Here is my attempt.
Statement A: The range only tells us the spread between the highest and the lowest. It is possible to have different values for remainders and still have the same range.
i.e., remainders could be 0,6,6,6,6,6 or 0,6, a, b, c, d, e with a, b, c, d and e being any integer between 0 and 6.
Hence statement A is insufficient
Statement B: Seven consecutive numbers would definitely have one number that is a multiple of 7 and other numbers would contribute a remainder that is less than 7.
Numbers could be 7x, 7x+1, 7x+2, ...... 7x+6
Hence statement B is sufficient.
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