In a certain sport, teams receive 3 points for each win, 1 p

Question

In a certain sport, teams receive 3 points for each win, 1 point for each draw, and no points for losses. In a five-team tournament in this sport, in which each of teams G, H, J, K, and L played each other team exactly once, did team L finish the tournament with the highest point total?
 
(1) Team L finished with 8 points.
 
(2) The sum of all five teams’ point totals for the tournament was 23 points.

AdlaT · Accepted Answer

In a certain sport, teams receive 3 points for each win, 1 point for each draw, and no points for losses. In a five-team tournament in this sport, in which each of teams G, H, J, K, and L played each other team exactly once, did team L finish the tournament with the highest point total?

(1) Team L finished with 8 points.

(2) The sum of all five teams’ point totals for the tournament was 23 points.

Statement(1) :Team L finished with 8 points.

Team L finished with 8 point= Against G( win,3)+Against H (Win,3)+Against J (draw,1)+Against K (draw,1)

for example Team G may or may not finish with higher points than L= Against H(Win,3)+ Against J(Win,3)+Against K(Win,3)= 9 points.

Not Sufficient.

Statement(2):The sum of all five teams’ point totals for the tournament was 23 points.

let X= number of matches resulted in a win.
Y = number of matches resulted in draw.

from st.2--->3X+2Y=23, and we know that X+Y=10. two unknowns and two equations, we can find out X and Y,

X=3, and Y=7, Still we can not decide whether Team L finished with 8 points or not.

From these values there is possibility that one of the 5 teams won 3 matches.

Not Sufficient.

Statement 1 and Statement 2 together : From statement 1 we know that Team L won 2 matches and played 2 matches resulted in draw.

From statement 2 we know that 3 matches were resulted in a win . Only one match which resulted in a win played by other than Team L.

So no team other than Team L finished the tournament with 8 points.

Sufficient.

Ans: C.

Vips0000 · Answer

There is enough data dude...

First we know that there are 5 teams in the tournament and therefore max matches one team could play is 4. Also since a win gives 3 points and a draw gives 1 while loss gives 0 points.

Statement 1: L finished with 8 points. Only way to achieve this is with 2 wins and 2 draws. This leaves a possibility that there could be at least 1 team which could still win 3 matches.... Also, there is a possibility that no other team won more than 2 matches.
Not sufficient.

Statement 2: total points was 23. Remember, in a match maximum points that are awarded could be 3 in case of win-loss and 2 in case of draw (1 point to each)
Therefore, possibility of max and min tally is 20 (all matches drawn) to 30 (all matches result in win-loss). 
For point tally to be 23, the only possibility is that there were 3 matches that resulted in win-loss and 7 that resulted in draws.
Not sufficient to tell which team won max.

However when you combine these two information, you'd know that out of 3 wins, team L won 2. That means all other team won only 1 match and drew rest of the matches. And therefore, no other team could have more points than L. 
Or simply, L won the tournament.

Ans C it is.

Observer · Answer

This is not a very rigorous approach but it works:

1. This tells us that Team L went 2-0-2 but we don't know anything about the other teams except 2 of them have at least 1 draw each and 2 have at least 1 loss each. Also no team went 4-0-0 since Team L did not have a loss. Insufficient.

2. Clearly insufficient.

1 and 2. 2-0-2 happens to be the best record possible for a team with 2 wins and the best record for a team with 1 win is 1-0-3 for a total of 6 points. So the question becomes was there a team with 3 wins? A possible scenario with a team with 3 wins is
3-0-1 (10)
L: 2-0-2 (8)
2-1-1 (7)
1-3-0 (3)
0-4-0 (0)
For a total of 10+8+7+3=28 points. The only way to lower this number is to convert wins and losses into draws for the lower 3 teams. Then the scenario with minimal points is:
3-0-1 (10)
L: 2-0-2 (8)
0-1-3 (3)
0-2-2 (2)
0-2-2 (2)
Points: 10+8+3+2+2=25.
Since 25>23, there could not have been a team with 3 wins. The answer is Yes. Sufficient. Answer C.

docdrizzeally · Answer

Actually kingflow, I'd still say it's E because we actually dont have data in (2) to say the three wins total in above explanation is ruled out

with a 3-0-1 record 10 points we have only 5 points for 3 remaining teams when the minimum is infact 0 possibly for two team we know L defeated

mau5 · Answer

The maximum total points any team can make is by winning all the 4 matches = 4*3 = 12 points. The next maximum point can be by a team, which loses one match and wins the next three = 3*3 = 9 points. By the same logic, the total maximum points is 12+9+6+3+0 = 30 points.

