Manhattan GMAT chapter 11 q11

[ayush.sharma]

A machinist's salary increases by $2000 at the end of each full year the machinist works. If his salary for the fifth year is 39000. What is the machinist's average annual salary for his first 21 years at the factory?

I tried setting this up and got an answer that was not close.
Here is what I did :
Y= salary at the beginning of year 1.
x= Number of years = given as 21.
Fifth year salary = y + 4(2000)=39000
( used 4 above since the question says that the salary for the fifth year - rather than the salary at the end of year 5).
y= 31000

Avg amount of money earned in 21 years :
((31000)21 + 2000(21))/21 = 33,000 ( after the end of 21 years)

The answer given is 51000.
The answer is derived by using the properties of evenly spaced sets -- Have I misunderstood the question?

[LazyNK]

Hey Ayush,
Notice following mistake in your calculation :

Average Salary= Sum of 21 years salary/21
But Sum of 21 years salary is not equal to 31000*21+2000*21 as you have used.
Instead as you can see, the sum will be 31000*21 + 2000 (for the second year) + 2000*2 (for third year) + 2000*3 (for fourth year) + ...2000*20 ( for 21st year) = 31000*21 + 2000* (1+2+3+4+...20) = 31000*21 + 2000* (20*21/2)= 31000*21+2000*210
So Average= 31000+20000=51000
Hope it is clear.
NK

[ayush.sharma]

thanks man -- that really helped :)

[jnelson0612]

LazyNK strikes again! Thanks so much! :-)