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A soccer league is divided into a junior and a senior division, separated not by age but by a player’s skill level. This year, to determine the division for which an aspirant is best qualified, the league held a week-long trial, after which coach A and coach B selected players. Coach A nominated sixteen of the forty players for the senior league. Amongst Coach B’s nominations for the senior division were four players not nominated by Coach A. Therefore, there will be twenty players in the senior division.

Which of the following, if true, provides the strongest basis for the conclusion above to be warranted?

(A) To be selected for the senior division, a player need only be nominated by one of the two coaches.

(B) Of the sixteen players nominated by the coach A, coach B nominated more than half to play in the senior division.

(C) All of the players not assigned to the senior division by both coaches were assigned to the junior division.

(D) Of those chosen by both coaches to play in the senior division all will end up playing in the senior league.

(E) The four players that Coach B but not Coach A selected for the senior division played the previous year in that division.

Official Explanation



For the conclusion to hold true—there will be 20 players on the team—players need only be selected by one coach. If both coaches have to choose a player, then there is no way that conclusion can be validly drawn. At most, 16 players could be chosen, but that’s assuming coach B would choose every play that cach A chose. Answer: (A)

(A) See above.

(B) If (B) is true, the conclusion isn’t necessarily valid. Say, coach B nominated 9 of the sixteen players that coach A nominated. This information alone doesn’t automatically equate to 20 players.

(C) Based on information in the prompt, there could be zero overlap in the two coach’s selection. None of the 16 players coach A chose could be chosen by coach B. Therefore, (C) does not inevitably lead to the conclusion.

(D) Based on the information in the prompt, we do not have a definite number for the number of players chosen by both coaches. That number could range from zero to sixteen.

(E) Who played the previous year is irrelevant to who is playing in the senior division this year.
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