According to the incomplete table above, if each of the 6 te

Team Number of Games Won
A 4
B 7
C 9
D 2
E 2
X

According to the incomplete table above, if each of the 6 teams in the league played each of the other teams exactly twice and there were no ties, how many games did team X win? (Only 2 teams play in a game.)
(A) 4
(B) 5
(C) 6
(D) 8
(E) 10

ans should be 6

each of 6 teams play 2 games with each of the other teams
so total of 30 games played........[ 2*(5+4+3+2+1)] = 30

there should be 30 wins, bcoz there were no ties.

total number of wins given in table adds up to 24, so X won remaining 6 games.

Hi All,

If you're comfortable using the Combination Formula, then calculating that 30 games were played is a fairly straight-forward task. If you're not comfortable with that formula yet, here's another way to figure out that 30 games were played.....

The teams are A, B, C, D, E and X

Team A plays each of the other 5 teams TWICE, so that's 2(5) = 10 games

Since B ALREADY played Team A twice, we won't count those games again; Team B plays each of the remaining 4 teams twice, so that's 2(4) = 8 games

Since C ALREADY PLAYED Team A and Team B, we won't count those games again, Team C plays each of the remaining 3 teams twice, so that's 2(3) = 6 games.

This pattern continues, giving us...

10+8+6+4+2+0 = 30 total games.

From there, the rest of the work is based on addition.

GMAT assassins aren't born, they're made,
Rich

Team A played 5*2= 10 matches with other teams
Team B played 4*2= 8 matches with other teams
Team C played 3*2= 6 matches with other teams
Team D played 2*2= 4 matches with other teams
Team E played 2 matches

Total Matches played= 30

Total Matches won by teams other than team X= 24

Total matches won by team X = 30-24= 6

C is the answer

6P2 = 30 games

24 won - 30 games = 6 won ans. C.

(n)(n-1)=6*5=30 total games=30 total wins
30-24=6
team x won 6 games

6P2 = "30 games" is fundamentally wrong!!!!!!! , as permutations considers order while counting the possibilites. ( A - B and B - A are both one match only, permutations method of counting will count it as 2)


While the Combinations doesnt concern with the order, hence we need to use combinations in this case to count. Which is 6C2 - 15 ( 2 times matches are played )

Please be carefull while using both the counting frameworks, ask the following question to yourself - Does the order matters?

Hi Jatro,

The prompt tells us that each team played each of the other teams TWICE.

While 6c2 = 15 games played, this accounts for each team playing each other team just ONCE; we have to double that result here (which gets us to the 30 total games played).

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: Rich.C@empowergmat.com

True that's what I stated above, I should have mentioned 30 after 6c2 ( 2 matches played) - 30

My intention was to cite the difference between combination and permutations as a comment earlier shows 6p2, though it gives 30 but it is wrong approach

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