A researcher plans to identify each participant in a certain : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 21 Feb 2017, 18:51

GMAT Club Daily Prep

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

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A researcher plans to identify each participant in a certain

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Intern
Joined: 12 May 2012
Posts: 24
Location: United States
Concentration: Technology, Human Resources
Followers: 0

Kudos [?]: 137 [2] , given: 19

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

Show Tags

17 Jun 2012, 03:13
2
KUDOS
76
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

54% (02:19) correct 46% (01:25) wrong based on 1812 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?

A. 4
B. 5
C. 6
D. 7
E. 8
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Jun 2012, 03:20, edited 1 time in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 37059
Followers: 7240

Kudos [?]: 96250 [11] , given: 10728

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

Show Tags

17 Jun 2012, 03:24
11
KUDOS
Expert's post
23
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);

We want $$C^2_n+n\geq{12}$$ --> $$\frac{n(n-1)}{2}+n\geq{12}$$ --> $$n(n-1)+2n\geq{24}$$ --> $$n(n+1)\geq{24}$$ --> $$n_{min}=5$$.

Hope it's clear.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 37059
Followers: 7240

Kudos [?]: 96250 [3] , given: 10728

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

Show Tags

17 Jun 2012, 03:34
3
KUDOS
Expert's post
20
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

Similar questions to practice:
if-a-code-word-is-defined-to-be-a-sequence-of-different-126652.html
all-of-the-stocks-on-the-over-the-counter-market-are-126630.html
the-simplastic-language-has-only-2-unique-values-and-105845.html
a-4-letter-code-word-consists-of-letters-a-b-and-c-if-the-59065.html
a-certain-stock-exchange-designates-each-stock-with-a-86656.html
a-5-digit-code-consists-of-one-number-digit-chosen-from-132263.html

Hope it helps.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 37059
Followers: 7240

Kudos [?]: 96250 [1] , given: 10728

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

Show Tags

17 Jun 2012, 03:49
1
KUDOS
Expert's post
8
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.

Hope it helps.
_________________
Intern
Joined: 27 Aug 2012
Posts: 20
Followers: 0

Kudos [?]: 4 [0], given: 55

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

Show Tags

01 Dec 2012, 19:10
Bunnel. Thaks for the reply and merging similar topics. Can u please explain how >= 12 ?
Math Expert
Joined: 02 Sep 2009
Posts: 37059
Followers: 7240

Kudos [?]: 96250 [0], given: 10728

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

Show Tags

02 Dec 2012, 03:51
SreeViji wrote:
Bunnel. Thaks for the reply and merging similar topics. Can u please explain how >= 12 ?

The number of letters should be enough to make at least 12 codes, thus the number of codes must be more than or equal to 12.
_________________
Senior Manager
Joined: 07 Apr 2012
Posts: 464
Followers: 2

Kudos [?]: 54 [2] , given: 58

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

Show Tags

02 Dec 2012, 13:48
2
KUDOS
Hi Bunnel

won't this $$C^2_n$$
just give you all the pairs available?
we need them also ordered....
Math Expert
Joined: 02 Sep 2009
Posts: 37059
Followers: 7240

Kudos [?]: 96250 [1] , given: 10728

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

Show Tags

03 Dec 2012, 01:30
1
KUDOS
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.

Hope it's clear.
_________________
Manager
Joined: 24 Mar 2010
Posts: 81
Followers: 1

Kudos [?]: 62 [0], given: 134

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

Show Tags

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);

We want $$C^2_n+n\geq{12}$$ --> $$\frac{n(n-1)}{2}+n\geq{12}$$ --> $$n(n-1)+2n\geq{24}$$ --> $$n(n+1)\geq{24}$$ --> $$n_{min}=5$$.

Hope it's clear.

Bunuel,

What if the question didn't say 'pair'.

If 3 letter combinations were also permitted. How would you express it in Combination formula?
_________________

- Stay Hungry, stay Foolish -

Math Expert
Joined: 02 Sep 2009
Posts: 37059
Followers: 7240

Kudos [?]: 96250 [2] , given: 10728

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

Show Tags

23 Dec 2012, 23:41
2
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);

We want $$C^2_n+n\geq{12}$$ --> $$\frac{n(n-1)}{2}+n\geq{12}$$ --> $$n(n-1)+2n\geq{24}$$ --> $$n(n+1)\geq{24}$$ --> $$n_{min}=5$$.

Hope it's clear.

Bunuel,

What if the question didn't say 'pair'.

If 3 letter combinations were also permitted. How would you express it in Combination formula?