From F.S 1 ,we know that Team L got 8 points. Let's assume that all the teams won the maximum points available = 12,9,6,3,0.

We redistribute the points, assuming that the team which had won all 3 matches didn't will all 3, rather had a tie in 2 matches : 12,9-2-2,6+1,3+1,0 = 12,5,7,4,0. Again, let the team with 12 points instead have a tie with the team which has 7 points = 12-2,5,7+1,4,0= 10,5,8,4,0.We see that there is a scenario where team L with 8 points doesn't end with the highest points. Again, we can have a different scenario where the team which had one 4 matches instead had 2 ties = 12-2-2,9,6+1,3+1,0 = 8,9,7,4,0 = Again, the team which had won all three matches instead had one tie = 8,9-2,6,4+1,0 = 8,7,6,5,0. Thus, there is a scenario possible where team L does have the highest points. As we get two different answers. Insufficient.

From F.S 2, we have to make the total sum as 23. We started with 12,9,6,3,0 = 30 points, and we need to get rid of 7 points. This can happen if we have 7 mathches as tie( Each tie redistributes the points as -2 and +1, giving a net decrease of 1 point). Thus, we can assume that the team which had won all 4 matches instead had 4 ties = 12-2-2-2-2,9+1,6+1,3+1,0+1 = 4,10,7,4,1. We have to get rid of 3 more points = 3 more draws = 4,10-2-2-2,7+1,4+1,1+1 = 4,4,8,5,2 = 23 points. Now, any team could be team L. Insufficient.

Combining both statements together, we see that team L does have the maximum points in the end,Sufficient.

C.

Observer · Answer

You're ignoring the point system itself by saying that. A draw nets 2 points because each team gets 1 point. A win and a loss nets 3 points. So if it were possible for the 2 bottom teams to have 0 points there would be more total points than if they had draws. Secondly, in any scenario it's only possible for 1 team at most to have 0 points. There simply can't be 2 teams with 4 losses each because the two teams had to have faced each other and the result was either a win for one and loss for the other or a draw for both. So it's not possible in any case that 2 teams have 0 points.

kingflo · Answer

Here is the OE for you.

Each team plays each other team once, so there are a total of 10 games played. (If you’re not sure about that, count it out! GH, GJ, GK, GL, HJ, HK, HL, JK, JL, KL). Each team plays a total of 4 games.
 
If one team wins, 3 points are awarded (total) for that game. If the teams tie, 2 points are awarded (total) for that game. If one team wins all four of its games, it would earn 12 points.
 
(1) INSUFFICIENT: We know that team L played four games and earned 8 points. The only way to get 8 points in four games is 3 + 3 + 1 + 1, so team L must have won two games, drawn two, and lost none.
 
With this win-loss record, it’s possible that team L finished first. For instance, say that all of the other games in the tournament were draws. In that case, team L would have 8 points, the two teams that lost to L would have 0 + 1 + 1 + 1 = 3 points, and the two teams that tied with L would have 1 + 1 + 1 + 1 = 4 points.
 
On the other hand, it’s also possible that team L finished second. For instance, team G could have tied team L and beaten all three of the other teams, finishing with 1 + 3 + 3 + 3 = 10 points to team L’s 8 points.
 
(2) INSUFFICIENT: This statement contains no information about the distribution of points among the teams, so we can’t tell how any individual team fared.
 
(1) AND (2) SUFFICIENT: To recap, there are 10 total games, and one game results in either 2 or 3 total points awarded. Say that x of the games were won by one team, and thus the remaining 10 – x games were ties. Each “won” game will result in 3 points awarded and each “tie” game will result in two points awarded:
3(x) + 2(10 – x) = 23
3x + 20 – 2x = 23
x = 3
 
Therefore, exactly 3 of the games were won by one team and lost by the other, and the other 7 were ties. Since team L won two games, none of the other teams could have won more than one game. The maximum point total for any of the other teams is 3 + 1 + 1 + 1 = 6 points, two points lower than team L’s total. Therefore, team L finished with the highest point total.
 
