Materials that are heavier can replace materials that are lighter than them in…

A data-sufficiency question only asks whether the statements together fix ONE unique value for the quantity asked, not to solve the puzzle exhaustively. Here, "X can replace Y" means the weight of X is strictly greater than the weight of Y; "X cannot replace Y" only means the weight of X is not greater than the weight of Y (X's weight could still equal Y's), and says nothing about how X compares with a third item.

1. Statement I: P can replace neither Q nor R means P is not heavier than Q and not heavier than R (P is at most equal to each of them). This already rules P out as the outright heaviest, but on its own it says nothing about how Q and R compare with each other -- either could be the heavier of the two.

2. Statement II: R can replace P establishes the strict relation that R is heavier than P. This sharpens the P-versus-R comparison beyond what Statement I alone gives, but it still adds nothing about how Q compares with R.

3. Combined: together, the statements only fix that P is not heavier than Q and is strictly lighter than R. Neither statement, alone or combined, ever compares Q and R with each other directly.

• Weight order Q > R > P satisfies both statements (P replaces neither Q nor R; R replaces P).

• Weight order R > Q > P also satisfies both statements equally well.

• Since both orders fit the given data but disagree on whether Q or R is heavier, the heaviest item cannot be pinned down -- confirming the two statements, even combined, are not sufficient.

Therefore, the correct conclusion is that both statements, put together, are still not sufficient to determine which of P, Q, R is the heaviest.