In a certain code language, the arithmetic symbols are replaced in the following way:\n\nThe plus sign (+) represents subtraction, the minus sign (–) represents addition, the multiplication sign (x) represents division and the division sign (÷) represents multiplication.\n\nWhich one of the following coded equations becomes numerically correct after decoding the symbols?

Introduction / Context:
This question tests your ability to decode a symbolic representation of arithmetic operations and then verify which complete equation is correct after applying the hidden rules. Such coded operator problems are common in verbal reasoning and help check conceptual clarity about basic operations and precedence.

Given Data / Assumptions:

• In the code language: + means subtraction, – means addition, x means division and ÷ means multiplication.
• We assume normal arithmetic precedence: division and multiplication before addition and subtraction.
• We must check each option by first decoding the symbols and then simplifying the left-hand side to see if it matches the right-hand side.

Concept / Approach:
The approach is to translate each coded expression into a normal arithmetic expression using the given mapping of symbols, then evaluate the left-hand side. If the evaluated result equals the right-hand side, that option is correct. Pay attention to the order of operations, because division and multiplication must be carried out before addition and subtraction to avoid incorrect results.

Step-by-Step Solution:
Step 1: Use the mapping + → minus, – → plus, x → division, ÷ → multiplication. Step 2: Decode option (d): 18 x 6 ÷ 8 – 12. Step 3: Replace x by division and ÷ by multiplication, and – by plus: 18 x 6 ÷ 8 – 12 becomes 18 ÷ 6 × 8 + 12. Step 4: Apply precedence: first 18 ÷ 6 = 3. Step 5: Then 3 × 8 = 24. Step 6: Finally 24 + 12 = 36, which matches the right-hand side 36.

Verification / Alternative check:
We can quickly re-calc option (d) to verify: 18 ÷ 6 = 3, 3 × 8 = 24 and 24 + 12 = 36. The equality holds, so option (d) is consistent with the given code. This confirms our decoding and evaluation are correct.

Why Other Options Are Wrong:
For option (a), decoding gives 16 ÷ 19 × 21 + 5, which does not equal 201 after calculation. Option (b) turns into 5 ÷ 6 - 4 × 3, which is a negative value, not 37/6. Option (c) becomes 6 ÷ 3 - 12 × 3, which is also not equal to 21. Therefore, only option (d) gives a correct equality.

Common Pitfalls:
A common mistake is to treat the coded symbol as if it still had its usual meaning, or to ignore operator precedence and simply calculate from left to right. Another frequent error is to misapply the mapping to only part of the expression instead of every occurrence of that symbol. Carefully substituting every coded symbol and respecting precedence avoids these issues.

Final Answer:
After proper decoding and evaluation, the only equation that becomes numerically correct is 18 x 6 ÷ 8 – 12 = 36, which corresponds to option (d).