kinds of pairs (AB) and (BA). Still confused .

Maybe the following example would help. Consider 4 letters {a, b, c, d}. How many 2-letter words in alphabetical order are possible? The answer is \(C^2_4=6\): ab; ac; ad; bc; bd; cd. _________________

Re: A researcher plans to identify each participant in a certain [#permalink]
22 Nov 2013, 14:53

Hi Bunuel,

From n letters we choose the number of pairs, the result will be \(C^2_n\) which may include 2 kinds of pairs (AB) and (BA). Still confused .[/quote]

Maybe the following example would help. Consider 4 letters {a, b, c, d}. How many 2-letter words in alphabetical order are possible? The answer is \(C^2_4=6\): ab; ac; ad; bc; bd; cd.[/quote][/quote]

Thanks a lot Bunuel. I got it now . Have a nice weekend!

Re: A researcher plans to identify each participant in a certain [#permalink]
25 Nov 2013, 03:38

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);

On September 6, 2015, I started my MBA journey at London Business School. I took some pictures on my way from the airport to school, and uploaded them on...

When I was growing up, I read a story about a piccolo player. A master orchestra conductor came to town and he decided to practice with the largest orchestra...

There is one comment that stands out; one conversation having made a great impression on me in these first two weeks. My Field professor told a story about a...

Our Admissions Committee is busy reviewing Round 1 applications. We will begin sending out interview invitations in mid-October and continue until the week of November 9th, at which point...