Directions: These questions are based on the following information: $CBA + CCA = ACD$, where $A$, $B$, $C$ and $D$ stand for distinct digits and $D = 0$. $C$ takes the value

### Concept & Logic This cryptarithm puzzle builds on the values discovered in the previous columns. By resolving the units and tens columns, we generate the exact carry-over needed to solve for the final variable $C$ in the hundreds column. ### Step-by-Step Solution * **Given:** $C B A$ $+ C C A$ $-------$ $A C D$ With $D = 0$. * **Recall Previous Deductions:** * **Units Column:** $A + A = 10 \implies A = 5$ (Carry $1$ to Tens). * **Tens Column:** $1 \text{ (carry)} + B + C = 10 + C \implies 1 + B = 10 \implies B = 9$ (Carry $1$ to Hundreds). * **Hundreds Column:** Using the carry-over from the tens column, set up the final equation. $$1 \text{ (carry)} + C + C = A$$ Substitute the known value of $A = 5$: $$1 + 2C = 5$$ $$2C = 4$$ $$C = 2$$ * **Verification:** Let us test all values ($A=5, B=9, C=2, D=0$). $CBA = 295$ $CCA = 225$ $295 + 225 = 520$. $520$ matches the format $ACD$ perfectly. ### Exam Strategy & Shortcut **Linked Question Advantage:** In sets of questions based on a single "Directions" block, always reuse your discovered values. You already know $A = 5$ and that a carry of $1$ came from the tens column. The hundreds equation $2C + 1 = 5$ can be solved mentally in under two seconds. ### Common Pitfall Losing track of the carry-over from the tens column ($1 + 9 + C = 10 + C$). If you forget this carry of $1$, your hundreds equation becomes $C + C = 5$, which would mean $C = 2.5$. Since digits must be whole numbers, getting a decimal is an immediate red flag that you dropped a carry-over! ### Final Answer Therefore, the correct answer is **2**.