Explanation

To compute a sum of consecutive integers, we can use the average formula. You may know a formula for the sum of consecutive integers; it's actually derived from the average formula. From the average formula, we have



In this case, we are summing numbers from . The number of items in this list is , the difference of the first and the last, plus 1. The average will be the middle number. We have numbers below this number and 182 numbers above this number, so it's the 183rd number and is equal to 183. On other side of 183, there is a pair of equally spaced numbers that cancel the offset from 183, indicating that itsss is in fact the mean of all the numbers, not just the median. Therefore,



This is a little on the unfriendlier side of what we'd be expected to calculate on the GMAT. We can multiply these directly, or break one into factors and do successive smaller multiplications. Actually, on that note, we can see that this product must be divisible by 3, from the first term, and 5, from the second term. Comparing that with the answer choices: (C) is out, because it is not divisible by 5. Then, (A) is out because 6 + 6 + 4 + 3 + 0 = 19, which is not divisible by 3. And (D) is out, because 6 + 7 + 1 + 6 + 0 = 20, which is not divisible by 3. In (E), 1 + 3 + 2 + 8 + 6 + 0 = 20, which is not divisible by 3. So we can actually rule out all the other answer choices based on divisibility rules. If we compute directly, we'll find that the product is indeed 66,795.

The correct answer is (B).