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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote In a business school case competition, the top three teams This topic has 3 expert replies and 0 member replies Top Member In a business school case competition, the top three teams Timer 00:00 Your Answer A B C D E Global Stats Difficult In a business school case competition, the top three teams receive cash prizes of$5,000, $3,000, and$2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes of the competition are possible?

A. 18
B. 20
C. 54
D. 84
E. 120

OA D

Source: Veritas Prep

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BTGmoderatorDC wrote:
In a business school case competition, the top three teams receive cash prizes of $5,000,$3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes of the competition are possible? A. 18 B. 20 C. 54 D. 84 E. 120 Case 1: Team A wins a prize, with the result that Team B must win a prize Number of prizes that could be won by A = 3. Number of remaining prizes that could be won by B = 2. Number of teams that could win the third prize = 4. (Any of the 4 remaining teams.) To combine these options, we multiply: 3*2*4 = 24. Case 2: Team A does NOT win a prize Number of teams that could win the first prize = 5. (Of the 6 teams, any team but A.) Number of teams that could win the second prize = 4. (Of the 5 remaining teams, any team but A.) Number of teams that could win the third prize = 3. (Of the 4 remaining teams, any team but A.) To combine these options, we multiply: 5*4*3 = 60. Total ways = Case 1 + Case 2 = 24 + 60 = 84. The correct answer is D. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 Top Reply BTGmoderatorDC wrote: In a business school case competition, the top three teams receive cash prizes of$5,000, $3,000, and$2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes of the competition are possible?

A. 18
B. 20
C. 54
D. 84
E. 120
Source: Veritas Prep
$$?\,\,\, = \underbrace {C\left( {4,1} \right) \cdot 3!}_{\,\,\,\,\,\,{\text{A}}\,{\text{yes}}{\text{,}}\,\,{\text{B}}\,\,{\text{too}}} + \,\,\,\,\underbrace {C\left( {5,3} \right) \cdot 3!}_{A\,\,{\text{no}}}\,\,\,\, = \,\,\,\,24 + 60\,\,\,\, = \,\,\,\,84$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

_________________
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BTGmoderatorDC wrote:
In a business school case competition, the top three teams receive cash prizes of $5,000,$3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes of the competition are possible? A. 18 B. 20 C. 54 D. 84 E. 120 OA D Source: Veritas Prep We have two cases to consider: 1) A is one of the top three teams, and 2) A is not one of the top three teams. Case 1: A is one of the top three teams If A is one of the top three teams, then B is also one of the top three teams. We have only 4C1 = 4 ways to choose the third top team. In other words, we have 4 possible sets of top three teams (or winning teams). However, for each set of 3 winning teams, there are 3! = 6 ways for the order in which they win the prizes. Therefore, there are 4 x 6 = 24 possible outcomes of the competition if A is one of the top three teams. Case 2: A is not one of the top three teams If A is not one of the top three teams, we could have 5C3 = 10 ways to choose the top three teams. (Note that Team B could be one of the top three teams, even if Team A is not in the top three.) In other words, we have 10 possible sets of top three teams (or winning teams). Similar to case 1, for each set of 3 winning teams, there are 3! = 6 ways for the order in which they win the prizes. Therefore, there are 10 x 6 = 60 possible outcomes of the competition if A is not one of the top three teams. Therefore, there are a total of 24 + 60 = 84 possible outcomes of the competition. Answer: D _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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