number properties

[sud21]

What is the average of 59 consecutive integers?
1) The sum of the largest number and the least number is 1
2) The sum of all is 1

[Brent@GMATPrepNow]

What is the average of 59 consecutive integers?
1) The sum of the largest number and the least number is 1
2) The sum of all is 1

This is an invalid question.
Here's why.

Statement 1 says that the sum of the largest number and the least number is 1.
Okay, let's let x = the smallest number
Since these are consecutive integers, x+1 will equal the 2nd number
x+2 will equal the 3rd number
x+3 will equal the 4th number
. . . and x+58 will equal the 59th (a.k.a the largest number)

So, if the sum of the largest number and the least number is 1, then we can write: x + (x+58) = 1
When we simplify we get: 2x + 58 = 1
When we solve for x, we get: x = -28.5
Since this is not an integer (as stated in the question), statement 1 makes no sense.

Using similar logic, we can show that statement 2 makes no sense.

Cheers,
Brent