St. Francis’s gym coach is planning a kickball tournament

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).

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

What about the fact that the question stem talks about fourth graders only, while the statements talk about 5th and 3rd graders?

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.