GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 18 Jul 2018, 07:49

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.

Close

Request Expert Reply

Confirm Cancel

S96-11

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47079
S96-11 [#permalink]

Show Tags

New post 16 Sep 2014, 01:51
2
6
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

63% (01:33) correct 37% (01:20) wrong based on 110 sessions

HideShow timer Statistics

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

_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47079
Re S96-11 [#permalink]

Show Tags

New post 16 Sep 2014, 01:51
Official Solution:

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


First, we should determine the number of games played in this competition. We can count them in at least 2 different ways:

(1) Brute force. Name the 6 teams A, B, C, D, E, and F. A plays each of the other teams once, so A plays 5 games. B also plays 5 games, but we've already counted 1 of those games (the game with A), so we have 4 "new" games. C also plays 5 games, but we've already counted 2 of those games (the games with A and with B), so we have 3 "new" games. Continuing, we get \(5 + 4 + 3 + 2 + 1 = 15\) games.

(2) Combinatorics. We have a pool of 6 teams, and we want to count how many different pairs of teams (to play a game) we can select, without caring about order. Using either the anagram method or the formula for combinations, we get \(\frac{6!}{2!4!} = 15\) games.

Now, to find the maximum and minimum total points earned by all teams in the competition, we should notice that if one team wins and the other team loses, then 3 points total are earned (3 for the win and 0 for the loss). On the other hand, if the game ends in a draw, then only 2 points total are earned (1 by each team). So the maximum total points are earned if every game ends in a win/loss, and the minimum total points are earned if every game ends in a draw.

\(\text{Maximum} = 3 \times 15 = 45\) points.

\(\text{Minimum} = 2 \times 15 = 30\) points.

The difference between the maximum and the minimum is therefore \(45 - 30 = 15\).


Answer: A
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
User avatar
B
Joined: 29 Aug 2013
Posts: 40
Location: Bangladesh
GPA: 3.76
WE: Supply Chain Management (Transportation)
Re S96-11 [#permalink]

Show Tags

New post 26 Nov 2015, 10:57
I think this the explanation isn't clear enough, please elaborate.
_________________

Appreciate Kudos if the post seems worthwhile!

Expert Post
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6232
Re: S96-11 [#permalink]

Show Tags

New post 29 Nov 2015, 20:34
shapla wrote:
I think this the explanation isn't clear enough, please elaborate.


Hi shapla,

let us count the number of games played first..
total 6 teams.. each team plays with each of the other 5 teams..
so total games is ways of choosing 2 teams out of 6 teams=6C2=6!/4!2!=15 games..

now lets see the max and min points in each game..
a) if there is a result as win/loss, total points earned=3(for the winning team ) + 0(for a losing team)=3..
b) if there is a tie = 1+ 1(1 each for both team)=2
therefore the difference is 3-2=1..

there are 15 games, so total difference can be 15*1=15..
A
hope it was helpful
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Intern
Intern
User avatar
B
Joined: 29 Aug 2013
Posts: 40
Location: Bangladesh
GPA: 3.76
WE: Supply Chain Management (Transportation)
Re: S96-11 [#permalink]

Show Tags

New post 30 Nov 2015, 01:16
thanks chetan...
_________________

Appreciate Kudos if the post seems worthwhile!

Intern
Intern
avatar
Joined: 09 Jul 2015
Posts: 15
Location: India
Concentration: Marketing, International Business
GPA: 3
WE: Analyst (Consulting)
Re: S96-11 [#permalink]

Show Tags

New post 04 Oct 2016, 22:29
Can the minimum not be zero? What if there's a team that has lost in every match?
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47079
Re: S96-11 [#permalink]

Show Tags

New post 05 Oct 2016, 02:26
Intern
Intern
avatar
B
Joined: 10 Sep 2016
Posts: 1
Re: S96-11 [#permalink]

Show Tags

New post 18 Mar 2017, 14:08
So here is how i approached this problem. I followed the steps below:

a) Create 6x6 matrix
b ) You eliminate the diagonal , now we have : 36-6=30 left
c) Since the teams play just one time with each other we need only 30/2=15 elements
d) 3*15( max points) - 1*2*15(min points and 2 is here because both teams will get points)= 15
So answer : 15
Intern
Intern
avatar
Joined: 20 Aug 2017
Posts: 2
Re: S96-11 [#permalink]

Show Tags

New post 23 Aug 2017, 19:13
will some one please explain how the minimum score is 30.
Intern
Intern
avatar
Joined: 11 Jan 2016
Posts: 1
Re: S96-11 [#permalink]

Show Tags

New post 23 Aug 2017, 19:35
Ajstyles wrote:
will some one please explain how the minimum score is 30.

Total number of games played =15 (6C2)

Total minimum score-> every match played was a draw (In every match 1 point was given to both the teams) so total points in that case= 15*2= 30
Intern
Intern
avatar
B
Joined: 13 Sep 2016
Posts: 3
S96-11 [#permalink]

Show Tags

New post 13 Apr 2018, 04:14
Lets go the literal way:

Total number of games: AB, AC, AD, AE, AF, BC, BD, BE, BF, CD, CE, CF, DE, DF, EF = 15 games

Team A winnings: A vrs B = 3 points + A vrs C = 3 + A vrs D = 3 + A vrs E = 3 + A vrs F = 3. This gives a total of 15
Team B winnings: B vrs A = 0 points because already lost to A above + B vrs C = 3 + B vrs D = 3 + B vrs E = 3 + B vrs F = 3. This gives a total of 12
Repeating the same logic: Team C winnings will equal 9, Team D will equal 6, Team E 3 and F 0.

TOTAL WINNING = 15+12+9+6+3+0 = 45 points

Total Draws: 1 point for both sides in a game gives us 2 points per game multiplied by 15 games = 30 points

Difference = 45 -30 = 15. Answer is A
Intern
Intern
avatar
Joined: 26 Jun 2018
Posts: 1
Re: S96-11 [#permalink]

Show Tags

New post 27 Jun 2018, 03:41
sommya wrote:
Can the minimum not be zero? What if there's a team that has lost in every match?

If a team has lost every match, another team has won 3 points in every match. Indeed, the case in which one team looses every match ( and by consequence another one won ) is the case with the maximum total.
Re: S96-11   [#permalink] 27 Jun 2018, 03:41
Display posts from previous: Sort by

S96-11

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Moderators: chetan2u, Bunuel

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.