Official Solution:In a certain company, employees receive their salaries monthly and are paid on either the 10th or 20th of each month. If 60% of all managers are paid on the 10th and 80% of employees paid on the 20th are not managers, what percentage of the company's employees are managers? A. 5%
B. 10%
C. 15%
D. 30%
E. Cannot be determined from the information given.
Let's assume there are a total of 100 employees. If we let \(x\) represent the number of employees who are managers (our target value to determine) and \(y\) represent the number of employees paid on the 20th, we can construct the following table based on the given information:
Observer that, from the table, we deduced that \(0.4x = 0.2y\), which simplifies to \(2x = y\). This establishes the ratio of employees who are managers, denoted by \(x\), to those paid on the 20th, represented by \(y\). However, this does not yield the precise value of \(x\). Let's illustrate this with two different cases:
Here, 10 employees are managers. Of these, 6 (or 60%) are paid on the 10th, and the remaining 4 are paid on the 20th. Among the 2*10 = 20 employees receiving their salaries on the 20th, 16 (or 80%) are not managers.
Here, 30 employees are managers. Of these, 18 (or 60%) are paid on the 10th, and the remaining 12 are paid on the 20th. Among the 2*30 = 60 employees receiving their salaries on the 20th, 48 (or 80%) are not managers.
As demonstrated, the exact value of \(x\) cannot be determined from the provided information.
Answer: E
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