Last visit was: 24 Apr 2026, 03:01 It is currently 24 Apr 2026, 03:01
Home
Messages
Tests
Schools
Events
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
Back to Forum
Create Topic
User avatar
shasadou
User avatar
Joined: 12 Aug 2015
Last visit: 24 Nov 2022
Posts: 219
Own Kudos:
3,179
 [31]
Given Kudos: 1,475
Concentration: General Management, Operations
Schools: Johnson '18 (WL) Duke '18 (M) Tuck '18 (D)
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE:Management Consulting (Consulting)
Schools: Johnson '18 (WL) Duke '18 (M) Tuck '18 (D)
GMAT 3: 600 Q47 V27
Posts: 219
Kudos: 3,179
 [31]
In a business school case competition, the top three teams receive cas 31 Oct 2015, 07:32
2
Kudos
Add Kudos
27
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

55% (02:37) correct 45% (02:45) wrong based on 391 sessions

History

Date
Time
Result
Not Attempted Yet
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
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 22 Apr 2026
Posts: 11,229
Own Kudos:
45,006
 [10]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,229
Kudos: 45,006
 [10]
In a business school case competition, the top three teams receive cas 31 Oct 2015, 07:44
7
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
shasadou
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
Show more


the ways the three teams can be selected is..
i) A is selected, B is also selected, third can be any of the remaining 4.. so total ways 4.. they can be arranged in 4*3!=24 ways..
ii) A is not selected. threee teams can be selected from remaining 5 so total arrangements =5C3*3!=60
total =84 outcomes
D
General Discussion
User avatar
GMATYoda
User avatar
Joined: 24 Sep 2018
Last visit: 18 Jan 2021
Posts: 101
Own Kudos:
194
Given Kudos: 14
Posts: 101
Kudos: 194
In a business school case competition, the top three teams receive cas 24 Sep 2018, 23:01
Kudos
Add Kudos
Bookmarks
Bookmark this Post
This may be approached in the following two ways:

Quote:
If there weren’t any constraints at all, this problem would have a simple solution: Six teams are competing for three slots, so N = 6 and K = 3. Plugging in these values into our equation for a permutation we discover:

A=N!/(N−K)!=6!/(6−3)!=6!/(3)!=6∗5!/6=120

Because the answer must be less than 120, we know the answer is not “E”.

Calculating the number of options without Team A is also easy. There are five remaining teams (B through F) vying for three possible slots (N = 5, K = 3). Because order matters, we plug these values into our equation for permutations:

A=N!/(N−K)!=5!/(5−3)!=5!/(2)!=120/2=60

Because 60 doesn’t even take into account the possibility of Team A winning, we know that the actual number of arrangements will be above 60, so answer choices “A”, “B”, and “C” cannot be correct. There is only one option between 60 and 120 in the answer choices: 84.

The answer is “D”.
Show more

Quote:
Alternately, we could calculate the number of arrangements where Team A is in the winner’s circle. Every time this happens, Team B will be there somewhere. Sketching this out might be the easiest to see. Here are the possible combinations:

AB? A?B ?AB BA? B?A ?BA

Notice that this is nothing more than a permutation of three elements: A, B, and ?, where “?” represents another team. There are 3! = 6 possible arrangements. This is also similar to a subgroup problem – for every arrangement of A, B, and ?, we can fit in four possible teams into the “?” slot. Therefore, the number of possible arrangements where A is included is 6 × 4 = 24. We could add these arrangements to the possibilities where Team A isn’t in the winner’s circle (60) to arrive at a total: 60 + 24 = 84. The answer is still “D”.

We could also take the total without constraints (120) and subtract the number of arrangements that wouldn’t work (where A is in the winner’s circle, but B isn’t.)
Show more

Notice there are multiple ways of solving many high-level combinatorics questions: by excluding answers using easy logic, by calculating pieces and adding them together, or by assuming there aren’t any constraints and subtracting the exceptions that wouldn’t work.
avatar
siddharthfrancis
avatar
Joined: 19 Sep 2016
Last visit: 10 Jan 2022
Posts: 57
Own Kudos:
5
Given Kudos: 292
Posts: 57
Kudos: 5
In a business school case competition, the top three teams receive cas 05 Oct 2018, 01:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
why are they considering the option of A not winning the prize when its already given that A wins a prize B also wins..we have to select one team out of 4..
User avatar
XavierAlexander
User avatar
Joined: 25 Aug 2015
Last visit: 17 Feb 2025
Posts: 42
Own Kudos:
412
 [1]
Given Kudos: 5,540
Products:
My Reviews
Posts: 42
Kudos: 412
 [1]
In a business school case competition, the top three teams receive cas 06 Oct 2018, 02:49
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
One of the quicker and easier approach:-

Three ranks are there to occupy.
Six teams are contenders.

Two possible cases (add them):-

1st Case: If 'A' is NOT selected:-
Three ranks are up for grab among 5 teams. So, it can be occupied in \(5 * 4 * 3 = 60\) ways.


2nd Case: If 'A' is selected:-
B would also get selected. So among 3 ranks,
2 ranks can be occupied by A & B in \(3P2\) = \(6\) ways
1 rank can be occupied by either of the other 4 teams in \(4\) ways.
\(6 * 4 = 24\) ways


Add both cases, to get all possible ways:-
\(60 + 24 = 84\) (answer)



shasadou
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
Show more
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 23 Apr 2026
Posts: 22,283
Own Kudos:
26,532
 [2]
Given Kudos: 302
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 22,283
Kudos: 26,532
 [2]
In a business school case competition, the top three teams receive cas 09 Oct 2018, 10:41
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
shasadou
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
Show more

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 only have 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 how 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, with Team A NOT being 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 how 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
User avatar
sarthak1701
User avatar
Joined: 11 Sep 2024
Last visit: 14 Apr 2026
Posts: 108
Own Kudos:
65
Given Kudos: 18
GMAT Focus 1: 575 Q77 V81 DI78
GMAT Focus 1: 575 Q77 V81 DI78
Posts: 108
Kudos: 65
In a business school case competition, the top three teams receive cas 17 Feb 2025, 04:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The Trap is that A can win any of the prizes, it does not say that B will win AFTER A has won, so in this case A can win the 3rd prize as well. We have 3 spots:

_ _ _

Let's take the case where A wins:

A can take any of the 3 spots (including the 3rd) = 3

If A has won, B must win too, B can take any of the 2 remaining spots: 2

The last spot can be taken by any of the 4 remaining players: 4

Number of combinations in which A is a winner = 3*2*4 = 24

Now, let us count the number of cases in which A does not win. Notice here that B will surely win if A does but B's win is not contingent on A winning, that is, it is not a necessary condition for B to win, he can win without A winning but if A does win, B will win too, if A does not win, B may or may not win.

Again, we have 3 spots:

_ _ _

The first spot can be taken by any player except A = 5

The second spot can be taken by any of the remaining players = 4

The third spot can be taken by any of the remaining players = 3

Total = 5*4*3 = 60

Total cases = Cases where A wins + Cases where A does not win = 24 + 60 = 84
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,966
Own Kudos:
1,117
Posts: 38,966
Kudos: 1,117
In a business school case competition, the top three teams receive cas 28 Mar 2026, 06:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109802 posts
Krunaal
Tuck School Moderator
853 posts