In a certain coded arithmetic system, "x" stands for minus, "+" stands for multiplication, "÷" stands for plus, and "-" stands for division. Using this coding, what is the correct value of the expression 175 - 25 ÷ 5 + 2 x 3 + 10?

Introduction / Context:
This question checks your understanding of coded arithmetic operations, where familiar symbols are reassigned new meanings. Instead of directly using plus, minus, multiplication, and division, the expression uses a coded mapping that you must decode correctly before performing any calculation. Such problems are common in coding decoding and quantitative aptitude sections because they combine symbol interpretation with arithmetic skills.

Given Data / Assumptions:
- "x" stands for minus (subtraction).
- "+" stands for multiplication.
- "÷" stands for plus (addition).
- "-" stands for division.
- The expression to evaluate is 175 - 25 ÷ 5 + 2 x 3 + 10, interpreted using the coded meanings.
- Normal arithmetic precedence applies after decoding: division and multiplication before addition and subtraction.

Concept / Approach:
The key approach is two step. First, rewrite the given expression by replacing each coded operator with its real arithmetic meaning. Second, once the decoded expression is obtained, evaluate it carefully using operator precedence. It is important not to mix up the original printed symbol and its actual mathematical role after decoding.

Step-by-Step Solution:
Step 1: Start with the given coded expression: 175 - 25 ÷ 5 + 2 x 3 + 10. Step 2: Replace "-" with division, "÷" with plus, "+" with multiplication, and "x" with minus. Step 3: After substitution, the expression becomes: 175 ÷ 25 + 5 * 2 - 3 * 10. Step 4: Apply operator precedence. First compute 175 ÷ 25 = 7. Step 5: Next compute 5 * 2 = 10 and 3 * 10 = 30. Step 6: Now handle addition and subtraction from left to right: 7 + 10 - 30 = 17 - 30 = -13.

Verification / Alternative check:
We can verify the decoding by rechecking each mapping carefully. Every symbol in the original expression has been replaced according to the statement of the question. Recomputing 175 ÷ 25, 5 * 2, and 3 * 10 clearly gives 7, 10, and 30. Combining them as 7 + 10 - 30 gives -13 consistently. No alternative decoding matches the given mappings, so the result is stable.

Why Other Options Are Wrong:
- Option 13 ignores the minus sign at the end and treats the result as positive, which is a sign error after 17 - 30.
- Option -3 might come from partial calculation such as 7 + 10 - 20, but that does not follow the given expression correctly.
- Option 3 is also a result of an incorrect order of operations or wrong decoding of one of the symbols. None of these alternatives respect both the mapping and proper precedence.

Common Pitfalls:
The most common errors include decoding only some of the symbols, using the printed symbol instead of the described meaning, or forgetting to apply standard operator precedence. Some learners also evaluate strictly from left to right without handling multiplication and division first, which leads to wrong answers. Always decode fully first and then compute carefully.

Final Answer:
After decoding the operators and evaluating with correct precedence, the value of 175 - 25 ÷ 5 + 2 x 3 + 10 in the coded system is -13.