The correct answer is C.

simba19 · Answer

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1. Insufficient. This tells us that Team L finished with two wins and two draws. Another team could have finished with three wins and one draw (because Team L did not lose, we know that no team finished with 4 wins), or could have also received 8 points by finishing with two wins and two draws.

2. Insufficient. While this tells us that 23 points were awarded in the tournament, we do not know how many points any of the teams accumulated individually.

Statements 1 and 2 together are sufficient.
 
In a five team round-robin tournament (each team plays every other team once), there will be a total of 10 games ((5*4)/2) played. Let W equal the number of games that end in a win or loss and let D equal the number of games that end in a draw. You are left with the following system:

W + D = 10
3W + 2D = 23 (Because 3 points are awarded for games that end in a win or loss and 2 points are awarded for games that end in a draw)

Thus, W = 3 and D = 7.

Because there were only 3 wins in the tournament and Team L won two of those games and drew their other two matches, we know that L finished the tournament with the highest point total.

Answer: C

tushain · Answer

Bunuel 
 VeritasPrepKarishma 
suppose the statement 2 had said
(2) The sum of all five teams’ point totals for the tournament was  24  points.
Then in this case , combining 1 and 2 both , there could be a scenario in which another team scores 8 points too.
Would then, L still be said to be "highest"? and the answer remained C?
OR is the term "highest" valid only if one gets maximum score and no other gets that maximum score?

Also, if the statement 2 had said 
(2) The sum of all five teams’ point totals for the tournament was  25  points.
Then would the answer had been E?, because then it is possible for another team to score 9 points, though it is also possible that no other team scored more than 8.

Lucky2783 · Answer

Hi  Bunuel  ,  VeritasPrepKarishma

could you please help with this question ? 
also i am not sure how it is expected to be done within 2 mins (or even 3 mins) ? 
It is too time taking and cumbersome. 
Is MGMAT is a true reflection of GMAT Test ? 
Anticipating your valuable reply.

thanks
Lucky

harshalsingla · Answer

We're told that there are 5 teams and that they each play one another once in a tournament (wins are worth 3 points each, ties are worth 1 point each and losses are with 0 points each). Using the Combination Formula, we can figure out how many total games are played:

5!/(2!3!) = 10 total games played.

So, each team will play in 4 games, but there are only 10 total games played. This is important for a couple of reasons: 
1) It establishes the maximum number of points that any team can score (12 points, if a team won ALL its games) 
2) It establishes the minimum and maximum points that could be scored by ALL teams (if ALL the games were ties, then there would be 20 points scored; if there are NO ties, then there will be 10 wins and 10 losses, for a total of 30 points).

We're asked if Team L finished with the HIGHEST point total? This is a YES/NO question.

Fact 1: Team L finished with 8 points.

To get 8 points, Team L would have had to have won 2 games and tied 2 games. We have to determine if that COULD have been the highest total and if that might not have been the highest...

IF... 
All of the other teams tied one another (except for the two that lost to Team L), then each of the other 4 teams would have scored 4 or fewer points, so Team L COULD have had the highest total and the answer to the question is YES.

IF... 
One team tied Team L, but won its other 3 games, then that team would have scored 10 points. In that situation, Team L would NOT have had the highest point total and the answer to the question is NO. 
Fact 1 is INSUFFICIENT

Fact 2: The Total Points scored in the tournament was 23 points.

This tells us NOTHING about how Team L performed in the tournament. Maybe it was highest (a YES answer), maybe it was lowest (a NO answer), maybe it was somewhere 'in between' (also a NO answer). 
Fact 2 is INSUFFICIENT

Combined, we know.... 
Team L had 8 total points (2 wins and 2 ties). 
The Total points for the tournament was 23 points (which is relatively low, implying lots of ties happened).

From here, we have to play around some more with the possibilities; since Team L scored 8 points, that means the other 4 teams scored just 15 points in total. So could another team have scored MORE than Team L?

