If the symbols A, B, C and D are code replacements for arithmetic operations such that A means "+", B means "−", C means "×" and D means "÷", then which of the following coded equations is mathematically true after decoding the symbols?

Introduction / Context:
This problem tests the ability to decode symbolic representations of arithmetic operations and then check which full equation is valid. It combines knowledge of basic arithmetic with logical checking of each option and is a staple pattern in verbal reasoning and aptitude tests.

Given Data / Assumptions:

• A represents addition, that is A means plus.
• B represents subtraction, that is B means minus.
• C represents multiplication, that is C means times.
• D represents division, that is D means divided by.
• We must decode each option and test whether the resulting numerical equation is correct.
• Standard operator precedence for multiplication and division over addition and subtraction applies.

Concept / Approach:
The method is straightforward. For each option, replace the coded letters A, B, C and D with their actual arithmetic operators. Then, evaluate the left side using proper precedence rules and see whether it equals the right side of the equation. Only one of the given options will satisfy the equality, and that will be the correct answer.

Step-by-Step Solution:
Step 1: Decode option A: 12 D 6 A 4 C 3 = 12 becomes 12 ÷ 6 + 4 × 3 = 12. Step 2: Evaluate option A: 12 ÷ 6 = 2 and 4 × 3 = 12, so left side is 2 + 12 = 14, which is not equal to 12. So option A is false. Step 3: Decode option B: 48 D 3 C 2 = 31 becomes 48 ÷ 3 × 2 = 31. Step 4: Evaluate option B: 48 ÷ 3 = 16 and 16 × 2 = 32, not 31. So option B is false. Step 5: Decode option C: 14 C 2 D 7 A 3 = 6 becomes 14 × 2 ÷ 7 + 3 = 6. Step 6: Evaluate option C: 14 × 2 = 28, 28 ÷ 7 = 4 and 4 + 3 = 7, not 6. So option C is also false. Step 7: Decode option D: 24 C 3 B 14 = 58 becomes 24 × 3 − 14 = 58. