Data Sufficiency

Statement (1) doesn't say that the range of the NUMBERS is 6, it says that the range of the REMAINDERS is 6.

So, even though we have 7 different numbers, we could have duplicate remainders.

Consider the set:

{7, 14, 21, 28, 35, 42, 48}

The biggest remainder is 6 (48/7 is 6rem6), the others all have rem0, so range=6.

The sum of the remainders is 0+0+0+0+0+0+6 = 6

Now consider the set:

{6, 13, 20, 27, 34, 41, 42}

The biggest remainder is 6 (each of the 1st 6 terms has rem6) and the smallest is 0, so the range=6.

However, the sum of the remainders is 0+6+6+6+6+6+6 = 36

We get two different answers to the question, therefore statement (1) is insufficient.