Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 22 Apr 2011
Posts: 145
Schools: Mccombs business school, Mays business school, Rotman Business School,

In a business school case competition, the top three teams
[#permalink]
Show Tags
Updated on: 06 Jul 2012, 01:11
Question Stats:
41% (02:34) correct 59% (02:31) wrong based on 224 sessions
HideShow timer Statistics
In a business school case competition, the top three teams receive cash prizes of $1000, $ 2000, and $ 3000. while remaining teams are not ranked and do not receive any prizes, there are 6 participating teams, named A, B, C, D, E, F. If team A wins one of the prizes, team B wins also one of the prizes. How many outcomes of the competition are possible ? A. 18 B. 28 C. 36 D. 84 E. 120
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
some people are successful, because they have been fortunate enough and some people earn success, because they have been determined.....
please press kudos if you like my post.... i am begging for kudos...lol
Originally posted by alchemist009 on 05 Jul 2012, 23:02.
Last edited by Bunuel on 06 Jul 2012, 01:11, edited 2 times in total.
Edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 50002

Re: In a business school case competition, the top three teams
[#permalink]
Show Tags
06 Jul 2012, 01:14
alchemist009 wrote: In a business school case competition, the top three teams receive cash prizes of $1000, $ 2000, and $ 3000. while remaining teams are not ranked and do not receive any prizes, there are 6 participating teams, named A, B, C, D, E, F. If team A wins one of the prizes, team B wins also one of the prizes. How many outcomes of the competition are possible ?
A. 18 B. 28 C. 36 D. 84 E. 120 We are told that " if team A wins one of the prizes, team B wins also one of the prizes". Consider following cases: A wins one of the prizes, then B must also win one of the prizes, and in this case we can have 4 triplets: {ABC}, {ABD}, {ABE}, {ABF}. Each triplet can be arranged in 3!=6 ways. Hence in the case when A wins one of the prizes 4*6=24 arrangements are possible. A does NOT win one of the prizes, then three winners must be from other 5 teams. 3 winners out of 5 (B, C, D, E, F) teams can be chosen in \(C^3_5=10\) ways and each case (for example {CDE}) can be arranged in 3!=6 ways, hence in the case when A does NOT win one of the prizes 10*6=60 arrangements are possible. Total = 24+60 = 84. Answer: D. Hope it's clear.
_________________
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




Math Expert
Joined: 02 Sep 2009
Posts: 50002

Re: In a business school case competition, the top three teams
[#permalink]
Show Tags
01 Jul 2013, 00:59



Manager
Joined: 20 Dec 2013
Posts: 238
Location: India

Re: In a business school case competition, the top three teams
[#permalink]
Show Tags
12 Apr 2014, 21:33
Option D. If we make cases: I:\(A\) doesn't win:\(5*4*3=60\) cases + II:\(A\) wins:\(C(3,1)*C(2,1)*C(4,1)=24\) cases Because \(A\) could take any one of three prizes \(B\) could take any of the 2 prizes left And the third leftover prize could be taken by any one of \(C,D,E,F\). Total=\(84\) cases



Intern
Joined: 10 Apr 2014
Posts: 33

Re: In a business school case competition, the top three teams
[#permalink]
Show Tags
13 Apr 2014, 02:55
Bunuel wrote: Bumping for review and further discussion*. Get a kudos point for an alternative solution!
Alternative solution: If there would have been no constraint the number of possible scenarios were: 6P\(3\) = 6!/3! = 120 Now we need to calculate cases where A is a winner but B is not So the other two positions can be taken by C, D , E, F . total number of combination = 4C2 = 4!/(2!*2!) = 6 As the three winners can be arranged among themselves in 3! ways, total number of outcomes with A as winner but no B = 6*6 = 36 Hence the number of outcomes which satisfy the constraint in the question = 120  36 = 84.  Kudos if the answer helped



Intern
Joined: 10 Apr 2014
Posts: 33

Re: In a business school case competition, the top three teams
[#permalink]
Show Tags
14 Apr 2014, 01:47
ind23 wrote: Bunuel wrote: Bumping for review and further discussion*. Get a kudos point for an alternative solution!
Alternative solution: If there would have been no constraint the number of possible scenarios were: 6P\(3\) = 6!/3! = 120 Now we need to calculate cases where A is a winner but B is not So the other two positions can be taken by C, D , E, F . total number of combination = 4C2 = 4!/(2!*2!) = 6 As the three winners can be arranged among themselves in 3! ways, total number of outcomes with A as winner but no B = 6*6 = 36 Hence the number of outcomes which satisfy the constraint in the question = 120  36 = 84.  Kudos if the answer helped is there any other alternate solution?



Manager
Joined: 12 Sep 2014
Posts: 151
Concentration: Strategy, Leadership
GPA: 3.94

Re: In a business school case competition, the top three teams
[#permalink]
Show Tags
22 Oct 2014, 07:10
I understand the explanation, however I'm confused about an "assumption."
It says if A wins, then B also wins. From this I assumed that if A didn't win, B didn't win either? Why is this wrong in the context of the wording?
I just assumed it like this because in DS questions, when it has a conditional (if ...), that is usually true.



Math Expert
Joined: 02 Sep 2009
Posts: 50002

Re: In a business school case competition, the top three teams
[#permalink]
Show Tags
22 Oct 2014, 07:58
intheend14 wrote: I understand the explanation, however I'm confused about an "assumption."
It says if A wins, then B also wins. From this I assumed that if A didn't win, B didn't win either? Why is this wrong in the context of the wording?
I just assumed it like this because in DS questions, when it has a conditional (if ...), that is usually true. Don't get your analogy with DS question... Anyways, if A wins, B wins does not mean if B wins, A wins.
_________________
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



NonHuman User
Joined: 09 Sep 2013
Posts: 8461

Re: In a business school case competition, the top three teams
[#permalink]
Show Tags
21 Apr 2018, 23:28
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 Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: In a business school case competition, the top three teams &nbs
[#permalink]
21 Apr 2018, 23:28






