GMAT Club World Cup 2022 (DAY 5): In professional soccer leagues, team

Question

In professional soccer leagues, teams are ranked based on a system of points awarded for wins (3 points) and draws (1 point). In the event that two or more teams have earned the same number of points, the team with the greatest cumulative goal difference is ranked above the others. This statistic represents the difference between goals scored and goals allowed for a given team. For instance, a team that loses a match 1-3 will earn a -2 goal difference.

On the basis of the above information, which of the following must be true?

(A) The cumulative goal difference for all teams in the league together will always be zero.
(B) The team with the greatest cumulative goal difference will be the highest ranked.
(C) In a league of twenty teams, a team with a cumulative goal difference of 0 will be ranked 10th or 11th.
(D) No team with a negative cumulative goal difference can have a winning record.
(E) A team with 6 points from four matches will have a positive goal difference for those matches.

AndrewN · Accepted Answer

If you replaced the text of the answer choices with numbers and altered the question stem, you would have a workable PS question. There are two types of numerical systems that we need to keep track of to tell what  must be true . The first is the points system for wins and draws, and the second is a sort of plus/minus relationship based on  cumulative goal difference . With an example in hand, there should be no confusion as to how goal difference works. How about we jump right in and get our hands dirty?

This might seem like an impossible task, to keep track of all the teams in a league at the same time across an entire season. We are also trained to be skeptical of absolute or overreaching language such as  always . But remember, a must-be-true framework deals in absolutes, so we just need to consider the logical implications of the statement. From the example provided at the end of the passage, we should be able to deduce that the winning team (which would walk away with 3 points) would consider the 1-3 loss for the other team a 3-1 personal victory, and that would mean the team would earn a +2 goal difference. It does not take a   Bunuel   to see that the net sum of +2 and -2 is 0, and that, regardless of a given outcome for any game, the sum would remain 0 for that game: +4/-4, 0/0, and so on. Since we cannot find an issue with this answer choice, we know we have the one we need.

This could or could not be true. Consider a team that won a match 5-0, thus earning 3 points and a +5 goal difference, and then lost a second match 0-1, keeping its points tally at 3 but dropping its cumulative goal difference to +4. A second team might win back-to-back matches 1-0 and thus earn 6 points and a +2 cumulative goal difference. The second team would outrank the first on points, despite having a lower cumulative goal difference.

You might be overwhelmed at the prospect of tracking twenty teams and simply reason that the top half of the table would probably have a positive cumulative goal difference while the bottom half would have a negative cumulative goal difference, leaving the teams in the middle to straddle that line. Again, this could or could not be true, depending on just how many goals a given team scored. There are so many possibilities here that it is not worth seeking to conjure up examples. (If you need some inspiration, though, feel free to borrow from the explanation above.)

An easy statement to disprove using no more than three matches. Say that a team wins the first and second matches 1-0 but loses a third 0-3. The goal difference for each match would be +1, +1, and -3, respectively, leading to a cumulative goal difference of -1. But that would not change the fact that the team would be sitting on a winning record.

In one scenario, this must be true: if the team wins one match and draws the other three (3 + 1 + 1 + 1 = 6 points). The cumulative goal difference for those matches would have to be positive, carrying over from the win. However, it could just as easily be the case that the team wins two matches and loses the other two by a larger cumulative margin, say 1-0, 1-0, 0-2, 0-3, or even 1-0, 1-0, 0-1, 0-1, the latter case leading to a cumulative goal difference of 0. (Quant reminder: 0 is neither positive nor negative, a one-of-a-kind number.)

Keep your approach to these numerical CR questions simple, and you will often find an answer with relative ease ( Moneyland casino  questions aside).

I suspect this question will prove easier than others in the competition, since it is purely quantitative, but I cannot say the topic is unfitting.

