Martin has worked for the last 30 years. If his average (arithmetic

­I think C.

Given - Martin has worked for the last 30 years. If his average (arithmetic mean) total annual earnings for the first 5 years is $15,000. 
To calculate his average total annual earnings for the last 5 years lets check conditions.

1st - Martin's average total annual earnings for the first 25 years is $27,000. From here we will only got data for first 25 years and from there will only able to calculate avg for later 20 years. Hence not sufficient.

2nd - Martin's average total annual earnings for the last 25 years is $34,000. Nothing to say here as well from this data we will only able to calculate data avg for all 30 years, but we cant say anything about last 5 years. Hence not sufficient.

Now combining both we can calculate the avg for last 5 years. How? 
Lets divide timeline of 30 years in 3 parts.
(First 5 years) --------- (Middle 20 years) --------- (Last 5 years)
from first statement we will able to calculate sum of middle 20 years = (25*27000) - (5*15000) = 675000 - 75000 = 600000 put this value in statement 2. sum for last 5 years = (25*34000) - 600000 = 850000 - 600000 = 250000 
average total annual earnings for the last 5 years = 250000 / 5 = 50000