As I am helping my younger brother on his math papers (bought on external sources), I came across a question that seems unsolvable.
I feel that the question is not complete as they did not state the overlapped area of A and B. And the answer is supposed to be 5/9 from the answer sheet with no workings.
Question:
The ratio of the area of Rectangle A to the area of Rectangle B to the area of Rectangle C is 1:2:3. If one-third of Rectangle B is shaded, what total fraction of the whole figure is not shaded if all three rectangles overlap?
As you suggested in your notes, you can assume that the areas $A$, $B$ and $C$ are respectively $3$, $6$ and $9$. The text indicates that "one-third" of $B$ is shaded (I assume by $A$). Hence only $\frac 23 \times 6 = 4$ is the visible area of $B$. Since $B$ fully overlaps $C$, only $9-6 = 3$ is the visible area of $C$. Hence, the total unshaded area is $3 + 4 + 3 = 10$ and the total area is $3+6+9=18$. Hence, the unshaded ratio is indeed $\frac 5 9$ as claimed in the answers sheet.
Compared with your reasoning, I guess the key part is that although the text does not explicitly give the overlap area of $A$ and $B$, they DO say that one-third of $B$ is shaded, which is sufficient information to conclude.