- Andrew

mainbhiankit · Answer

Let's take this one option at a time:

(A) The cumulative goal difference for all teams in the league together will always be zero. 
Cumulative goal diff taken together will always be zero since a goal scored for one team is a goal scored against the other team. Consider a tournament of three teams where A wins both matches with a 2-1, B wins one match with a 2-1, and C loses both matches. The scoreboard would look something like this:
A: 6 pts, gd=2
B: 3 pts, gd=0
C: 0 pts, gd=-2
Their cumulative goal difference or gd will be 2+0+(-2)=0

(B) The team with the greatest cumulative goal difference will be the highest ranked. 
Nope, the team with the most number of points would the highest ranked team

(C) In a league of twenty teams, a team with a cumulative goal difference of 0 will be ranked 10th or 11th. 
This  can be  true, but it isn't a  must be  true statement. Think about it, you can find exceptions to this statement.

(D) No team with a negative cumulative goal difference can have a winning record. 
Consider a team A which has won all of its matches except one with just +1 goal difference. But the match it lost, it lost 0-20, say. It can have a negative goal difference if the number of matches is less than 20.

(E) A team with 6 points from four matches will have a positive goal difference for those 
Again, as pointed out in option D, it's not necessarily the case.

manish1708 · Answer

Answer: A

In professional soccer leagues, teams are ranked based on a system of points awarded for wins (3 points) and draws (1 point). In the event that two or more teams have earned the same number of points, the team with the greatest cumulative goal difference is ranked above the others. This statistic represents the difference between goals scored and goals allowed for a given team. For instance, a team that loses a match 1-3 will earn a -2 goal difference.

On the basis of the above information, which of the following must be true?

(A) The cumulative goal difference for all teams in the league together will always be zero.  -->  Correct . Cumulative goal difference for all teams will be zero. A winning team will get +ve GD and losing team will get same as -ve GD. Post all the matches the sum total of +ve will be equal to sum total of -ve and hence zero. 
(B) The team with the greatest cumulative goal difference will be the highest ranked. - -> Incorrect. Not necessarily. Consider 4 teams. Lets say winning team draws one match and wins 3 out of 4 matches but wins each by GD of 1, Then total points will be 10 and GD will be 3. team ranked second draws two matches and wins 2 with GD of 5 each. Then total points for second placed team will be 8 but GD will be 10 which is way higher than the winning team. 
(C) In a league of twenty teams, a team with a cumulative goal difference of 0 will be ranked 10th or 11th.  --> Incorrect. There is a possibility that no team ends up with 0 GD. 
(D) No team with a negative cumulative goal difference can have a winning record.  --> Incorrect. losing maximum games with small or big margin can generate a negative GD but the team can still draw or win few games.  
(E) A team with 6 points from four matches will have a positive goal difference for those  --> Incorrect. This is only possible if team wins 1 and draws 3 matches. If team wins 2 matches then it will lose other two for it to have 6 points. In this case, if the losing margin is higher then GD can be negative.

soudipsengupta · Answer

(A) The cumulative goal difference for all teams in the league together will always be zero.
  CORRECT  . Consider a game with two teams and A scored 2 goals and B scored 0. So in effect A scored +2 and B scored -2 on GD scale. The cumulative goal score for two teams in any match will always add to 0 and thus he cumulative goal difference for all teams in the league together will always be zero

(B) The team with the greatest cumulative goal difference will be the highest ranked.
  INCORRECT  . It could be the case the team scored many goals and allowed only few, but it lost many matches to make it slip down the points table. Remember, points (+3 for win and +1 for draw) take priority over goal difference in determining rankings.

(C) In a league of twenty teams, a team with a cumulative goal difference of 0 will be ranked 10th or 11th.
  INCORRECT  . This is not true. The said team can be placed anywhere in points table. Points and Goad Difference are two different things and points (+3 for win and +1 for draw) take precedence over goal difference in determining rankings.

