When all the numbers of a sequence or set are multiplied by a number, then the mean also gets multiplied by the same number.
If the mean remains same, then this can only happen if the mean = 0. Statement I is true.
Statement 2 is not necessarily true as the sequence (-8, 1, 7) has mean = 0, yet the largest and smallest elements are not additive inverses.
Statement 3 is also not necessarily because the set may contain all zeros. Sequences can contain repeats, and nothing in the stem indicates that all numbers in the sequence must be unique.
The correct answer is A.