CHALLENGE: 10 teams (A, B, C, D, E, F, G, H, I and J) partic

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Oct 22, 2018 10:08 am

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10 teams (A, B, C, D, E, F, G, H, I and J) participate in a soccer tournament in which each team plays every other team once.
For each game played, points are awarded to the teams as follows:

0 points for losing the game
1 point each for tying the game
2 points for winning the game

After all the games are played, we learn that:
- teams A, B, C, D and E each won 5 games and tied 3 games.
- teams F, G, H and I each tied 2 games and lost 5 games.

How many games did team J lose?

A) 0
B) 2
C) 4
D) 6
E) 8

Answer: E
Source: www.gmatprepnow.com
Difficulty level: 700+

Brent Hanneson - Creator of GMATPrepNow.com

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Source: Beat The GMAT — Problem Solving | Mon Oct 22, 2018 10:08 am

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

CHALLENGE: 10 teams (A, B, C, D, E, F, G, H, I and J) partic

by regor60 » Tue Oct 23, 2018 4:40 am

Brent@GMATPrepNow wrote:10 teams (A, B, C, D, E, F, G, H, I and J) participate in a soccer tournament in which each team plays every other team once.
For each game played, points are awarded to the teams as follows:
0 points for losing the game
1 point each for tying the game
2 points for winning the game
After all the games are played, we learn that:
- teams A, B, C, D and E each won 5 games and tied 3 games.
- teams F, G, H and I each tied 2 games and lost 5 games.

How many games did team J lose?

A) 0
B) 2
C) 4
D) 6
E) 8

Answer: E
Source: www.gmatprepnow.com
Difficulty level: 700+

The number of wins has to equal the number of losses. Each team plays 9 times.

Point scores irrelevant.

Teams A-E won 5 times each for a total of 25 wins. They tied 3 times, which means they lost 1 game each for a total of 5 games lost.

Teams F-I lost 5 games each for a total of 20 losses. Since they tied twice each, 2 games each are unaccounted for, which they must have won, for a total of 8 games won.

Adding up the wins for teams A-I yields 33. Adding up the losses yields 25.

Since wins must equal losses, thus leaves 33-25 =8,E lost by J

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Oct 24, 2018 10:15 am

Brent@GMATPrepNow wrote:10 teams (A, B, C, D, E, F, G, H, I and J) participate in a soccer tournament in which each team plays every other team once.
For each game played, points are awarded to the teams as follows:
0 points for losing the game
1 point each for tying the game
2 points for winning the game
After all the games are played, we learn that:
- teams A, B, C, D and E each won 5 games and tied 3 games.
- teams F, G, H and I each tied 2 games and lost 5 games.

How many games did team J lose?

A) 0
B) 2
C) 4
D) 6
E) 8

Answer: E
Source: www.gmatprepnow.com
Difficulty level: 700+

First determine the TOTAL number of games played.
We can select 2 teams from 10 teams in 10C2 ways (= 45 ways)
So, there will be 45 games in TOTAL

IMPORTANT: Each team plays 9 games

For each game, 2 points are awarded.
So, the TOTAL number of POINTS awarded = (2)(45) = 90

Teams A, B, C, D and E each won 5 games and tied 3 games.
NOTE: This info tells about 8 of the games. Since each team plays 9 games, we can conclude that each of the above teams LOST 1 game each.
For ONE team, 5 wins = 10 points, and 3 ties = 3 points, for a total of 13 points.
So, the total points awarded to all 5 teams = (5)(13) = 65 points

Teams F, G, H and I each tied 2 games and lost 5 games.
NOTE: Since each team plays 9 games, we can conclude that each of the above teams WON 2 games each.
For ONE team, 2 wins = 4 points, and 2 ties = 2 points, for a total of 6 points.
So, the total points awarded to all 4 teams = (4)(6) = 24 points

How many games did team J lose?
So, far we've accounted for 89 points [65 + 24 = 89 points]
We know that a TOTAL of 90 points are awarded
So, Team J must have received 1 point
If Team J received only 1 point, then we know that Team J TIED 1 game
This also means that Team J WON 0 games (otherwise, Team J's point total would be greater than 1)
So, we can conclude that Team J LOST 8 games

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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