set of n numbers

[Makumajon]

1) if the n numbers in the set are listed in the increasing order, then the difference between any pair of successive numbers in the set is 2.

We know in case of any arithmetic series, the difference between successive terms is always constant. For example 3, 7, 11, ... is an arithmetic series, with common difference 4. Similarly, 1, 3, 5, ... is another arithmetic series, with common difference 2.

Now as long as you know that a series is arithmetic, you can draw a few important conclusions:
(i) Mean = median
(ii) Average=sum of all terms/no. of terms OR (smallest no. + largest no.)/2
So, here (1) is sufficient.

(2) Range=2(n-1). So, largest no. - smallest no. = 2(n-1). But we do not about the other numbers. For example,

if the smallest number is 3 and no. of terms is 4, then the largest number is 3+ 2*(4-1)=9.
So, the series may be 3, 3, 3, 9 or 3, 5, 7, 9 etc. Insufficient.

[bose]

imo A.

[borntorun]

IMO A

makumajon: well explained

[TaTum]

Thanks Makumajon for your excellent explanation.