GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Dec 2018, 05:41

### 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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

December 14, 2018

December 14, 2018

09:00 AM PST

10:00 AM PST

10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.
• ### Typical Day of a UCLA MBA Student - Recording of Webinar with UCLA Adcom and Student

December 14, 2018

December 14, 2018

10:00 PM PST

11:00 PM PST

Carolyn and Brett - nicely explained what is the typical day of a UCLA student. I am posting below recording of the webinar for those who could't attend this session.

# M04-14

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51214

### Show Tags

15 Sep 2014, 23:22
1
3
00:00

Difficulty:

35% (medium)

Question Stats:

73% (00:59) correct 27% (01:33) wrong based on 171 sessions

### HideShow timer Statistics

In how many ways 5 identical blue marbles and 6 identical green marbles can be arranged in a row, so that all the blue marbles are together?

A. 120
B. 30
C. 24
D. 11
E. 7

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 51214

### Show Tags

15 Sep 2014, 23:22
Official Solution:

In how many ways 5 identical blue marbles and 6 identical green marbles can be arranged in a row, so that all the blue marbles are together?

A. 120
B. 30
C. 24
D. 11
E. 7

There are 7 possibilities:

bbbbbgggggg

gbbbbbggggg

ggbbbbbgggg

gggbbbbbggg

ggggbbbbbgg

gggggbbbbbg

ggggggbbbbb

Formally, $$\frac{7!}{6!} = 7$$.

Alternative explanation:

Think of all 5 blue marbles as a single unit. Together with 6 green marbles we'd have a total of 7 units. The difference between the arrangements is the position of the blue marbles (as a single unit). So the problem reduces to finding the number of unique patterns generated by changing the position of the blue marbles which can occupy 1 of 7 available positions. If the number of available unique positions is 7, then the number of unique patterns equals 7 as well.

_________________
Senior Manager
Joined: 01 Nov 2013
Posts: 293
GMAT 1: 690 Q45 V39
WE: General Management (Energy and Utilities)

### Show Tags

12 Jun 2015, 10:20
Bunuel wrote:
Official Solution:

If a choir consists of 5 boys and 6 girls, in how many ways can the singers be arranged in a row, so that all the boys are together? Do not differentiate between arrangements that are obtained by swapping two boys or two girls.

A. 120
B. 30
C. 24
D. 11
E. 7

There are 7 possibilities:

bbbbbgggggg

gbbbbbggggg

ggbbbbbgggg

gggbbbbbggg

ggggbbbbbgg

gggggbbbbbg

ggggggbbbbb

Formally, $$\frac{7!}{6!} = 7$$.

Alternative explanation:

Think of all 5 boys as a single unit. Together with 6 girls it makes a total of 7 units. The difference between the arrangements is the position of the boys (as a single unit). So the problem reduces to finding the number of unique patterns generated by changing the position of the boys who can occupy 1 of 7 available positions. If the number of available unique positions is 7, then the number of unique patterns equals 7 as well.

Hi Bunnel

What do we mean by the following statement-
Do not differentiate between arrangements that are obtained by swapping two boys or two girls.

Do we mean to say that we need to ignore the {5!} and {6!} ways in which the boys and girls can be arranged among themselves....??

This is what I understood.Please clarify.

Thanks
_________________

Our greatest weakness lies in giving up. The most certain way to succeed is always to try just one more time.

I hated every minute of training, but I said, 'Don't quit. Suffer now and live the rest of your life as a champion.-Mohammad Ali

Math Expert
Joined: 02 Sep 2009
Posts: 51214

### Show Tags

13 Jun 2015, 07:52
samichange wrote:
Bunuel wrote:
Official Solution:

If a choir consists of 5 boys and 6 girls, in how many ways can the singers be arranged in a row, so that all the boys are together? Do not differentiate between arrangements that are obtained by swapping two boys or two girls.

A. 120
B. 30
C. 24
D. 11
E. 7

There are 7 possibilities:

bbbbbgggggg

gbbbbbggggg

ggbbbbbgggg

gggbbbbbggg

ggggbbbbbgg

gggggbbbbbg

ggggggbbbbb

Formally, $$\frac{7!}{6!} = 7$$.

Alternative explanation:

Think of all 5 boys as a single unit. Together with 6 girls it makes a total of 7 units. The difference between the arrangements is the position of the boys (as a single unit). So the problem reduces to finding the number of unique patterns generated by changing the position of the boys who can occupy 1 of 7 available positions. If the number of available unique positions is 7, then the number of unique patterns equals 7 as well.

Hi Bunnel

What do we mean by the following statement-
Do not differentiate between arrangements that are obtained by swapping two boys or two girls.

Do we mean to say that we need to ignore the {5!} and {6!} ways in which the boys and girls can be arranged among themselves....??

This is what I understood.Please clarify.

Thanks

Yes, you are correct.
_________________
Intern
Joined: 08 Aug 2014
Posts: 8

### Show Tags

14 Jul 2015, 12:34
Bunuel

I don't understand. I've seen any number of questions of this type. They are invariably permutations questions. If a bunch of people are put in a row then every arrangement, whether Paul is to the left of Michael or Michael is to the left of Paul, is different from every other arrangement.

In this case, the answer should be 5! x 7!
Math Expert
Joined: 02 Sep 2009
Posts: 51214

### Show Tags

15 Jul 2015, 00:03
hessen923 wrote:
Bunuel

I don't understand. I've seen any number of questions of this type. They are invariably permutations questions. If a bunch of people are put in a row then every arrangement, whether Paul is to the left of Michael or Michael is to the left of Paul, is different from every other arrangement.

In this case, the answer should be 5! x 7!

Have you read this part of the question: Do not differentiate between arrangements that are obtained by swapping two boys or two girls.
_________________
Intern
Joined: 08 Aug 2014
Posts: 8

### Show Tags

15 Jul 2015, 08:57
I read that part but, to be honest, did not understand what it meant.
Math Expert
Joined: 02 Sep 2009
Posts: 51214

### Show Tags

15 Jul 2015, 09:01
hessen923 wrote:
I read that part but, to be honest, did not understand what it meant.

It means that we are not interested in arrangements of girls and boys in their groups.
_________________
Intern
Joined: 12 Jul 2015
Posts: 5

### Show Tags

05 Aug 2015, 03:40
Bunuel wrote:
hessen923 wrote:
I read that part but, to be honest, did not understand what it meant.

It means that we are not interested in arrangements of girls and boys in their groups.

I think that should be re-worded in a clearer fashion. The fact that the problem mentioned two girls led me to look at permutation gbbbbbggggg as being able to rotate the first girl with any of the other remaining 5 girls. Apologies but the sentence " swapping two boys or two girls" does not make much sense to me...
Math Expert
Joined: 02 Sep 2009
Posts: 51214

### Show Tags

20 Aug 2015, 07:43
CountClaud wrote:
Bunuel wrote:
hessen923 wrote:
I read that part but, to be honest, did not understand what it meant.

It means that we are not interested in arrangements of girls and boys in their groups.

I think that should be re-worded in a clearer fashion. The fact that the problem mentioned two girls led me to look at permutation gbbbbbggggg as being able to rotate the first girl with any of the other remaining 5 girls. Apologies but the sentence " swapping two boys or two girls" does not make much sense to me...

Edited the question. Is it OK now?
_________________
Intern
Joined: 12 Jul 2015
Posts: 5

### Show Tags

30 Aug 2015, 07:46
Bunuel wrote:
CountClaud wrote:

I think that should be re-worded in a clearer fashion. The fact that the problem mentioned two girls led me to look at permutation gbbbbbggggg as being able to rotate the first girl with any of the other remaining 5 girls. Apologies but the sentence " swapping two boys or two girls" does not make much sense to me...

Edited the question. Is it OK now?

Much clearer. Thanks, Bunuel!
Intern
Joined: 22 Jun 2016
Posts: 10

### Show Tags

20 Jul 2016, 18:43
Should clarify to say "unique patterns." The problem attempts to do this by saying "identical" marbles. But this technically doesn't imply that marble 1,2,3,4,5,6,7 are interchangeable. I can move 2,1,3,4,5,6,7 and that seems like a different position to me, even if they are all the same size, weight, color etc. Unless, that's exactly what "identical" means on the GMAT, would be good to know if I am right or wrong. Logically, it doesn't seem like a strong enough implication per my example.
Intern
Joined: 04 Jan 2017
Posts: 7

### Show Tags

06 May 2017, 00:40
How is 7!/6! coming up??
Intern
Joined: 30 Apr 2017
Posts: 14

### Show Tags

15 Jun 2017, 04:39
Bunuel
If the question had been about unique Bs & Gs, then the answer should have been 7*5!*6!, correct?
Math Expert
Joined: 02 Sep 2009
Posts: 51214

### Show Tags

15 Jun 2017, 05:38
kerin wrote:
Bunuel
If the question had been about unique Bs & Gs, then the answer should have been 7*5!*6!, correct?

No, in this case the answer would be 7!*5!.

Glue b's together, we'll get 7 units:
{bbbbb}{g}{g}{g}{g}{g}{g}

# of arrangements = 7!. 5 g's within their unit can be arranged in 5! ways. So, 7!*5!.
_________________
Intern
Joined: 26 Aug 2017
Posts: 11

### Show Tags

02 Oct 2018, 11:20
Question wording is wrong:

In how many ways 5 identical blue marbles and 6 identical green marbles can be arranged in a row, so that all the blue marbles are together?
Intern
Joined: 06 Mar 2018
Posts: 1

### Show Tags

02 Oct 2018, 23:19
"Do not differentiate between arrangements that are obtained by swapping two boys or two girls" is missing in the question.
Re M04-14 &nbs [#permalink] 02 Oct 2018, 23:19
Display posts from previous: Sort by

# M04-14

Moderators: chetan2u, Bunuel

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne 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®.