NEW HERE? LEARN MORE
closeclose
Last visit was: 12 May 2024, 02:42 It is currently 12 May 2024, 02:42
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

A scientist used a unique two-color code to identify each

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
goodyear2013
Senior Manager
Senior Manager
Joined: 21 Oct 2013
Posts: 392
Own Kudos [?]: 5112 [13]
Given Kudos: 289
Send PM
A scientist used a unique two-color code to identify each [#permalink] New post   05 Feb 2014, 12:53
13
Bookmarks
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

72% (01:24) correct 28% (01:47) wrong based on 451 sessions
Hide Show timer Statistics
A scientist used a unique two-color code to identify each of the test subjects involved in a certain study. If the scientist found that choosing from among six colors produced enough color codes to identify all but 5 of the test subjects, how many test subjects were in the study? (Assume that the order of the colors in the codes does not matter.)

7
10
15
17
20

OE
Show Spoiler
If 6 colors have to be divided into groups of 2, the number of unique groupings 6C2 = 6! / (2!)(4!) = 15.
Number of combinations was sufficient to account for all but 5 of the subjects
Number of subjects = 15 + 5 = 20.


Hi, I found this question stem not clear. Can anyone explain this for me, please.
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93172
Own Kudos [?]: 623058 [10]
Given Kudos: 81833
Send PM
CAT Tests Forum Quiz Mode
Re: A scientist used a unique two-color code to identify each [#permalink] New post   05 Feb 2014, 23:29
1
Kudos
9
Bookmarks
Expert Reply
goodyear2013 wrote:
A scientist used a unique two-color code to identify each of the test subjects involved in a certain study. If the scientist found that choosing from among six colors produced enough color codes to identify all but 5 of the test subjects, how many test subjects were in the study? (Assume that the order of the colors in the codes does not matter.)

7
10
15
17
20

OE
Show Spoiler
If 6 colors have to be divided into groups of 2, the number of unique groupings 6C2 = 6! / (2!)(4!) = 15.
Number of combinations was sufficient to account for all but 5 of the subjects
Number of subjects = 15 + 5 = 20.


Hi, I found this question stem not clear. Can anyone explain this for me, please.


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
the-telephone-company-wants-to-add-an-area-code-composed-of-20252.html
a-company-that-ships-boxes-to-a-total-of-12-distribution-95946.html

Hope this helps.
User avatar
G
mikemcgarry
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4454
Own Kudos [?]: 28618 [5]
Given Kudos: 130
Re: A scientist used a unique two-color code to identify each [#permalink] New post   05 Feb 2014, 15:40
3
Kudos
2
Bookmarks
Expert Reply
goodyear2013 wrote:
A scientist used a unique two-color code to identify each of the test subjects involved in a certain study. If the scientist found that choosing from among six colors produced enough color codes to identify all but 5 of the test subjects, how many test subjects were in the study? (Assume that the order of the colors in the codes does not matter.)

7
10
15
17
20

OE
Show Spoiler
If 6 colors have to be divided into groups of 2, the number of unique groupings 6C2 = 6! / (2!)(4!) = 15.
Number of combinations was sufficient to account for all but 5 of the subjects
Number of subjects = 15 + 5 = 20.


Hi, I found this question stem not clear. Can anyone explain this for me, please.

Dear goodyear2013,
I'm happy to help. :-) I'm not entirely sure I understand what you found unclear. I will try telling the story in my own words.

A scientist was conducting a study, and he had to test individual subjects. As a way to identify the subjects, the scientist gave each subject something, say a badge, with two colors on it, and the scientist wanted the color combination to be different for each subject. Say there were N subjects in total. The scientist used six different individual colors, and different pairs formed from these six colors formed enough combinations to make unique color combinations for (N - 5) of the subject, so the scientist probably had to "double up" or do something different for those last 5 subjects.

