Interesting GMATFix Problem-7

[arora007]

If a,b,c,d and e are consecutive integers, which of the following must be true?
I. The mean of a and b is smaller than the mean of d and e
II. (a+b+c+d+e)/5n is and integer if n is an integer
III.The product of the mean and the median of the five integers is a positive integer.
A) None
B)I only
C)I and II
D)I and III
E)I,II and III

[goyalsau]

B) I only.

[arora007]

OA is A, None

cannot assume consecutive increasing or consecutive decreasing

[goyalsau]

OA is A, None

cannot assume consecutive increasing or consecutive decreasing

can you explain it with some example.

[diebeatsthegmat]

If a,b,c,d and e are consecutive integers, which of the following must be true?
I. The mean of a and b is smaller than the mean of d and e
II. (a+b+c+d+e)/5n is and integer if n is an integer
III.The product of the mean and the median of the five integers is a positive integer.
A) None
B)I only
C)I and II
D)I and III
E)I,II and III

i think only III is right
I is not right because we dont know if those numbers are e d c b a or abcde, i meant its orders are not very clear to conclude anything
II is also not right because they are consecutive interger thus they can be a, a+1, a+2, a+3 a+4 and added em together we will get 5a+10=5(a+2)/5n=a+2/n , if a is 1 and n = 3 sure, correct but what if n = 4, because we dont know n thus nothing can say about this
III is surely right i think becuase median is possitive integer for sure, and mean=(5a+10)/5 is an integer for sure if a, b, c, d, e are positive integer but we dunno if a b c d e are all positive or some negative
nothing can be sure much
thus A is correct