Since no team won against Team L, for another Team to score MORE than Team L, that team would need to have tied with Team L and WON ALL 3 of its other games... 
Team L = 8 points 
Team G = 10 points 
7 games played so far

This leaves 5 points and 3 remaining games for the other 3 teams. Since each game will generate either 2 points (if the teams tie) or 3 points (if one wins and one loses), 3 remaining games will generate AT LEAST 6 points. Here, there are only 5 points to spare, so this situation is IMPOSSIBLE - It cannot happen - thus, NO TEAM could have scored higher than Team L under these conditions, so Team L's total IS the highest and the answer to the question is ALWAYS YES. 
Combined, SUFFICIENT

alpham · Answer

The best strategy for this problem with time constraint is to recognize from statement 1 is to recognize that it would be possible for another team to have 3 wins and 1 draw which would lead to 10 points. This can be deduced from knowing 8 points is (2 wins and 2 draws). It could be possible for the another time to have not played team L at all and won against another team. Once this can be found out you know A and B are both insufficient.

Knowing there is a total of 23 points, you know the aggregate will be 3 wins. Given from statement 1, that team L had 2 wins and 2 draws it would mean no other team would have to more points than team L. There would be only 1 win that would be handed out for the other 4 teams. Therefore, team L are the champions!!!

Therefore the answer is  C

shashankism · Answer

Given : Win points =3, Draw points = 1 and Loss point = 0.
There are 5 times G,H,J,K,L which play exactly once with each other. So total matches played = 5C2 = 10.

DS : L has the highest point ?

Since total 10 matches are played, maximum total points = (3+0)*10 = 30 if all matches has win and loss scenario.
Also minimum total points = (1+1)*10 = 20 if all the matches has draw scenario. 
So 20 <= Total points <=30

Statement 1: L got 8 points. 
If a team wins all matches, it will get 3*4 =12 points
If a team wins 3 matches and loose 1, it will get 3 * 3 + 1*0 = 9 points.

So if L has 8 points, it means it won 2 matches and has drawn 2 matches. It clearly indicates that 2 of the team from G,H, J,K lost at least 1 match and 2 of the team has drawn atleast 1 match 
So maximum point which can be attained by other teams may be 10 (3 win and 1 draw).

NOT SUFFICIENT

Statement 2 : The sum of all five teams’ point totals for the tournament was 23 points.
This means there matches with w-l situation and 7 matches with d-d situation.
w = win , l = Loss, d = Draw.
NOT SUFFICIENT , who won which of the 3 matches and whose match ended in a draw.

Combined : 
Out of 3 w-l match 2 were won by L, so only one team out of other teams might have won a match.
Hence for that team the scenario will be w-d-d-d in the best condition which will result in a total point of (2+1+1+1) = 5 points. 
L with 8 points has maximum total points.

Answer C

rekhabishop · Answer

Answer should be E.
statement 1 is clearly insufficient. But tells that L won 2 matches. The other two ended in a draw.
statement 2 is also insufficient.
now combining the two,
Let D be draw, L' be loss and W be win.
G D+L+W+L
H D+W+W+W
I L+L+L+L
K L+L+W+W
L W+W+D+D

Per this, H is the winner!
There is no mention of "no player lost all the matches".

carcass  and  pushpitkc  please help.

rekhabishop · Answer

Hi, Please explain the highlighted, as I couldn't really deduce that.

shashankism · Answer

Ok to understand this lets start with case scenario.. So, if all the 10 matches ends in d-d scenario.. the total points will be 10*(1+1) = 20 If 1 out of 10 match end in w-l scenario and other 9 ends in d-d scenario.. the total points will be 1*(3+0) + 9*(1+1) = 21 If 2 out of 10 match ends in w-l scenario and other 8 ends in d-d scenario.. the total points will be 2*(3+0) + 8*(1+1) = 22 If 3 out of 10 match ends in w-l scenario and other 7 ends in d-d scenario.. the total points will be 3*(3+0) + 7*(1+1) = 23 and so on.. If all the 10 matches ends in w-l scenario.. the total points will be 10*(3+0) = 30 Note: In the w-l scenario , winning team will get 3 points and losing team will get 0 point. In the d-d scenario, both teams will get 1 point each. This is the basis of the total points calculation done above. Hope that helps ..

pushpitkc · Answer

As per your logic, since we get 3 points for a win and 1 point for a draw :
There are a total of 8 wins giving 24 points and 2 draws giving 2 points each!
Hence, the total of all the 5 teams total was 28(which is greater than 23) and that's not possible
as the second statement explicitly states that.

That is the primary reason the answer will be C.
Hope that helps!

bumpbot · Answer

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