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]

Show Tags

17 Jun 2012, 04:13

3

This post received KUDOS

44

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

54% (02:13) correct
46% (01:26) wrong based on 1264 sessions

HideShow timer Statistics

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]

Show Tags

17 Jun 2012, 04:24

6

This post received KUDOS

Expert's post

21

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]

Show Tags

17 Jun 2012, 04:34

3

This post received KUDOS

Expert's post

14

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]

Show Tags

27 Dec 2014, 11:22

3

This post received KUDOS

Expert's post

Hi All,

In these sorts of questions, when the answer choices are relatively small, it's often fairly easy to "brute force" the correct answer and avoid complicated calculations entirely.

BrainLab's idea to just "map out" the possibilities is a relatively simple, effective approach. Since we're asked for the LEAST number of letters that will give us 12 unique codes, we start with Answer A.

If we had 4 letters: A, B, C, D

1-letter codes: A, B, C, D 2-letter alphabetical codes: AB, AC, AD, BC, BD, CD Total Codes = 4 + 6 = 10

This result is TOO LOW.

From here, you know that we just need 2 more codes, so adding 1 more letter would give us those extra codes (and more)...but here's the proof that it happens....

If we had 5 letters: A, B, C, D, E

1-letter codes: A, B, C, D, E 2-letter alphabetical codes: AB, AC, AD, AE, BC, BD, BE, CD, CE, DE Total Codes = 5 + 10 = 15 codes

Re: A researcher plans to identify each participant in a certain [#permalink]

Show Tags

24 Dec 2012, 00:41

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]

Show Tags

14 Mar 2014, 02:48

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]

Show Tags

17 Jun 2012, 04:49

1

This post received KUDOS

Expert's post

6

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]

Show Tags

24 Dec 2012, 01:28

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]

Show Tags

24 Dec 2012, 01:49

1

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

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]

Show Tags

25 Nov 2013, 04:41

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]

Show Tags

29 Nov 2013, 20:18

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]

Show Tags

14 Aug 2014, 00:54

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]

Show Tags

09 Feb 2015, 01:43

1

This post received KUDOS

Expert's post

ProblemChild wrote:

Bunuel wrote:

kevn1115 wrote:

Hi Bunuel,

I'm confused on when you show that n! = (n-2)!*(n-1)*n...why is n! only limited to those 3 factors? I guess the question is why do you start at (n-2)!?

Thanks.!

\(C^2_n=\frac{n!}{2!(n-2)!}\). Now, notice that \(n!=(n-2)!*(n-1)*n\), hence \(C^2_n=\frac{n!}{2!(n-2)!}=\frac{(n-2)!*(n-1)*n}{2!(n-2)!}=\frac{(n-1)n}{2}\).

Hope it's clear.

n! is the product of positive integers from 1 to n, inclusive: n! = 1*2*...*(n-4)*(n-3)(n-2)(n-1)n. To simplify \(\frac{n!}{2!(n-2)!}\) I wrote n! as (n-2)!*(n-1)*n this enables us to reduce by (n-2)! to get \(\frac{(n-1)n}{2}\).

Hope it's clear.

Hi bunuel!

Sorry for opening the old topic but my question is why are you and everyone else writing the "c(n, k)" upside down. Have a look at the screenshot of the gmat club math book and the equation everyone is referring to.

Thanks!

\(C^1_3\), \(C^3_1\), 3C1, mean the same thing choosing 1 out of 3, just different ways to write. Can it be choosing 3 out of 1??? _________________

Re: A researcher plans to identify each participant in a certain [#permalink]

Show Tags

03 Dec 2012, 02:30

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]

Show Tags

23 Dec 2012, 13:22

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]

Show Tags

22 Nov 2013, 15:15

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, 15:22, edited 1 time in total.

gmatclubot

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

http://blog.ryandumlao.com/wp-content/uploads/2016/05/IMG_20130807_232118.jpg The GMAT is the biggest point of worry for most aspiring applicants, and with good reason. It’s another standardized test when most of us...

I recently returned from attending the London Business School Admits Weekend held last week. Let me just say upfront - for those who are planning to apply for the...