If X is the sum of first 100 positive even integers and Y is the sum of first 100 positive odd integers, what is the value of x-y?
Please try to explain your answers  Choose the most appropriate option.
A) 0 B) 25 C) 50 D) 75 E) 100

Rationale: first even minus first odd = 2 - 1 = 1 ; the sum of first 2 even integers minus the sum of first 2 odd integers = ( 2 + 4 ) - ( 1 + 3 ) = 2 ; the sum of first 3 even integers minus the sum of first 3 odd integers = ( 2 + 4 + 6 ) - ( 1 + 3 + 5 ) = 3 ; we can see the patterns here , so the sum of first 100 positive even integers minus the sum of first 100 positive odd integers will be 100 . answer : e .
Answer: E