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22 Nov 2023, 02:30
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A
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Difficulty:
95%
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Question Stats:
31% (02:19) correct
69%
(02:34)
wrong
based on 51
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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.
(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.
24 Nov 2023, 15:21
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Bunuel
(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.
If there were \(18\) jerseys initially then after \(17\) we have \(35\) Jerseys. Number of players must be a factor of \(35\), i.e. \(1,5,7\) and \(35\). However none of the factors can divide \(18.\) We have a NO.
If there were \(19 \) Jerseys initially then after \(17 \) we have \(36\) Jerseys. Number of players must be a factor of \(36\). However as \(19\) is a prime number we know it will not have any factors in the space between \(2-16\) players.
Similarly if we check other number of jerseys i.e ,\(20,21\)...etc we will find that we cannot divide the orginal number of jerseys by the number of players in the space between \(2-16.\)
Thus we can answer with a definite NO.
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 there are \(17\) Jerseys then after adding \(15\) we have \(32\) jerseys . Number of players must be a factor of \(32\). However as \(17\) is a prime number we know that none of the factors of \(32\) would divide \(17\). This gives us a NO.
Lets check a non-prime number # of jerseys
IF initially there are \(20 \) Jerseys then after adding \(15\) we have \(35\) jerseys . Number of players must be a factor of \(35.\) If the number of players is \(5\) then we have a YES. If the number of players is \(7\) then we have a NO.
So we can have both a YES and a NO.
INSUFF.
Ans A
Hope it helped.
