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10 teams (A, B, C, D, E, F, G, H, I and J) participate in a soccer tou
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Updated on: 23 Oct 2018, 08:15
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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 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
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Originally posted by GMATPrepNow on 22 Oct 2018, 10:11.
Last edited by GMATPrepNow on 23 Oct 2018, 08:15, edited 2 times in total.




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10 teams (A, B, C, D, E, F, G, H, I and J) participate in a soccer tou
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22 Oct 2018, 14:04
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 winloss) 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 methodThe 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.
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Re: 10 teams (A, B, C, D, E, F, G, H, I and J) participate in a soccer tou
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22 Oct 2018, 12:53
"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 21 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 31 1 F 2 2 5 G 2 2 5 H 21 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
FI 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



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Re: 10 teams (A, B, C, D, E, F, G, H, I and J) participate in a soccer tou
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22 Oct 2018, 15:38
UPDATE: Since posting this question, I've realized that it can be answered in 1015 seconds, if we use some GMATstyle reasoning. So, that's the updated challenge: find a 10second solution to the question. Cheers, Brent
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Re: 10 teams (A, B, C, D, E, F, G, H, I and J) participate in a soccer tou
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23 Oct 2018, 08:08
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 or tRying 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 t Ried 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 UPDATE: My solution was going to be similar to pushpitkc's solution (below), but I've since realized that this question can be answered in 1015 seconds, if we use some GMATstyle reasoning. So, that's the real challenge: find a 10second solution. Cheers, Brent 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 ?



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Re: 10 teams (A, B, C, D, E, F, G, H, I and J) participate in a soccer tou
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23 Oct 2018, 08:12
So, just as I was going to bed last night, it dawned on me that my 10second 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 "10second" solution didn't drive some people crazy! Cheers, Brent
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Re: 10 teams (A, B, C, D, E, F, G, H, I and J) participate in a soccer tou
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23 Oct 2018, 08:18
dave13 wrote: 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 or tRying 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 t Ried 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 UPDATE: My solution was going to be similar to pushpitkc's solution (below), but I've since realized that this question can be answered in 1015 seconds, if we use some GMATstyle reasoning. So, that's the real challenge: find a 10second solution. Cheers, Brent 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 ? 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
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Re: 10 teams (A, B, C, D, E, F, G, H, I and J) participate in a soccer tou
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23 Oct 2018, 09:42
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 953=1 Teams F,G,H and I won 2 games and tied 2 games > implication: they all lost 5 games, hence 922=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 3325 = 8 defeats.
Answer E



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Re: 10 teams (A, B, C, D, E, F, G, H, I and J) participate in a soccer tou
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24 Oct 2018, 10:20
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 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 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 gamesFor each game, 2 points are awarded. So, the TOTAL number of POINTS awarded = (2)(45) = 90Teams 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 pointsTeams 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 pointsHow 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
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Re: 10 teams (A, B, C, D, E, F, G, H, I and J) participate in a soccer tou
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25 Oct 2018, 00:57
Points are extra unnecessary information First reply shows it can be answered just using wins ties losses
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Re: 10 teams (A, B, C, D, E, F, G, H, I and J) participate in a soccer tou
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25 Oct 2018, 06:34
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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Re: 10 teams (A, B, C, D, E, F, G, H, I and J) participate in a soccer tou
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