$1234 + 2345 - 3456 + 4567 = x$

### Concept & Strategy This question tests basic addition and subtraction of large numbers. The strategy is to either group numbers with the same mathematical sign or use the unit digit methodology to quickly eliminate incorrect options. ### Step-by-Step Solution * **Given:** Find the value of $x$ in $1234 + 2345 - 3456 + 4567$. * **Step 1:** Group all the positive numbers together to make addition easier. $(1234 + 2345 + 4567) - 3456$ * **Step 2:** Calculate the sum of the positive terms. $1234 + 2345 = 3579$ $3579 + 4567 = 8146$ * **Step 3:** Subtract the negative term from the obtained sum. $8146 - 3456 = 4690$ ### Exam Strategy & Shortcut Use the **Unit Digit and Tens Digit Method** to save time. * Unit digit calculation: $4 + 5 - 6 + 7 = 10$. The unit digit is $0$, with a carry of $1$. * Tens digit calculation: $3 + 4 - 5 + 6 + 1 (\text{carry}) = 9$. The last two digits must be $90$. Looking at the options, only (a) and (d) end in $90$. A quick scan of the thousands places ($1+2-3+4 = 4$) confirms the answer should be in the 4000s, verifying $4690$. ### Common Pitfall A frequent mistake is performing the operations strictly sequentially without proper carrying/borrowing, especially when subtracting a larger component mid-sequence. Grouping positive terms first prevents negative intermediate steps. ### Final Answer Therefore, the correct answer is **4690**.