Sum of the first n natural numbers is n(n+1)/2.
So sum of the first 600 numbers is 600x601/2 = 300x601=180300
Next even numbers from 460 to 600
Totally there will be 141 numbers from 460 to 600
Out of these 141 numbers, 71 will even and 70 will be odd.
I mean to say that from 460 to 600 there will be 71 even numbers.
So the sum of the above series (which is in ARITHMETIC PROGRESSION) will be N/2(FIRST TERM + LAST TERM), where N = number of terms in the series.
So 71/2(460+600) = 71x530 = 37630.
Hence the answer will be 180300-37630=142,670
Averages Accelerated:Guide to solve Averages Quickly(with 10 practice problems)