10 teams (A, B, C, D, E, F, G, H, I and J) participate in a soccer tou

Question

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 or 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

Cheers,
Brent

pushpitkc · Accepted Answer

Given:   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

Every game is either decided(by win-loss) or remains undecided(tie). In any case, both the
games have 2 points up for grabs. For 10 teams, where one team plays another - there are
a total of  \frac{10*9}{2} = 45  games played and 90 points to be won.

Teams A, B, C, D and E each won 5 games and tied 3 games - 5*2 + 3*1 = 13 
Teams F, G, H and I each tied 2 games and lost 5 games - 2*1 + 2*2 = 6
The first five teams win 13 points each and the other 4 teams win 6 points.

A total of 5*13 + 4*6 = 65 + 24 = 89 of the total points have been won by these 9 teams.
Team J needs to win only 90 - 89 or 1 point in their remaining 9 matches.

Therefore, Team J has to lose  8(Option E)  of 9 matches and draw 1 match to get the one point.

Alternate method

The number of wins = the number of losses(irrespective of the number of games)

Number of wins = (A,B,C,D,E) 5*5 + (F,G,H,I) 4*2 = 25 + 8 = 33 wins
Number of losses = (A,B,C,D,E) 5*1 + (F,G,H,I) 4*5 = 5 + 20 = 25 losses

The remaining 8 losses have to be contributed by Team J in order to restore the balance.

jantwarog · Answer

Solution in 10 seconds.

Teams A, B, C, D and E won 5 games and tied 3 games -> implication: they all lost 1 game, hence 9-5-3=1
Teams F,G,H and I won 2 games and tied 2 games -> implication: they all lost 5 games, hence 9-2-2=5

Ok, so temas A,B,C,D and E won in overall 25 (5*5) games and lost 5 (5*1). Teams F,G,H and I won in overall 8 (4*2) games and lost 20 (4*5), therefore 9 teams won in overall 25+8 = 33 games and lost 20+5 = 25 games. Matches lost must always equal matches won, so we're missing 33-25 = 8 defeats.

Answer E

philipssonicare · Answer

"10 teams" "in which each team plays every other team once"
When there are 10 teams, each team plays 9 games to play each other team once (think total games is 9+8...+2)

Options are: win, tie, lose
For one team to win, another must lose. For one team to win, another must tie

Note that not all info was given, had to infer losses/wins for each group

To be clear, here is how to solve with a table
.. W T L
A 5 3 1
B 5 3 1
C 5 3 1
D 5 3 1
E 5 3 1
F 2 2 5
G 2 2 5
H 2 2 5
I 2 2 5
J x y z

Since each win must have an opposing loss
.. W T L
A  5  3  1 
B  5  3  1 
C  5  3  1 
D  5  3  1 
E 5 3  1 
F  2  2  5 
G  2  2  5 
H  2 1 2  5 
I 2 2  5 
J x y z

Since each tie must have an opposing tie
 W T L
A  5   3   1 
B  5   3   1 
C  5   3   1 
D  5   3   1 
E 5  3 1  1 
F  2   2   5 
G  2   2   5 
H  2 1  2   5 
I 2  2   5 
J x y z

So, J must match the remaining numbers
8W 1T 0L for the others
0W 1T 8L for J

E

OR

A to E is 5 teams. Each plays 9 games
25W 15T 5L

F-I is 4 teams. Each plays 9 games
8W 8T 20L

W cancel with L
15T
8W 8T

T cancel with T
1T
8W

and J has the opposite
1T
8L

E

BrentGMATPrepNow · Answer

UPDATE: Since posting this question, I've realized that it can be answered in 10-15 seconds, if we use some GMAT-style reasoning. 
So, that's the updated challenge:   find a 10-second solution to the question.

Cheers,
Brent

dave13 · Answer

hey Brent

GMATPrepNow i guess you were getting tied just like me now

as you were were typing the above question full of typos

i think you mean tried instead of tied

they tried games right ? i corrected your tupos (see above) no need to thank me

ok so we have - teams A, B, C, D and E each won 5 games and tRied 3 games. - teams F, G, H and I each tied 2 games and lost 5 games. here is my reasoning - teams A, B, C, D and E each won 5 games and tRied 3 games. (from here i can conclude that if 5 games won than logically 5 games were lost) - teams F, G, H and I each tied 2 games and lost 5 games. (same here if 2 games were won than 3 games were lost) 5+3 = 8 is my reasoning correct ?

BrentGMATPrepNow · Answer

So, just as I was going to bed last night, it dawned on me that my 10-second solution "theory" is incorrect.

That said, here's the general idea (of my flawed theory) ... Step 1. We COULD determine the total number of games (45), which means we COULD calculate the total number of points to be awarded (90 points in total, since 2 points are awarded with each game). Step 2. We COULD determine the total number of points awarded to teams A, B, C, D, E, F, G, H and I. Step 3. Whatever points are unaccounted for would be the number of points that Team J must have received. For example: If, in step 2 we found that a total of 85 points were awarded, then we'd know that there are 5 unaccounted points, which means Team J must have received those 5 points. So far, this is similar to pushpitkc's solution. However, we may not need to perform any of the above calculations. Here's why. If it turned out that Team J must have received 5 points (as in the above example), then we'd be hard pressed to determine Team J's record, since there's more than 1 way for a team to receive 5 points. For example, Team J could have won 0 games, tied 5 games and lost 4 games Or Team J could have won 1 game, tied 3 games and lost 5 games Or Team K could have won 2 games, tied 1 game and lost 6 games As you can see, each possibility yields a different answer to the question. Since there can be only one correct answer to the question, my reasoning was that there must be exactly 1 point that's unaccounted for. Consider these cases: CASE A: If there were 0 points unaccounted for, then that would mean Team J lost all 9 of its games. HOWEVER, 9 is not among the answer choices. So, the answer choices tells us that CASE A cannot occur. CASE B: If there was 1 point unaccounted for, then that would mean Team J tied 1 game and lost 8 games (answer E). At this point, I incorrectly concluded that, if there is more than 1 point unaccounted for, then there will be more than 1 possible outcome (as is the above case, when we had 5 points unaccounted for) This conclusion is wrong. To see why, check out case C below. CASE C: If there were 2 points unaccounted for, then COULD would mean Team J won 1 game, and lost 8 games (answer E) OR it COULD would mean Team J won 0 games, tied 2 games and lost 7 games (but 7 is not among the answer choices) So, if there were 2 points unaccounted for, the correct answer would have to be E. CASE D: If there were 3 points unaccounted for, then COULD would mean Team J won 1 game, tied 1 game and lost 7 games (but 7 is not among the answer choices) OR it COULD would mean Team J won 0 games, tied 3 games and lost 6 games (answer D) So, if there were 3 points unaccounted for, the correct answer would have to be D. And so on. I hope my "10-second" solution didn't drive some people crazy! Cheers, Brent

BrentGMATPrepNow · Answer

Hey Dave13,

No, I meant "tied" (as in both teams scored the same number of goals in the game)

Given this, your solution is not correct.

Cheers,
Brent

BrentGMATPrepNow · Answer

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

AsianInAus2018 · Answer

Points are extra unnecessary information
First reply shows it can be answered just using wins ties losses

Posted from my mobile device

uttam94317 · Answer

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 tRied 3 games. 
- teams F, G, H and I each tied 2 games and lost 5 games.

D

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