Question

There are exactly 6 teams in league X. What was the total number of games played by the 6 teams last season?
I. Each team in league X played each of the other teams atleast once.
II. No team in league Xplayed more than 7 games.
Decide whether the data in the statements are sufficient to answer the question.

• A. if Statement I alone is sufficient but Statement II alone is not sufficient to answer the question
• B. if Statement II alone is sufficient but Statement I alone is not sufficient to answer the question
• C. if both statements taken together are sufficient to answer the question but neither Statement alone is sufficient
• D. if Statements I and II together are not sufficient, and additional data is needed to answer the question

Answer 1

Answer: (D)

if Statements I and II together are not sufficient, and additional data is needed to answer the question

Answer 2

Statement 1:
Each team in league x played each of the other teams at least once So, if each team played each of the other teams ONLY once then there was total games played $^{6}C_2 = 15$.
but if each team played each of the other teams TWICE then there was total of $2\times^{6}C_2 = 30$ games played.
Not sufficient
Statement 2:
No team in league x played more than 7 games.
So, insufficient.
Both together:
If each team played each of the other teams only once then there was total of $^{6}C_2 = 15$ games played (each of the 6 teams played 5 games), but if after each team played each of the other teams only once, some two teams played between each other once more then the total number of games played was 16 (4 teams played 5 games and 2 teams played 6 games).
Not sufficient.
So the correct option is (D) .