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Every employee of the Zenith Corporation who receives the executive bonus has completed the advanced leadership training. Furthermore, no employee who has completed the advanced leadership training is eligible for the standard overtime rate. Some employees in the marketing department receive the executive bonus, and every employee in the marketing department was hired within the last five years.

Which of the following must be true based on the information provided?

  1. A
    Any employee of the Zenith Corporation who has completed the advanced leadership training receives the executive bonus.
  2. B
    No employee in the marketing department is eligible for the standard overtime rate.
  3. C
    If an employee was not hired within the last five years, that employee does not receive the executive bonus.
  4. At least some employees who were hired within the last five years are not eligible for the standard overtime rate.Cevap
  5. E
    At least some employees who were hired within the last five years are eligible for the standard overtime rate.

Cevap

At least some employees who were hired within the last five years are not eligible for the standard overtime rate.
The stimulus provides a chain of facts. First, we know that some marketing department employees receive the executive bonus. Second, anyone receiving the bonus has completed advanced leadership training, meaning these specific marketing employees have completed the training. Third, no one who has completed the training is eligible for the standard overtime rate, so these specific marketing employees are not eligible for standard overtime. Finally, because every marketing employee was hired within the last five years, these specific marketing employees who are ineligible for overtime were hired within the last five years. Thus, it is mathematically provable that at least some employees hired within the last five years are not eligible for standard overtime.

Adım Adım Çözüm

1
Identify the primary conditional chain regarding the executive bonus.
Executive Bonus (EB) → Advanced Leadership Training (ALT) → NOT eligible for Standard Overtime Rate (~SOR).
This establishes the absolute rules that apply to anyone receiving the executive bonus.
2
Analyze the quantifier statements regarding the marketing department.
Marketing Department (MD) has 'some' employees with EB. Also, MD → Hired within last 5 years (H5).
We must map how a specific subset of employees fits into the absolute rules.
3
Combine the 'some' statement with the conditional chain.
Since 'some' MD employees have EB, and all EB employees are ~SOR, it follows that 'some' MD employees are ~SOR.
What is true of all members of a group (EB) must be true of any specific subset (the MD employees who have EB).
4
Combine the resulting 'some' statement with the remaining 'all' condition.
The MD employees who are ~SOR are in the marketing department. Since all MD employees are H5, those specific ~SOR employees are also H5. Therefore, some H5 employees are ~SOR.
This yields the final, 100% provable deduction connecting the hiring timeline to overtime eligibility.

Anahtar Kavram

Formal logic deductions combining universal conditionals (all/none) with existential quantifiers (some).
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