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25 Jun 2021, 04:45
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C
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Difficulty:
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76% (02:08) correct
24%
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based on 93
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For a cricket match team selection, 2 batsmen, 3 bowlers, and 1 wicketkeeper are to be picked. There are 23 players available to play as batsmen, 21 other players available to play as bowlers, and 9 other players available to play as wicketkeepers. If the maximum possible number of complete sets of 6 players are formed, how many of the available players will not be on a team?
(A) 7
(B) 9
(C) 11
(D) 13
(E) 15
(A) 7
(B) 9
(C) 11
(D) 13
(E) 15
27 Apr 2025, 07:36
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Bunuel
Hi guys, please refer to the written solution below, let us know if u need further help with this.
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For a cricket match team selection, 2 batsmen, 3 bowlers, and 1 wicke Problem Solving (PS).jpeg.png [ 252.03 KiB | Viewed 1207 times ]
For a cricket match team selection, 2 batsmen, 3 bowlers, and 1 wicke Problem Solving (PS).jpeg.png [ 252.03 KiB | Viewed 1239 times ]
General Discussion
Alekhya1
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Last visit: 31 Jan 2022
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25 Jun 2021, 07:34
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From 23 batsmen, 10 pairs of 2 batsmen can be chosen and 3 will be remaining.
From 21 bowlers, 7 sets of 3 bowlers can be chosen with 0 remaining.
From 9 wicket-keepers, 9 each can be selected with 0 remaining.
Now since perfect sets of 6 players have to be selected, (2 batsmen, 3 bowlers and 1 wicket-keeper), the maximum number of sets chosen from each category is 7.
So 7 sets of 2 batsmen out of the 23 batsmen leaves 23- (2*7) = 9 batsmen
and 7 sets of 1 wicket keeper each leaves 9-7 = 2 wicket-keepers
Therefore 9+2=11 players will not be on a team.
ANSWER - C
From 21 bowlers, 7 sets of 3 bowlers can be chosen with 0 remaining.
From 9 wicket-keepers, 9 each can be selected with 0 remaining.
Now since perfect sets of 6 players have to be selected, (2 batsmen, 3 bowlers and 1 wicket-keeper), the maximum number of sets chosen from each category is 7.
So 7 sets of 2 batsmen out of the 23 batsmen leaves 23- (2*7) = 9 batsmen
and 7 sets of 1 wicket keeper each leaves 9-7 = 2 wicket-keepers
Therefore 9+2=11 players will not be on a team.
ANSWER - C
