good one

vaivish wrote:If the sum of even numbers from 1 to 500, inclusive, is 125,500, what is the sum of odd numbers from 1 to 500, inclusive?
(A) 125,000
(B) 125,125
(C) 125,250
(D) 125,375
(E) 125,500

The even numbers are 2, 4, 6, 8, 10, ... 500
The odd numbers are 1, 3, 5, 7, 9, ... 499

If we compare the lists, we see that every odd number corresponds to an even number on the list - 1 (e.g. 1 = 2-1... 3=4-1... 5=6-1).

Since there are 250 even numbers and 250 odd numbers, the sum of the odd numbers will be 250(1) less than the sum of the even numbers.

So: 125500-250 = 125250.. choose (C).

Sum of all even numbers
2+4+6+8+...+498+500
Sum of all odd numbers
1+3+5+7+...+497+499

Since there are 250 pairs of odd/even numbers from 1 to 500, for each pair, the odd number is the even number minus 1, so for 250 pairs, you'd minus 250 from 125,500, which gets C.

The question must be finding the pattern, because if you do the actual math
(1+499) + (3+497) + (5+495) + ... + (249+251) = 500 x 125 = 62500
(2+500) + (4+498) + (6+496) + ... + (250+252) = 502 x 125 = 62750