This question is about counting techniques. See:
https://magoosh.com/gmat/2012/gmat-quant-how-to-count/
https://magoosh.com/gmat/2012/gmat-permu ... binations/
If we have six colors, the number of unique pairs of color we can create is
6C2 = 15
Each of the first 15 subjects got her or his unique pair of colors, leaving the last 5 with some other arrangement. Total = 15 + 5 = 20

Does all this make sense?
Mike :-)
General Discussion
avatar
B
GSBae
Manager
Manager
Joined: 23 May 2013
Posts: 170
Own Kudos [?]: 402 [0]
Given Kudos: 42
Location: United States
Concentration: Technology, Healthcare
Schools: Stanford '19 (M$)
GMAT 1: 760 Q49 V45
GPA: 3.5
Send PM
GMAT ToolKit User
A scientist used a unique two-color code to identify each [#permalink] New post   31 Dec 2014, 08:12
Hi all,

By using 6 choose 2, aren't we ignoring the possibility of having a badge with two of the same color; i.e., RR,OO, YY, etc? In this case, we have to add 6 for this possibility, and then add 5 for the extra subjects that couldn't be included. I think the OA should be 26.

Can anyone give some insight?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93172
Own Kudos [?]: 623058 [0]
Given Kudos: 81833
Send PM
CAT Tests Forum Quiz Mode
Re: A scientist used a unique two-color code to identify each [#permalink] New post   31 Dec 2014, 08:15
Expert Reply
speedilly wrote:
Hi all,

By using 6 choose 2, aren't we ignoring the possibility of having a badge with two of the same color; i.e., RR,OO, YY, etc? In this case, we have to add 6 for this possibility, and then add 5 for the extra subjects that couldn't be included. I think the OA should be 26.

Can anyone give some insight?


A scientist used a unique two-color code... I think from this we can assume that the two colors must be different.
avatar
B
GSBae
Manager
Manager
Joined: 23 May 2013
Posts: 170
Own Kudos [?]: 402 [0]
Given Kudos: 42
Location: United States
Concentration: Technology, Healthcare
Schools: Stanford '19 (M$)
GMAT 1: 760 Q49 V45
GPA: 3.5
Send PM
GMAT ToolKit User
Re: A scientist used a unique two-color code to identify each [#permalink] New post   31 Dec 2014, 08:21
I guess that makes sense, but I as a reader would interpret that to mean that they used two 'slots' for the colors.

I imagine that by not using this possibility they're being highly inefficient - no wonder they weren't able to account for all of their test subjects.
User avatar
pacifist85
Senior Manager
Senior Manager
Joined: 07 Apr 2014
Status:Math is psycho-logical
Posts: 340
Own Kudos [?]: 388 [0]
Given Kudos: 169
Location: Netherlands
GMAT Date: 02-11-2015
WE:Psychology and Counseling (Other)
Re: A scientist used a unique two-color code to identify each [#permalink] New post   10 Jan 2015, 12:14
When you have this small selection of choices it is also easy to write them down in a table and cross out the ones you have used:
A_B_C_D_E_F--> the 6 colours, and we add them again beneath each colour to make the combinations.
A_A_A_A_A__A
B_B_B_B_B__B
C_C_C_C_C_C
D_D_D_D_D_D
E_E_E_E_E__E
F_F_F_F_F___F

So, you start by crossing out the same colours, e.g AA,BB,CC etc, and then the reverse colours, e.g, cross out BA because you have AB.
Then starting with A you've got:
AB - AC - AD - AE - AF
BC_BD_BE_BF
CD_CE_CF
DE_DF
EF
Nothing from F because all the colours have been used before.

So, 15 combinations, which are used for 15 people, plus 5 missing: 15+5=20.
User avatar
pacifist85
Senior Manager
Senior Manager
Joined: 07 Apr 2014
Status:Math is psycho-logical
Posts: 340
Own Kudos [?]: 388 [0]
Given Kudos: 169
Location: Netherlands
GMAT Date: 02-11-2015
WE:Psychology and Counseling (Other)
Re: A scientist used a unique two-color code to identify each [#permalink] New post   10 Jan 2015, 12:20
That in case 6!/(2!*4!) doesn't cross your mind... or you are slow with calculations, as I am.
User avatar
Lucky2783
Senior Manager
Senior Manager
Joined: 07 Aug 2011
Posts: 425
Own Kudos [?]: 1758 [0]
Given Kudos: 75
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
Send PM
GMAT ToolKit User
Re: A scientist used a unique two-color code to identify each [#permalink] New post   21 Jan 2015, 07:46
mikemcgarry wrote:
goodyear2013 wrote:
A scientist used a unique two-color code to identify each of the test subjects involved in a certain study. If the scientist found that choosing from among six colors produced enough color codes to identify all but 5 of the test subjects, how many test subjects were in the study? (Assume that the order of the colors in the codes does not matter.)

