def group_by_range(numbers: list[int], range_size: int) -> dict[str, list[int]]:
    groups = {}
    for num in numbers:
        lower_bound = (num // range_size) * range_size
        upper_bound = lower_bound + range_size

        key = f"{lower_bound}-{upper_bound}"
        if key not in groups:
            groups[key] = []

        groups[key].append(num)
    return groups