Bunuel wrote:
The coach of an athletic team has a certain number of jerseys that he will distribute among his players. If there are more than 16 jerseys, and between 2 and 16 players, is it possible to distribute all of the jerseys so that each player receives the same number of jerseys?
(1) If there were 17 more jerseys, it would be possible to distribute all of the jerseys so that each player receives the same number of jerseys.
(2) If there were 15 more jerseys, it would be possible to distribute the jerseys so that each player receives the same number of jerseys.
Project DS Butler Data Sufficiency (DS3)
For DS butler Questions Click Here (1) If there were 17 more jerseys, it would be possible to distribute all of the jerseys so that each player receives the same number of jerseys.
Let the no. of Jerseys start from \(17\) onwards and check .
Initially if the no. of Jerseys is \(17 \) then adding another \(17\) we get \(=34\) , to distribute \(34 \) jerseys no. of players needs to be a factor of 34 i.e. either of 1 or 2, or 17 or 34 , but we are told that \(2 <\) players \(<16\), hence if there \(17 \) Jerseys ,which is also a prime , the same cannot be distributed if there are any number of players between \(2\) and \(16\)
If initially there are \(18 \) Jerseys then after adding further \(17\) we have \(35 \) Jerseys , no. of players can be \(1, 5, 7\), or \(35,\) among which \(5\) and \(7\) qualify within the range .
So we have \(5\) or \(7\) players and \(18 \) Jerseys , again this cannot be distributed equally among the \(5 \) or \(7\) players .
If initially there are \(19 \) Jerseys then after adding further \(17 \) we have \(36\) Jerseys , no. of players can be \(1,2,3,4,9,12,18,36-\)> among which \(3, 4,9,12, \)qualify within the range. Hence if we have \(19\) Jerseys and \(3,4,9 \) or \(12\) players again the Jerseys cannot be distributed equally among the players.
Similarly if we check more cases we will always find that the no. of Jerseys
CANNOT be equally distributed among the players.
SUFF.(2) If there were 15 more jerseys, it would be possible to distribute the jerseys so that each player receives the same number of jerseys.If initially we have \(17 \) jerseys then after adding \(15 \) we get \(32\) Jerseys. Now straight away we cen tell since \(17\) is a prime it will have no factors in the range \(3\) to \(15\) inclusive hence \(17\) Jerseys cannot be distributed equally.
if initially there are \(18\) jerseys then after adding \(15\) we get \(33 \) jerseys. No. of players can be \(3\) or \(11.\)
So if there are \(18 \) jerseys and \(3 \) players we can distribute the same equally \(3*6 =18.\)
But if there are \(18\) jerseys and \(11 \) players we cannot distribute the same equally.
Since we have two cases for this statement. This is
INSUFF.Ans A
Hope it's clear.
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