(D) No team with a negative cumulative goal difference can have a winning record.
  INCORRECT  . A Team can win 5 matches with 1-0 score (GD + 5) and then lose to another team by 0-7 (GD=-7+5=-2).

(E) A team with 6 points from four matches will have a positive goal difference for those
  INCORRECT  . This may be true but NOT must be true. It can have 6 points from 4 matches and have a negative goal difference, just like the example given in D

Kinshook · Answer

Given: In professional soccer leagues, teams are ranked based on a system of points awarded for wins (3 points) and draws (1 point). In the event that two or more teams have earned the same number of points, the team with the greatest cumulative goal difference is ranked above the others. This statistic represents the difference between goals scored and goals allowed for a given team. For instance, a team that loses a match 1-3 will earn a -2 goal difference.

Asked: On the basis of the above information, which of the following must be true?

If a team A scores a goal against another team B, 1 goal score is added for the team A and 1 goal alllowed is added for another team B, goal difference for team A increases by 1 and goal difference for team B decreases by 1.
The cumulative goal difference for all teams in the league together will always be zero since there will be no net change in cumulative goal difference of all teams by any goal.
Correct

The statement is not necessarily true since the team may win a match with big goal difference e.g. 10-0 and lose all other matches with small goal diffence 0-1; It may have greatest cumulative goal differnce but may not be highest ranked since teams are ranked based on points. 
Incorrect

The statement is not necessarily true since cumulative goal difference has no relation with points or rank as discussed earlier in option B. 
Incorrect

Let us say a team A has following goal differences: 
A - B = 1 - 0 = 1
A - C = 1 - 0 = 1
A - D = 0 - 10 = -10
Cumulative goal differnce of team A after 3 matches = 1 + 1 - 10 = - 8, still team A has won 2 matches out of 3 and has a good winning record.
Incorrect

Let us say a team A has following goal differences: 
A - B = 1 - 0 = 1 : 3 points
A - C = 1 - 0 = 1 : 3 points
A - D = 0 - 10 = -10 : 0 points
A - E = 0 - 9 = -9 : 0 points
Cumulative goal difference = 1 + 1 - 10 - 9 = - 19: Negative goal difference
Incorrect.

IMO A

Fido10 · Answer

(A) The cumulative goal difference for all teams in the league together will always be zero.
This is the correct answer , because, all goals scored by the teams are scored against the same teams, and same reasoning for the goals conceived.At the end, the cumulative goals will lead to a goal average of 0 for all the teams
 (B) The team with the greatest cumulative goal difference will be the highest ranked. 
Teams are ranked according to the points earned not according to the highest goal average. 
A team, for instance, in a league of 20 teams a team could loose all its games by 1-0 and win the last game by 100-0 (technically not possible, but theoretically possible), then it will has just 3 points and an average score possibly bigger thatn that of the other teams, Wrong answer
 (C) In a league of twenty teams, a team with a cumulative goal difference of 0 will be ranked 10th or 11th. 
Teams are ranked according to the points earned not according to goal average.
a team can win a game with 5-0 and have 3 points
and loose 5 games with 1-0 at each games and loose 15 points, 
this reasoning, conduct us to conclude that an average of 0 could lead you to a position worst than 10th or 11th, Wrong answer
 (D) No team with a negative cumulative goal difference can have a winning record. 
Wrong answer, a team can, for instance, win 10 games with 1-0 and loose all the remaining games with 4-0, then it will have a negative goal average, 
 (E) A team with 6 points from four matches will have a positive goal difference for those 
Wrong answer, this team could have won 2 games with 1-0, and loose the 2 remaining games with 4-0 will have a negative goal average, not a positiveone

PRamesh2008 · Answer

In professional soccer leagues, teams are ranked based on a system of points awarded for wins (3 points) and draws (1 point). In the event that two or more teams have earned the same number of points, the team with the greatest cumulative goal difference is ranked above the others. This statistic represents the difference between goals scored and goals allowed for a given team. For instance, a team that loses a match 1-3 will earn a -2 goal difference.

