Chapter4, Number Properties: Problem 17

[guy29]

I was hoping someone could explain this to me:

On p81, consecutive integers are described as multiples of 1, which I believe implies that 0 cannot be a part of that sort of set. This is further pushed in as a point, when on p85 it is said that there is no such set of consecutive integers without a multiple of 2 and 3; making a set like {0,1,2} impossible. Yet for problem no 17,

is the average of n consecutive integers equal to 1?

1 n is even
2 If S is the sum of the n consecutive integers, then 0<S<n

the footnote after the explanation states: This situation, i.e. 0<S<n, can happen ONLY when there is an even number of integers, and when the "middle numbers" in the set are 0 and 1. For example, the set of consecutive integers {0,1} has a median number of 0.5. Similarly, the set of consecutive integers {-3,-2,-1,0,1,2,3,4} has a median number of 0.5.

I don't understand, id the footnote is correct, not all consecutive integers are multiples of 1, and not all consecutive integer sets contain multiples of 2 & 3. What's the proper version?

[guy29]

Emily answered the question for me: the question is correct.

[esledge]

I'll just post the link to our other discussion for the benefit of anyone who later searches this thread.

http://www.manhattangmat.com/forums/mis ... t5850.html