For an employee to qualify for early retirement at a certain company, the sum of the employee's age and years of service must be at least 70. If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement?

Rationale

(70 + K)/2

To qualify for early retirement, the sum of Sue's age and her years of service must be at least 70. If she was K years old when hired, her years of service would be her current age minus K, leading to the equation K + (Current Age - K) ≥ 70, which simplifies to the minimum age being (70 + K)/2.

A (K + 35) YOUR ANSWER

This choice suggests that Sue can qualify for early retirement simply by being K + 35 years old. However, this does not account for her years of service correctly, as it does not ensure that the sum of her age and years of service meets the required total of 70.

B (2K + 35) YOUR ANSWER

This option incorrectly assumes that Sue's age should be significantly higher than necessary. It implies a linear relationship that does not reflect the requirement that her age plus years of service must equal or exceed 70, resulting in an inflated minimum age.

C ((70 + K)/2) CORRECT

This choice correctly represents the minimum age at which Sue could qualify for early retirement. It accounts for both her age K and her years of service, ensuring that the sum meets the required threshold of 70, thereby accurately determining her eligibility.

D ((70 - K)/2) YOUR ANSWER

This response suggests a minimum age that is half of the difference between 70 and K. This formula does not satisfy the condition for early retirement, as it fails to ensure that the combined age and years of service reach the necessary sum of 70.

E (2(70 - K)) YOUR ANSWER

This choice implies that Sue would need to be twice the difference between 70 and her initial age K, leading to an excessively high and incorrect minimum age that does not appropriately satisfy the retirement qualification criteria.

Conclusion

To determine Sue's minimum age for early retirement, it is essential to equate her age and years of service to a total of at least 70. The correct expression, (70 + K)/2, fulfills this requirement by balancing her starting age K with the necessary service years. Other options either misrepresent the relationship or lead to incorrect minimum age calculations.

For an employee to qualify for early retirement at a certain company, the sum of the employee's age and years of service must be at least 70. If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement?

(70 + K)/2

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