Practice GMAT Problem Solving Question

If the sum of the consecutive integers from –35 to n inclusive is 150, what is the value of n?

Correct Answer: B

Consecutive integers are integers that follow in sequence, where the difference between two successive integers is 1. You are told that the sum of the consecutive integers from –35 to n inclusive is 150. The sum of all the consecutive numbers from –35 to –1 will be negative, yet the sum of the entire set is positive. This means that there must be positive integers in the set that go beyond +35 to result in a positive sum.
Consider that a number plus its opposite sum to zero:
–5 + 5 = 0, –13 + 13 = 0, etc.
Therefore:
(–35) + (–34) + … + (–1) + 0 + 1 + … + 34 + 35 = 0
The next consecutive number in the set would be 36. Could this be n? If it were the sum of the set would be 0 + 36 = 36. So there must be more integers in the set. Move forward one number at a time, until the sum is 150:
0 + 36 = 36
36 + 37 = 73
73 + 38 = 111
111 + 39 = 150
Since the addition of 39 makes the sum 150, it must be the last consecutive integer in the set and the value of n. Therefore choice (B) is correct.