Practice: try to use the same concept.
_________________
Manager
Joined: 24 Mar 2010
Posts: 81
Followers: 1

Kudos [?]: 62 [1] , given: 134

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

Show Tags

24 Dec 2012, 00:28
1
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); $$nC3$$

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?
_________________

- Stay Hungry, stay Foolish -

Math Expert
Joined: 02 Sep 2009
Posts: 37059
Followers: 7240

Kudos [?]: 96250 [2] , given: 10728

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

Show Tags

24 Dec 2012, 00:49
2
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;
BC;
BD;
CD;
ABC;
ABD;
ACD;
BCD;
ABCD.
_________________
Manager
Joined: 24 Mar 2010
Posts: 81
Followers: 1

Kudos [?]: 62 [0], given: 134

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

Show Tags

24 Dec 2012, 00:53
Thanks a ton Bunuel,

Its crystal clear now.
_________________

- Stay Hungry, stay Foolish -

Intern
Joined: 12 Mar 2011
Posts: 24
Followers: 0

Kudos [?]: 17 [0], given: 57

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

Show Tags

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);

We want $$C^2_n+n\geq{12}$$ --> $$\frac{n(n-1)}{2}+n\geq{12}$$ --> $$n(n-1)+2n\geq{24}$$ --> $$n(n+1)\geq{24}$$ --> $$n_{min}=5$$.

Hope it's clear.

Hi Bunuel,

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.
Math Expert
Joined: 02 Sep 2009
Posts: 37059
Followers: 7240

Kudos [?]: 96250 [0], given: 10728

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

Show Tags

22 Nov 2013, 14:19
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);

We want $$C^2_n+n\geq{12}$$ --> $$\frac{n(n-1)}{2}+n\geq{12}$$ --> $$n(n-1)+2n\geq{24}$$ --> $$n(n+1)\geq{24}$$ --> $$n_{min}=5$$.

Hope it's clear.

Hi Bunnel,

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

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 37059
Followers: 7240

Kudos [?]: 96250 [0], given: 10728

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

Show Tags

22 Nov 2013, 14:21
Expert's post
7
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);

We want $$C^2_n+n\geq{12}$$ --> $$\frac{n(n-1)}{2}+n\geq{12}$$ --> $$n(n-1)+2n\geq{24}$$ --> $$n(n+1)\geq{24}$$ --> $$n_{min}=5$$.

Hope it's clear.

Hi Bunnel,

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

Similar questions to practice:
each-student-at-a-certain-university-is-given-a-four-charact-151945.html
all-of-the-stocks-on-the-over-the-counter-market-are-126630.html
if-a-code-word-is-defined-to-be-a-sequence-of-different-126652.html
a-4-letter-code-word-consists-of-letters-a-b-and-c-if-the-59065.html
a-5-digit-code-consists-of-one-number-digit-chosen-from-132263.html
a-company-that-ships-boxes-to-a-total-of-12-distribution-95946.html
a-company-plans-to-assign-identification-numbers-to-its-empl-69248.html
the-security-gate-at-a-storage-facility-requires-a-five-109932.html
all-of-the-bonds-on-a-certain-exchange-are-designated-by-a-150820.html
a-local-bank-that-has-15-branches-uses-a-two-digit-code-to-98109.html
a-researcher-plans-to-identify-each-participant-in-a-certain-134584.html
baker-s-dozen-128782-20.html#p1057502
in-a-certain-appliance-store-each-model-of-television-is-136646.html
m04q29-color-coding-70074.html
john-has-12-clients-and-he-wants-to-use-color-coding-to-iden-107307.html
how-many-4-digit-even-numbers-do-not-use-any-digit-more-than-101874.html
a-certain-stock-exchange-designates-each-stock-with-a-85831.html
the-simplastic-language-has-only-2-unique-values-and-105845.html
m04q29-color-coding-70074.html

Hope this helps.
_________________
Intern
Joined: 12 Mar 2011
Posts: 24
Followers: 0

Kudos [?]: 17 [0], given: 57

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

Show Tags

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 .
Math Expert
Joined: 02 Sep 2009
Posts: 37059
Followers: 7240

Kudos [?]: 96250 [0], given: 10728

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

Show Tags

22 Nov 2013, 14:43
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;
bc;
bd;
cd.
_________________
Intern
Joined: 12 Mar 2011
Posts: 24
Followers: 0

Kudos [?]: 17 [0], given: 57

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

Show Tags

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;
bc;
bd;
cd.[/quote][/quote]

Thanks a lot Bunuel. I got it now . Have a nice weekend!
Director
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 635
Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
Followers: 70

Kudos [?]: 442 [0], given: 297

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

Show Tags

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);

We want $$C^2_n+n\geq{12}$$ --> $$\frac{n(n-1)}{2}+n\geq{12}$$ --> $$n(n-1)+2n\geq{24}$$ --> $$n(n+1)\geq{24}$$ --> $$n_{min}=5$$.

Hope it's clear.

we can take 1,2 and 3
like
A, B, C
AB, BC
ABC

Why did you ignored possibility of 3 or 4 alphabets taken together, this will give us 4 letters?
_________________

Like my post Send me a Kudos It is a Good manner.
My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html

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

Go to page    1   2   3   4    Next  [ 78 posts ]

Similar topics Replies Last post
Similar
Topics:
4 At a certain laboratory, chemical substance are identified by an unord 8 04 Jan 2015, 09:22
2 Of the twelve participants in a certain competition 3 05 Feb 2014, 12:04
25 A certain research group plans to create computer models of 20 09 Sep 2013, 09:59
21 If each participant of a chess tournament plays exactly one 10 10 Nov 2012, 13:06
4 Each participant in a certain study was assigned a sequence 6 27 May 2010, 10:30
Display posts from previous: Sort by

A researcher plans to identify each participant in a certain

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.