Yesterday, Integrated Learning posted a 700 level GMAT question on our blog. Today, they have followed up with the answer:
This set of consecutive numbers begins with -16, and then increases, like this: -16, -15, -14, …
Note that if the highest number in the set were negative, the sum of the numbers would be a negative number. Since the sum is positive, we must be crossing zero into positive numbers.
Once you do, the positive numbers will start canceling the negative numbers. 1 cancels -1, 2 cancels -2, etc. As the sequence increases to 16, the sum gets closer and closer to zero. Finally, at 16, the sum of the whole thing is zero.
But we are told that the sum is 35. The next term is 17, and the next is 18. At this point, the sum is 35. So the sequence looks like: 16, -15, -14, … 16, 17, 18.
So how many terms are there? The number of terms in a consecutive number sequence is found by doing:
Highest – lowest + 1
So in this case, we get: 18 – (-16) + 1 = 35.
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