Statement 1: 17 students will play with one as alternate, that means, actually only 16 need to be allocated to the existing teams.This can be done in multiple ways:
Say there are 4 teams, then 16/4=4 players can be added to each team.Also, say there are 8 teams, then 16/8=2 players can be added to each team. Multiple options hence Not Sufficient.

Statement 2 : 5 students will play with one as alternate,so actually only 4 need to be allocated to the existing teams.Noe the question stem says there must be more than 2 teams.So if there are are 3 teams then we cannot evenly divide the 4 students to each team, but if there are 4 existing teams then we can evenly add 1 player to each.This is the only possible option.Hence,Sufficient.

So Answer is B.

Hope this helps.

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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Thanks for confirming my approach Bunuel!

HI Bunel ,

I feel the answer should be D !

In the first statement, how can there be 8 teams of 2 players each ? Please note, the question says "with each team having more than 2 students" so 8 cannot be the number of teams.

Please correct me if I am wrong.

Cheers,
~Pegasus.

What Bunuel is trying to say is not that there are 8 teams with 2 players each. But rather if you look at the statement it says that if the 16 extra players from the 5th grade are to be allocated to the existing teams. So if there are 4 existing teams with 10 players each then we can add 4 more players to each. Or, if there are 8 existing teams with 5 players each, then we can add 2 more to each of them.

Note that in the stem it says that the teams are to be made from the 40 students of 4th grade.

Hope this helps.

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

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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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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