7
10
15
17
20

OE
Show Spoiler
If 6 colors have to be divided into groups of 2, the number of unique groupings 6C2 = 6! / (2!)(4!) = 15.
Number of combinations was sufficient to account for all but 5 of the subjects
Number of subjects = 15 + 5 = 20.


Hi, I found this question stem not clear. Can anyone explain this for me, please.

Dear goodyear2013,
I'm happy to help. :-) I'm not entirely sure I understand what you found unclear. I will try telling the story in my own words.

A scientist was conducting a study, and he had to test individual subjects. As a way to identify the subjects, the scientist gave each subject something, say a badge, with two colors on it, and the scientist wanted the color combination to be different for each subject. Say there were N subjects in total. The scientist used six different individual colors, and different pairs formed from these six colors formed enough combinations to make unique color combinations for (N - 5) of the subject, so the scientist probably had to "double up" or do something different for those last 5 subjects.

This question is about counting techniques. See:
https://magoosh.com/gmat/2012/gmat-quant-how-to-count/
https://magoosh.com/gmat/2012/gmat-permu ... binations/
If we have six colors, the number of unique pairs of color we can create is
6C2 = 15
Each of the first 15 subjects got her or his unique pair of colors, leaving the last 5 with some other arrangement. Total = 15 + 5 = 20

Does all this make sense?
Mike :-)

Hi Mike,

I thought that since it is a code the order matters. let say we have Red/Green two color, Color code RG is different from GR and So 2! *6C2 + 5 = 35 .
I agree with mikemcgarry that the question stem is ambiguous.

thanks
User avatar
G
mikemcgarry
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4454
Own Kudos [?]: 28618 [0]
Given Kudos: 130
Re: A scientist used a unique two-color code to identify each [#permalink] New post   21 Jan 2015, 10:42
Expert Reply
Lucky2783 wrote:
Hi Mike,

I thought that since it is a code the order matters. let say we have Red/Green two color, Color code RG is different from GR and So 2! *6C2 + 5 = 35 .
I agree with mikemcgarry that the question stem is ambiguous.

thanks

Dear Lucky2783,
I'm happy to reply. :-) Here's the question prompt again.
A scientist used a unique two-color code to identify each of the test subjects involved in a certain study. If the scientist found that choosing from among six colors produced enough color codes to identify all but 5 of the test subjects, how many test subjects were in the study? (Assume that the order of the colors in the codes does not matter.)
Notice that the question states, quite explicitly, that the order of the colors in the code doesn't matter. Remember never to let your own interpretation trump what is explicitly stated in the text of the problem.
Does this make sense?
Mike :-)
User avatar
G
testcracker
Manager
Manager
Joined: 24 Mar 2015
Status:love the club...
Posts: 220
Own Kudos [?]: 112 [1]
Given Kudos: 527
Send PM
Re: A scientist used a unique two-color code to identify each [#permalink] New post   25 Dec 2017, 01:19
1
Kudos
goodyear2013 wrote:
A scientist used a unique two-color code to identify each of the test subjects involved in a certain study. If the scientist found that choosing from among six colors produced enough color codes to identify all but 5 of the test subjects, how many test subjects were in the study? (Assume that the order of the colors in the codes does not matter.)

7
10
15
17
20

OE
Show Spoiler
If 6 colors have to be divided into groups of 2, the number of unique groupings 6C2 = 6! / (2!)(4!) = 15.
Number of combinations was sufficient to account for all but 5 of the subjects
Number of subjects = 15 + 5 = 20.


Hi, I found this question stem not clear. Can anyone explain this for me, please.


hi

6 * 6 = 36
means we can use the same color for a code, but it cannot be the case, for example, "Red + Red" cannot itself constitute any code

6 * 5 = 30
means we are distinguishing between "Red + Green" and "Green + Red ", but, according to the question, essentially they are the same

so, actually this is a combination as follows

6!
______
2! 3!

= 15

but, this amount falls short of encompassing all the studies, as we are left with 5 studies not coded
so the number of study is (15 + 5) = 20

thanks
:cool:
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32953
Own Kudos [?]: 828 [0]
Given Kudos: 0
Send PM
Re: A scientist used a unique two-color code to identify each [#permalink] New post   25 Jan 2023, 21:01
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: A scientist used a unique two-color code to identify each [#permalink]
25 Jan 2023, 21:01
Moderators:
Bunuel
Math Expert
93172 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions