Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49858

Question Stats:
73% (00:59) correct 27% (01:33) wrong based on 171 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Sep 2009
Posts: 49858

Re M0414
[#permalink]
Show Tags
16 Sep 2014, 00:22
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. Answer: E
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 01 Nov 2013
Posts: 301
WE: General Management (Energy and Utilities)

Re: M0414
[#permalink]
Show Tags
12 Jun 2015, 11:20
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.
Answer: E 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: 49858

Re: M0414
[#permalink]
Show Tags
13 Jun 2015, 08:52
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.
Answer: E 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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 08 Aug 2014
Posts: 8

Re: M0414
[#permalink]
Show Tags
14 Jul 2015, 13:34
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: 49858

Re: M0414
[#permalink]
Show Tags
15 Jul 2015, 01:03



Intern
Joined: 08 Aug 2014
Posts: 8

Re: M0414
[#permalink]
Show Tags
15 Jul 2015, 09:57
I read that part but, to be honest, did not understand what it meant.



Math Expert
Joined: 02 Sep 2009
Posts: 49858

Re: M0414
[#permalink]
Show Tags
15 Jul 2015, 10:01



Intern
Joined: 12 Jul 2015
Posts: 5

Re: M0414
[#permalink]
Show Tags
05 Aug 2015, 04:40
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 reworded 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: 49858

Re: M0414
[#permalink]
Show Tags
20 Aug 2015, 08:43



Intern
Joined: 12 Jul 2015
Posts: 5

Bunuel wrote: CountClaud wrote:
I think that should be reworded 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

Re: M0414
[#permalink]
Show Tags
20 Jul 2016, 19:43
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

Re: M0414
[#permalink]
Show Tags
06 May 2017, 01:40
How is 7!/6! coming up??



Intern
Joined: 30 Apr 2017
Posts: 14

Re: M0414
[#permalink]
Show Tags
15 Jun 2017, 05:39
BunuelIf 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: 49858

Re: M0414
[#permalink]
Show Tags
15 Jun 2017, 06:38



Intern
Joined: 26 Aug 2017
Posts: 11

Re: M0414
[#permalink]
Show Tags
02 Oct 2018, 12:20
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

Re M0414
[#permalink]
Show Tags
03 Oct 2018, 00:19
"Do not differentiate between arrangements that are obtained by swapping two boys or two girls" is missing in the question.










