NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 14:21 It is currently 26 Apr 2024, 14:21
Decision Tracker
My Rewards
New posts
New comers' posts

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

In the Mundane Goblet competition, 6 teams compete in a

SORT BY:
Date
Kudos
   1   2 
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14831
Own Kudos [?]: 64940 [0]
Given Kudos: 427
Location: Pune, India
Send PM
Re: MBAmission: The Quest for 700 [#permalink] New post   03 Jun 2013, 21:17
Expert Reply
cumulonimbus wrote:
Hi Karishma,

Can you please explain why did we add = 5+4+3+2+1 here?


We need to find the total number of points that can be gained by all teams together. For this, we need the total number of matches played since each match can give either (3 + 0) points to the two teams or (1 + 1) points to the two teams.

We say there are 6 teams - A, B, C, D, E and F

A plays a match with all 5 so 5 matches have been played.
Then B plays a match with C, D, E and F so another 4 matches were played (note that B has already played with A above).
Then C played with D, E and F so another 3 matches were played.

Like this, we get that the total number of matches played = 5 + 4 + 3 + 2 + 1 = 15

The 15 matches could have contributed a maximum of 3*15 = 45 points and a minimum of 2*15 = 30 points (since each match would have a winner-loser or it would be a draw).
Required difference = 45 - 30 = 15
avatar
sanket1991
Manager
Manager
Joined: 14 Sep 2014
Posts: 74
Own Kudos [?]: 95 [0]
Given Kudos: 51
WE:Engineering (Consulting)
Send PM
Re: In the Mundane Goblet competition, 6 teams compete in a [#permalink] New post   18 Jan 2015, 21:41
when two teams compete there are 2 results :
1) either team win: 3 points to one team and none to other team3
2) Match Drawn : 1 point to each team that is 2 points
so for maximum points maximum wins
and for minimum points all matches should draw.
It's a round robin process with 6 teams
that means each team will play with 5 other teams exactly once
so, Table will look like this
A 5w 0L 0D 15pts.
B 4w 1L 0D 12pts.
C 3w 2L 0D 9pts.
D 2w 3L 0D 6pts.
E 1w 4L 0D 3pts.
F 0w 5L 0D 0pts.

total points 45
for all draws total points will be 30
so difference will be 15
avatar
B
Joc456
Manager
Manager
Joined: 26 Jan 2016
Posts: 78
Own Kudos [?]: 46 [0]
Given Kudos: 55
Location: United States
Schools: CBS '19 (D) Anderson '19 (A) Marshall '19 (A) Stern '19 (A)
GPA: 3.37
Send PM
Re: In the Mundane Goblet competition, 6 teams compete in a [#permalink] New post   11 Oct 2016, 15:33
The first step is to see how many games can be played. It helps to draw a grid. So if there are 6 teams the first team cannot play itself so it goes 5 games+4 games... you get 15 games.

Then to maximize it we can have each team win every game they play. Lets call the teams A-F. So A wins all the games it plays (5 games) 3*5=15, B wins all the games it plays 3*4, etc etc 45 total points.

Now to minimize the number of points we can have every game tie. If there are 15 games and all tie then each team gets a point--30 points.

45-30=15. A.
avatar
B
zanaik89
Manager
Manager
Joined: 19 Aug 2016
Posts: 56
Own Kudos [?]: 6 [0]
Given Kudos: 30
Send PM
Re: In the Mundane Goblet competition, 6 teams compete in a [#permalink] New post   18 Nov 2017, 05:10
Bunuel wrote:
zisis wrote:
In the Mundane Goblet competition, 6 teams compete in a “round robin” format: that is, each team plays every other team exactly once. A team gets 3 points for a win, 1 point for a tie (a draw), and 0 points for a loss. What is the difference between the maximum total points and the minimum total points that can be gained by all teams (added together) in the Mundane Goblet competition?

(A) 15

(B) 30

(C) 45

(D) 60

(E) 75


There will be \(C^2_6=15\) games needed so that each team to play every other team exactly once (\(C^2_6=15\) is the # of ways we can pick two different teams to play each other).

Now, in one game max points (3 points) will be obtained if one team wins and another looses and min points (1+1=2 points) will be obtained if there will be a tie. Hence, maximum points that can be gained by all teams will be 15 games * 3 points=45 and the minimum points that can be gained by all teams will be 15 games * 2 points=30, difference is 45-30=15.

Answer: A.

Hope it helps.


Hi Bunuel

Cant it be 6*5 = 30 games, then one team won and another lost?

so 15 games won so total max points is 45

Total games 30 ties 15 points to each team

Therefore 45-30=15

Pls help
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619230 [0]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: In the Mundane Goblet competition, 6 teams compete in a [#permalink] New post   19 Nov 2017, 03:34
Expert Reply
zanaik89 wrote:
Bunuel wrote:
zisis wrote:
In the Mundane Goblet competition, 6 teams compete in a “round robin” format: that is, each team plays every other team exactly once. A team gets 3 points for a win, 1 point for a tie (a draw), and 0 points for a loss. What is the difference between the maximum total points and the minimum total points that can be gained by all teams (added together) in the Mundane Goblet competition?

(A) 15

(B) 30

(C) 45

(D) 60

(E) 75


There will be \(C^2_6=15\) games needed so that each team to play every other team exactly once (\(C^2_6=15\) is the # of ways we can pick two different teams to play each other).

Now, in one game max points (3 points) will be obtained if one team wins and another looses and min points (1+1=2 points) will be obtained if there will be a tie. Hence, maximum points that can be gained by all teams will be 15 games * 3 points=45 and the minimum points that can be gained by all teams will be 15 games * 2 points=30, difference is 45-30=15.

Answer: A.

Hope it helps.


Hi Bunuel

Cant it be 6*5 = 30 games, then one team won and another lost?

so 15 games won so total max points is 45

Total games 30 ties 15 points to each team

Therefore 45-30=15

Pls help


6 teams = 15 games. There are 15 different pairs possible from 6 teams. You could check with smaller numbers, for example, list number of games for 3 teams. Is it 3C2 = 3 or 3*2 = 6?
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32689
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: In the Mundane Goblet competition, 6 teams compete in a [#permalink] New post   02 Jan 2023, 04:50
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 Club Bot
gmatclubot
Re: In the Mundane Goblet competition, 6 teams compete in a [#permalink]
02 Jan 2023, 04:50
   1   2 
Moderators:
Bunuel
Math Expert
92948 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions