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There are four different positions on a lacrosse team: goalie, defense, attack, and midfield. A certain school's traveling team has 7 defense players, and \(\frac{1}{4}\) of the team are attackers. How many total players comprise this team?
1) Goalies make up \(\frac{1}{12}\) of the team.
2) The team has 9 midfielders.
1) Goalies make up \(\frac{1}{12}\) of the team.
2) The team has 9 midfielders.
19 Apr 2018, 10:55
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itisSheldon
There are four different positions on a lacrosse team: goalie, defense, attack, and midfield. A certain school's traveling team has 7 defense players, and \(\frac{1}{4}\) of the team are attackers. How many total players comprise this team?
1) Goalies make up \(\frac{1}{12}\) of the team.
2) The team has 9 midfielders.
1) Goalies make up \(\frac{1}{12}\) of the team.
2) The team has 9 midfielders.
So number of defense players is given and number of attackers is not given as such but given as a fraction (1/4) of total. So rest of the team apart from attackers = 1 - 1/4 = 3/4 of total, out of which 7 players are defense.
(1) Out of remaining 3/4, goalies are 1/12, so that means apart from attackers and goalies, remaining players (defense + midfeld) are 3/4 - 1/12 = 8/12 or 2/3. So defense + midfield constitute 2/3 of the team, out of which 7 players are defense. But this is not sufficient to find the total number of players.
(2) 9 midfield, 7 defense, and attackers = 1/4 of total. But this information is also not sufficient to determine the total number of players.
Combining the statements, midfield = 9, defense = 7, these are 16 in total. Goalies + attackers = 1/4 + 1/12 = 1/3 of total, so that means midfield + defense must constitute 2/3 of total, but these are 16 in number. So 2/3 of total = 16 , hence total = 24 players. Sufficient.
Thus C answer
