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05 Apr 2024, 23:39
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Least value of X: 5
Greatest value of X: 10
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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50%
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A certain company has the following policy regarding membership in committees A, B, C: each of the committees have exactly 40 members, and each employee must be a member of at least one of the committees. The company currently has 110 employees.
Let X be the current number of employees who are members of more than one of the committees. Based on the current total number of employees, select the least value of X that is compatible with the policy and select the greatest value of X that is compatible with the policy.
Let X be the current number of employees who are members of more than one of the committees. Based on the current total number of employees, select the least value of X that is compatible with the policy and select the greatest value of X that is compatible with the policy.
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Official Answer
Least value of X: 5
Greatest value of X: 10
06 Apr 2024, 00:53
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unicornilove
Let X be the number of employees that joined all two committees. Let Y be the number of employees that joined three committees.
Recall the formula for number of unique elements:
(Total # in A) + (Total # in B) + (Total # in C) - (# in groups of exactly 2) - 2*(# in groups of exactly 3) + (# in neither)
Applying this formula,
40+40+40-X-2(Y)+0=110
To solve for min and max,
(1) Assume X=0, 120-0-2(Y)=110
Y=5
(2) Assume Y=0, 120-X-2(0)=110
X=10
Therefore, Min is 5, Max is 10
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12 May 2024, 20:19
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unicornilove
Short and simple..
If each employee was part of exactly one company, then total employee would have been 40+40+40 or 120. But there are 110 employees, so these 10 extra, 120-110, must get adjusted in employees being part of more than one company.
Least value of X: This would happen when the extra are adjusted in the overlap area of all three companies, that is the individual is part of all three companies. So each individual would account for 3 employees, one each in A, B and C. Thereby, that employ is accounting for two more employees.
If 2 employees are catered for by one employee, then 10 employees will get catered by 10/2 or 5 employees.
Maximum value of X: This would happen when the extra are adjusted in the overlap area of exactly two companies, that is the individual is part of only two companies. So each individual would account for 2 employees, one each in A and B or A and C or B and C. Thereby, that employ is accounting for one more employee.
If 1 employee is catered for by one employee, then 10 employees will get catered by 10/1 or 10 employees.
