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27 Aug 2015, 01:33
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
32% (02:46) correct
68%
(03:01)
wrong
based on 31
sessions
History
Date
Time
Result
Not Attempted Yet
A 6-student Senior Sports Committee is being selected from the seniors who play basketball, soccer, and football at a certain school. The committee consists of one student who is on both the basketball and soccer teams, one who is on both the football and soccer teams, and one who is on the basketball and football teams, as well as one additional student from each of the teams; the last three students may play on one or two teams. There are 10 seniors on the basketball team, 8 on the football team, and 6 on the soccer team. If more than one senior plays each pair of sports, and no senior plays all three sports, is the number of different 6-student committees that can be selected a multiple of 4?
(1) The number of seniors on both the basketball team and the soccer team is the same as the number of seniors on both the football team and soccer team, and three less than the number of seniors on both the basketball and football team.
(2) There are 5 seniors that play one pair of sports, 2 that play another pair, and 2 that play the last pair.
Kudos for a correct solution.
(1) The number of seniors on both the basketball team and the soccer team is the same as the number of seniors on both the football team and soccer team, and three less than the number of seniors on both the basketball and football team.
(2) There are 5 seniors that play one pair of sports, 2 that play another pair, and 2 that play the last pair.
Kudos for a correct solution.
27 Aug 2015, 05:19
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Bookmarks
IMO: D
Question Stem:
B=10
S=6
F=8
No. of players playing all 3 sports = 0
No. of players playing 2 sports \(\geq\)1
Selection:
1 player from B&S
1 player from S&F
1 player from F&B
Then remaining 3 players are selected one after the other from the set of players who play either 1 or 2 sports
St 1: The number of seniors on both the basketball team and the soccer team is the same as the number of seniors on both the football team and soccer team, and three less than the number of seniors on both the basketball and football team.
Consider the following fig:
Capture.JPG [ 22.33 KiB | Viewed 1719 times ]
If x is count of players who play both F&B
Then No. of players who play S&F = B&S = x+3
Now given S = 6
6 = 2x+s
B=10
10=2x+b
F=8
8 = 2x+3
Thus
If x=1 then
1c1 1c1 4c1 9c1 7c1 5c1 = 1*1*4*9*7*5 = 1260 ==>multiple of 4
If x =2 then
2c1 2c1 5c1 9c1 7c1 5c1 = 2*2*5*9*7*5 = 6300 ==> multiple of 4
St 2: There are 5 seniors that play one pair of sports, 2 that play another pair, and 2 that play the last pair.
It doesn't matter which pair of sport is played 5 or 2 or 2. We end up with same selection
2c1 2c1 5c1 9c1 7c1 5c1 = 2*2*5*9*7*5 = 6300==>multiple of 4
Hence Suff
Question Stem:
B=10
S=6
F=8
No. of players playing all 3 sports = 0
No. of players playing 2 sports \(\geq\)1
Selection:
1 player from B&S
1 player from S&F
1 player from F&B
Then remaining 3 players are selected one after the other from the set of players who play either 1 or 2 sports
St 1: The number of seniors on both the basketball team and the soccer team is the same as the number of seniors on both the football team and soccer team, and three less than the number of seniors on both the basketball and football team.
Consider the following fig:
Attachment:
Capture.JPG [ 22.33 KiB | Viewed 1719 times ]
If x is count of players who play both F&B
Then No. of players who play S&F = B&S = x+3
Now given S = 6
6 = 2x+s
B=10
10=2x+b
F=8
8 = 2x+3
Thus
If x=1 then
1c1 1c1 4c1 9c1 7c1 5c1 = 1*1*4*9*7*5 = 1260 ==>multiple of 4
If x =2 then
2c1 2c1 5c1 9c1 7c1 5c1 = 2*2*5*9*7*5 = 6300 ==> multiple of 4
St 2: There are 5 seniors that play one pair of sports, 2 that play another pair, and 2 that play the last pair.
It doesn't matter which pair of sport is played 5 or 2 or 2. We end up with same selection
2c1 2c1 5c1 9c1 7c1 5c1 = 2*2*5*9*7*5 = 6300==>multiple of 4
Hence Suff
29 Oct 2019, 14:39
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Hello from the GMAT Club BumpBot!
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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