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Question
Of the 50 researchers in a work group, 40 percent will be assigned to Team A and the remaining 60 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer?
Of the 50 researchers in a work group, 40 percent will be assigned to Team A and the remaining 60 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer?
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Solution
The correct option is A 15
The number of researchers assigned to team A will be (0.40)(50)=20 and 30 will be assigned to Team B. the number of researchers who prefer Team A is (0.70)(50)=35 and the rest 15 prefer to Team B.If all 15 who prefer to Team B are assigned to Team B, which is to have 30 researchers, then 15 who prefer Team A will need to be assigned to Team B.Alternatively, since there are only 20 spots on Team A, 35−20=15 who prefer Team A but will have to go to Team B instead.Hence, option A is the correct answer.
The number of researchers assigned to team A will be (0.40)(50)=20 and 30 will be assigned to Team B.
the number of researchers who prefer Team A is (0.70)(50)=35 and the rest 15 prefer to Team B.
If all 15 who prefer to Team B are assigned to Team B, which is to have 30 researchers, then 15 who prefer Team A will need to be assigned to Team B.
Alternatively, since there are only 20 spots on Team A, 35−20=15 who prefer Team A but will have to go to Team B instead.
Hence, option A is the correct answer.
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