When a GMAT Quant question asks you to deal with a big group of numbers, there's almost always a built-in pattern that can help you to avoid a lengthy "math approach."
Here, we're given two groups:
Group A = the sum of all the EVEN integers from 2 to 200, inclusive
Group B = the sum of all the ODD integers from 1 to 199, inclusive
We're asked for the value of A - B
Calculating any of these individual totals would take some work, but notice how the two groups follow a pattern:
(The first term in A) - (The first term in B) = 2 - 1 = 1
(The second term in A) - (The second term in B) = 4 - 3 = 1
This pattern will continue as you compare each successive term in each group
Since we're dealing with just the even numbers in Group A, 200/2 = 100 total terms.
This means that we'll have 100 differences of "1"
The Total difference will be 100(1) = 100
GMAT assassins aren't born, they're made,