Question 6

(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 Sue was K years old when hired, the minimum age for qualifying can be expressed mathematically as (70 + K)/2.

A) K + 35

This option suggests that Sue can retire at age K + 35. However, this does not account for the years of service required to meet the total of 70, making this option insufficient for qualifying for early retirement.

B) 2K + 35

This choice implies that Sue would need to be 2K + 35 years old to qualify. This answer overshoots the requirement by more than necessary, as the formula does not align with the condition of the sum being 70, making it incorrect.

C) (70 + K)/2

This is the correct answer because it accurately calculates the minimum age at which Sue can qualify for early retirement by considering both her age and years of service. This formula correctly ensures that the sum of her age and years of service equals 70, confirming her eligibility.

D) (70 - K)/2

This option suggests that Sue could retire at (70 - K)/2, which does not satisfy the requirement of the sum being at least 70. Instead, it implies a nonsensical age that does not reflect the years of service needed, thus making it incorrect.

E) 2(70 - K)

This choice indicates that Sue could retire at 2(70 - K), which would also yield an inappropriate age for retirement. This calculation fails to meet the condition of combining age with years of service to total 70, rendering it incorrect.

Conclusion

The answer (70 + K)/2 is the only option that correctly incorporates both Sue's age and her years of service to fulfill the retirement qualification criteria. All other options either miscalculate the age needed or fail to account for the necessary combination of age and service years, thus disqualifying them.