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are you sure the question and answer choices are written correctly?
The answer would be B if the question was "what is the sum of the integers between 101 and 150"
i dont see how it could possibly be B, when the ssum of the first 50 is 2550 already.
here is the method i use:
since we know that sum of 1-50 is 2550, we can find the sum of 102 to 151 (which is 50 numbers as well), by noticing that every respective number in these two sets differs by 101. (ie 102-1 = 101, 103-2 = 101, 104-3 = 101, etc)
so if we take 101x50 = 5050, and then add this to the sum of 1-50, 2550, we get 7600 as the sum of the integers from 102 to 151. You can repeat this process to get the sum of 152-200, but we're already beyond the OA of 7550 and im thoroughly confused because the final answer i'm getting is like 17,499.
I apologize. I copied the question from the test incorrectly, again. I fixed it in the first message, but here it is again just for clarification.
The questions asks:
The sum of the first positive even integers is 2550. What is the sum of the even integers from 102 to 200, inclusive.
Sorry for the confusion. I know the OA is still B because I did a quick spreadsheet total, and 7550 is correct. Unfortunately, we do not have Excel at Pearson Vue, so how do I solve this during the actual test?
The question needs a little more clarification, djhouse.
I think the question is saying that the sum of the first 100 even integers is 2550. This makes the problem a lot easier than before =P
we know that there are 50 even integers from 2 to 100, and we can see that there are 50 even integers from 102 to 200. Each of the numbers in the latter set is 100 greater than the previous, so we can find the sum of the even intgers from 102 to 200 by multiplying the difference by the number of values, (100 x 50), then add on the sum of the integers from 2 to 100.
I would have loved it if they clarified it for me. However, the question was written as I have written it: the sum of the first 50 even integers...
Classic case of the GMAT not necessarily testing your quantitative abilities, but more so your ability to spot the little tricks they put in there to throw you off.
However, thanks to everyone for providing the solutions. The formulas are good ones to remember.
without knowing the formulas.
the question gives you a clue. It says "The sum of the first 50 positive even integers is 2,550."
So
2+4+6+8....100 = 2550
you are trying to find
102+104+106+108....200
notice the terms here can be rewritten as (100+2)+(100+4)+(100+6)+(100+8)...(100+100)
which can be simplified to 100*50+(2+4+6+8...100)