Question
Here’s the question from Monday:
The sum of m consecutive integers is 8. If the sum of n consecutive integers is m, what is the value of n?
(A) 15
(B) 16
(C) 31
(D) 32
(E) Cannot be determined by the information provided.
Answer and Explanation
The trick here is taking into account negative numbers. Anytime you sum negative integers and end with a positive integer that is equal to the absolute value of the lowest number, you get zero. For instance, if I add -2 + -1 + 0 + 1 + 2, I get zero. Using this logic, I can figure out that a bunch of consecutive numbers that sum to 8 must start at -7, since all the numbers up to, and including, 7 will cancel out to zero, leaving 8 (meaning the series sums to 8).
Counting all the integers from -7 to 8, inclusive, can be a little bit tricky, because we will have to include zero. Doing so, gives us 16, the value of m. So now, which consecutive integers sum to 16? Using the same logic, we can see that the series would have to start at -15 so that all the digits are canceled out, leaving us with 16. That gives us a total of 32 digits (don’t forget the zero!). Answer: (D)
