Statement (1) If we know the total number of items bought, we can distribute them by dividing the number of objects (27) by the number of parts of the ratio (1 + 3 + 5 = 9).

There is no need to solve the question any further. This statement alone is sufficient.

Alternatively, let x be the number of potatoes bought by Bill. Then total items = x + 3x + 5x = 27, which is a single-variable equation that we could easily solve. This statement alone is sufficient. The correct answer is either A or D. Statement (2) If we know the quantity of one item purchased, we can find the values of the other items from the ratio. There is no need to solve the question. This statement alone is sufficient.

Alternatively, if Bill bought 9 onions and x is the number of potatoes, then 9 = 3x, i.e. x = 3. This statement alone is sufficient.

The correct choice is D.