Inclusive Sums 1

If the sum of the consecutive integers from -22 to x, inclusive, is 72, what is the value of x?

A. 23

B. 25

C. 50

D. 75

E. 94

With problems like this it is important to realize, first of all, that since 22 is negative, all positive integers up until 22 will cancel out. All that remains then is to find the numbers after 22 which have a sum of 72. A number line will help illustrate this concept:

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-3, -2, -1, 0, 1, 2, 3

The sum of the negative numbers from -3 to -1 is -6. The sum of the positive numbers 1 to 3 is 6. -6 and 6 together are 0, so they cancel out.

Back at the original problem, you can cancel out all numbers up to positive 22. However, this doesn't help us, since all the options listed have higher values than 22.

However, you have another way of finding the solution. You can plug in the given answers. The number that is the answer, added with the number values that come before it but are after 22, will have a value of 72.

Is 23 the answer? No, since no numbers can be added to it, it alone has a value of 23 and not 72. Try the next one down, 25. The number values after 22, but before 25, are 23 and 24.

23+24+25=72!

B's the answer.