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Of the 50 researchers in a workgroup, 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?
- a)15
- b)17
- c)20
- d)25
- e)30
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Of the 50 researchers in a workgroup, 40 percent will be assigned to T...
To find the lowest possible number of researchers who will not be assigned to the team they prefer, we need to determine the allocation of researchers to Team A and Team B based on the given percentages.
Out of the 50 researchers, 40% will be assigned to Team A, which is (40/100) * 50 = 20 researchers.
The remaining 60% will be assigned to Team B, which is (60/100) * 50 = 30 researchers.
However, 70% of the researchers prefer Team A, which is (70/100) * 50 = 35 researchers.
And 30% of the researchers prefer Team B, which is (30/100) * 50 = 15 researchers.
To minimize the number of researchers who will not be assigned to their preferred team, we need to assign the researchers who prefer Team A to Team A and the researchers who prefer Team B to Team B.
Since there are only 20 researchers assigned to Team A, which is fewer than the number of researchers who prefer Team A (35), we will have 35 - 20 = 15 researchers who will not be assigned to their preferred team.
Therefore, the lowest possible number of researchers who will not be assigned to the team they prefer is 15.
The correct answer is A: 15.
Most Upvoted Answer
Of the 50 researchers in a workgroup, 40 percent will be assigned to T...
To find the lowest possible number of researchers who will not be assigned to the team they prefer, we need to determine the maximum number of researchers that can be assigned to the team they prefer.
Given:
Total number of researchers = 50
Percentage of researchers who prefer Team A = 70%
Percentage of researchers who prefer Team B = 30%
Percentage of researchers assigned to Team A = 40%
Percentage of researchers assigned to Team B = 60%
Finding the maximum number of researchers assigned to the preferred team:
Number of researchers who prefer Team A = 50 * 70% = 35
Number of researchers who prefer Team B = 50 * 30% = 15
Number of researchers assigned to Team A = 50 * 40% = 20
Number of researchers assigned to Team B = 50 * 60% = 30
Since the number of researchers who prefer Team A is 35, but only 20 researchers can be assigned to Team A, there will be 35 - 20 = 15 researchers who will not be assigned to the team they prefer.
Therefore, the lowest possible number of researchers who will not be assigned to the team they prefer is 15, which corresponds to option (a).
Given:
Total number of researchers = 50
Percentage of researchers who prefer Team A = 70%
Percentage of researchers who prefer Team B = 30%
Percentage of researchers assigned to Team A = 40%
Percentage of researchers assigned to Team B = 60%
Finding the maximum number of researchers assigned to the preferred team:
Number of researchers who prefer Team A = 50 * 70% = 35
Number of researchers who prefer Team B = 50 * 30% = 15
Number of researchers assigned to Team A = 50 * 40% = 20
Number of researchers assigned to Team B = 50 * 60% = 30
Since the number of researchers who prefer Team A is 35, but only 20 researchers can be assigned to Team A, there will be 35 - 20 = 15 researchers who will not be assigned to the team they prefer.
Therefore, the lowest possible number of researchers who will not be assigned to the team they prefer is 15, which corresponds to option (a).
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Community Answer
Of the 50 researchers in a workgroup, 40 percent will be assigned to T...
To find the lowest possible number of researchers who will not be assigned to the team they prefer, we need to determine the allocation of researchers to Team A and Team B based on the given percentages.
Out of the 50 researchers, 40% will be assigned to Team A, which is (40/100) * 50 = 20 researchers.
The remaining 60% will be assigned to Team B, which is (60/100) * 50 = 30 researchers.
However, 70% of the researchers prefer Team A, which is (70/100) * 50 = 35 researchers.
And 30% of the researchers prefer Team B, which is (30/100) * 50 = 15 researchers.
To minimize the number of researchers who will not be assigned to their preferred team, we need to assign the researchers who prefer Team A to Team A and the researchers who prefer Team B to Team B.
Since there are only 20 researchers assigned to Team A, which is fewer than the number of researchers who prefer Team A (35), we will have 35 - 20 = 15 researchers who will not be assigned to their preferred team.
Therefore, the lowest possible number of researchers who will not be assigned to the team they prefer is 15.
The correct answer is A: 15.
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