N, which is a set of natural numbers is partitioned into subsets S1 = {1}, S2 = {2,3}, S3 = {4,5,6}, S4 = {7,8,9,10} and so on. The sum of the elements of the subset S50 is Choose the correct choice from the following
A) (a) 61250
B) (b) 65525
C) (c) 42455
D) (d) 62525
E) (e) 55425
The question is based heavily on pattern-matching skills, and is far more 'layered' than what you would likely see on the Official GMAT on this subject. You'll likely find it easiest to define the patterns one-at-a-time, so that you can see how they impact the question.   To start, we're given information on the sub-sets of numbers:   -The 1st set has 1 number   -The 2nd set has 2 numbers   -The 3rd set has 3 numbers   Etc.   So the 50th set will have 50 numbers in it.   Since the numbers in the subsets are consecutive, we can figure out ALL of the numbers that show up BEFORE we get to the 50th set by usingbunching...   The 1st set has 1 number and the 49th set has 49 numbers....1 + 49 = 50 numbers   The 2nd set has 2 numbers and the 48th set has 48 numbers...2 + 48 = 50 numbers   Etc.   This pattern will continue all the way down to...   The 24th set has 24 numbers and the 26th set has 26 numbers...24 + 26 = 50 numbers   Thus, we have 24 'pairs' of 50 numbers and one set (the 25th set with 25 numbers) that doesn't have a 'pair-match'...   So 24(50) + 25 = 1225 consecutive numbers exist in the 49 sets BEFORE the 50th set - that's the numbers 1 to 1225, inclusive...   Thus, the 50th set starts with 1226 and ends with 1275. We can use 'bunching' again to figure out the sum of this group (although there's no 'middle term' this time)...   25(1226+1275) =   25(2501) =   62525   (d) 62525
<result>D</result>
N, which is a set of natural numbers is partitioned into subsets S1 = {1}, S2 = {2,3}, S3 = {4,5,6}, S4 = {7,8,9,10} and so on. The sum of the elements of the subset S50 is