On the basis of the above information, which of the following must be true?

Let's say three teams are there -- A, B & C

Scores : A v/s B (6-3)
 B v/s C (5-5)
 A v/s C (4-2)

Now, let's calculate the cumulative goal difference for the 3 teams :-

for A, 10-5 = 5
for B, 8-11 = -3
for C, 7-9 = -2

Hence, Together the cumulative goal difference = 5 + (-3) + (-2) = 0

This sum will always be Zero, since Goals Scored (by a team) is attibuted in a negative manner for the opponent team in the form of Goals Allowed (against a team),; thus leading to Zero.

(A) The cumulative goal difference for all teams in the league together will always be zero.
  It is always true (as explained above)

(B) The team with the greatest cumulative goal difference will be the highest ranked.
  Need not always be true

(C) In a league of twenty teams, a team with a cumulative goal difference of 0 will be ranked 10th or 11th.
  Rank initially determined oon the points (accrued as result of Wins and Draws)..Rank will vary

(D) No team with a negative cumulative goal difference can have a winning record.

As a result of one loss by a large margin,and all other wins for balance matches..will lead to a negative cumulative goal difference..!!

(E) A team with 6 points from four matches will have a positive goal difference for those

Not necessary..that such a team will always have a positive goal difference

(A) is the CORRECT answer

gmatophobia · Answer

(A) The cumulative goal difference for all teams in the league together will always be zero.

This is true, if a team looses it would earn a negative goal difference while the winning team will earn the same value of the goal difference but positive. Hence the cumulative goal difference for all teams in the league together will always be zero.

(B) The team with the greatest cumulative goal difference will be the highest ranked.

This is not true.

(C) In a league of twenty teams, a team with a cumulative goal difference of 0 will be ranked 10th or 11th.

We cannot infer this from the passage.

(D) No team with a negative cumulative goal difference can have a winning record.

A team can win a match with smaller goal difference and loose with large goal difference. Hence the cumulative goal difference for that team will be negative. Hence this statement is incorrect.

(E) A team with 6 points from four matches will have a positive goal difference for those

We can't infer this. If the team has lost with high margin, the difference may not be positive.

IMO A

desertEagle · Answer

(A) The cumulative goal difference for all teams in the league together will always be zero. -- Let there are only two teams, then score line is A(a,b)B. then goal difference for A will be a-b and that of B will be b-a. Adding this we get zero. Similarly if there are more teams, then any two teams will have equal goal difference in magnitude but different in sign. So total will be zero.  CORRECT 
(B) The team with the greatest cumulative goal difference will be the highest ranked.--- suppose three teams ABC .. scoreline AB 1-0, BC 10-0, CA 0-1. Total point of A = 6, Point of B = 3, Point of C = 0. A will be ranked highest. However Goal difference of A = 2, Goal Difference of B = 8. Incorrect
(C) In a league of twenty teams, a team with a cumulative goal difference of 0 will be ranked 10th or 11th. - Similar to B. If the last team wins only one match with a big goal difference like 100-0 and loses in next 19 matches with 18 matches 0-5 and one match 0-10, cumulative goal difference will be zero but it may be ranked at bottom. INCORRECT
(D) No team with a negative cumulative goal difference can have a winning record.-- Suppose four teams ABCD. AB = 1-0, AC=1-0, A-D=0-10. Cumulative Goal difference is -8 but it has won 2 matches. INCORRECT
(E) A team with 6 points from four matches will have a positive goal difference for those - Let teams be ABCDE. Let AB=1-0, AC=1-0, AD=0-10, AE=0-10 Points of A = 6 Goal difference = -18. INCORRECT

Ans A

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GMAT Club World Cup 2022 (DAY 5): In professional soccer leagues, team

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GMAT Club World Cup 2022 (DAY 5): In professional soccer leagues, team

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