The number of years the employee has been employed by the city is at least 25 years. The sum of the employee's age and number of years employed by the city is at least 90 years. Larry has been employed by the city since his 38th birthday. Assuming he continues to work for the city, at what age will he first qualify for full retirement benefits?

Rationale

Larry will first qualify for full retirement benefits at age 64.

To determine when Larry qualifies for full retirement benefits, we analyze the conditions given: he must be at least 25 years employed and the sum of his age and years of employment must be at least 90 years. Given he started working at age 38, he reaches the required age for retirement at 64.

A (52) YOUR ANSWER

At age 52, Larry would have only been employed for 14 years (from age 38 to 52). This does not meet the requirement of at least 25 years of employment, making this choice invalid for retirement qualification.

B (55) YOUR ANSWER

At age 55, Larry would have worked for 17 years. Adding this to his age results in a total of 72 years (55 + 17), which also fails to satisfy the requirement of 90 years when combined with years of service. Therefore, this option does not meet the retirement criteria.

C (62) YOUR ANSWER

Reaching age 62 means Larry has been employed for 24 years, which is just shy of the 25-year requirement. Additionally, his combined age and employment (62 + 24 = 86) also does not meet the minimum of 90 years, disqualifying this choice.

D (63) YOUR ANSWER

At age 63, Larry would have 25 years of employment (63 - 38 = 25). While this meets the employment requirement, the total (63 + 25 = 88) is still below 90, making this option also invalid for retirement qualification.

E (64) CORRECT

When Larry turns 64, he will have worked for 26 years (64 - 38 = 26). Adding his age to his years of service totals 90 (64 + 26 = 90), fulfilling both conditions for full retirement benefits.

Conclusion

Larry will first qualify for full retirement benefits at age 64, when he meets both the employment duration of at least 25 years and the age plus years of service requirement of at least 90 years. All other options fall short of either the employment requirement or the total age threshold, confirming 64 as the correct age for retirement eligibility.