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"Average of consecutive integers": If they're negative, shouldn't the list use x-1, x-2, etc?

Link

https://gre.magoosh.com/questions/354

 

Question

Because they're negative, shouldn't we use x, x-1, x-2, etc.? And then we would get (x - 4) - x = -4. What am I missing?

 

Answer

The problem is that (x - 4) is less than x. So you are taking the difference between the least and greatest. We actually need to flip those around; it should be x - (x - 4) which equals 4.

Let's say the integers are as follows: -6, -5, -4, -3, -2

If we let x = -6, then we would write the remaining integers as: x+1, x+2, x+3, x+4

Using that same list, if we let x = -2, then we would write the remaining integers as: x-1, x-2, x-3, x-4

Either one works, but the key is that we need to take the difference between the greatest and the least, so it would either be: (x+4) - x which equals 4 or it could be x - (x-4) which equals 4

 

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