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acegmat1
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St. Francis’s gym coach is planning a kickball tournament 04 May 2014, 20:12
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56% (02:28) correct 44% (02:33) wrong based on 399 sessions

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St. Francis’s gym coach is planning a kickball tournament for the 40 students in the fourth grade. How many teams are there if the coach wants to evenly divide the students to make sure there are more than 2 teams, with each team having more than 2 students?

(1) If 17 fifth-graders are allowed to play in the tournament, one will have to serve as an alternate to evenly assign the fifth-graders to teams.

(2) If 5 third-graders are allowed to play in the tournament, one will have to serve as an alternate to evenly assign the third-graders to teams.
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St. Francis’s gym coach is planning a kickball tournament 05 May 2014, 01:25
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St. Francis’s gym coach is planning a kickball tournament for the 40 students in the fourth grade. How many teams are there if the coach wants to evenly divide the students to make sure there are more than 2 teams, with each team having more than 2 students?

To meat the constraints the following cases are possible>

Teams - # of players in each team
4 - 10
5 - 8
8 - 5
10 - 4

(1) If 17 fifth-graders are allowed to play in the tournament, one will have to serve as an alternate to evenly assign the fifth-graders to teams.

This statement implies that we can assign 16 players to the teams, or that 16 is divisible by the number of teams. Thus there can be either 4 teams or 8 teams. Not sufficient.

(2) If 5 third-graders are allowed to play in the tournament, one will have to serve as an alternate to evenly assign the third-graders to teams.

This statement implies that we can assign 4 players to the teams, or that 4 is divisible by the number of teams. Thus there can be only 4 teams. Sufficient.

Answer: B.

Does this make sense?
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sfgh
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St. Francis’s gym coach is planning a kickball tournament 05 Dec 2014, 20:47
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The answer is being based on the assumption that after the 4th graders team has been formed the 5th or 3 Rd graders join. However the case would have been different if the 3rd 5th graders join and the teams are formed.the question does not clarify the underlying assumption
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St. Francis’s gym coach is planning a kickball tournament 16 Sep 2018, 09:31
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The question stem tells us that 40 students will be evenly divided into more than 2 teams. Let’s list out the possible teams:

4 teams of 10

5 teams of 8

8 teams of 5

10 teams of 4

Other possible groupings are not permitted, as there must be more than 2 teams, and each team must have more than 2 fourth-graders.

For sufficiency, we need to narrow down the list of possible teams to only one choice.

Evaluate the Statements:

Statement (1): We are told that if 16 fifth-graders are allowed to join the teams, they can be evenly divided among the teams; 16 new competitors could be evenly assigned either to 4 teams or to 8 teams, so Statement (1) is Insufficient to answer the question with a single value. Eliminate choices (A) and (D).

Statement (2): We are told that 4 third-graders could be evenly assigned to the teams. Of the possible numbers of teams from the question stem, only the case of 4 teams fits Statement (2), so it is Sufficient to answer the question. Eliminate choices (C) and (E).

Therefore, the correct answer is Choice (B).
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St. Francis’s gym coach is planning a kickball tournament 12 Sep 2019, 09:18
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acegmat1
St. Francis’s gym coach is planning a kickball tournament for the 40 students in the fourth grade. How many teams are there if the coach wants to evenly divide the students to make sure there are more than 2 teams, with each team having more than 2 students?

(1) If 17 fifth-graders are allowed to play in the tournament, one will have to serve as an alternate to evenly assign the fifth-graders to teams.

(2) If 5 third-graders are allowed to play in the tournament, one will have to serve as an alternate to evenly assign the third-graders to teams.
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Given:
1. St. Francis’s gym coach is planning a kickball tournament for the 40 students in the fourth grade.
2. The coach wants to evenly divide the students to make sure there are more than 2 teams, with each team having more than 2 students.

Asked: How many teams are there ?

Let the number of teams be t; where t>2
Each team has 40/t students > 2
40/t >2; t<20
2<t<20
40/t is an integer
t = {4,5,8,10]

(1) If 17 fifth-graders are allowed to play in the tournament, one will have to serve as an alternate to evenly assign the fifth-graders to teams.
If t = 4; Students/team = 10; 4 students can be assigned to a team and 1 will have to server as an alternate.
If t = 5; Students/team = 8; 2 students have to serve as an alternate
If t=8; Students /team = 5; 1 student has to serve as an alternate
If t =10; Students/team = 4; 7 students have to serve as an alternate
t = {4,8}
NOT SUFFICIENT

(2) If 5 third-graders are allowed to play in the tournament, one will have to serve as an alternate to evenly assign the third-graders to teams.
If t=4; 1 has to serve as an alternate
If t =5; 0 has to serve as an alternate
If t=8; 5 have to serve as an alternate
If t=10; 5 have to serve as an alternate
t = 4
SUFFICIENT

IMO B
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St. Francis’s gym coach is planning a kickball tournament 12 May 2023, 00:58
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What about the fact that the question stem talks about fourth graders only, while the statements talk about 5th and 3rd graders?
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St. Francis’s gym coach is planning a kickball tournament 12 May 2023, 02:10
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sonalshenoy
What about the fact that the question stem talks about fourth graders only, while the statements talk about 5th and 3rd graders?
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The statements talk about the hypothetical scenarios when some of the fifth-graders or some of the third-graders are allowed to play in the tournament WITH fourth-graders.
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St. Francis’s gym coach is planning a kickball tournament 28 Oct 2025, 13:22
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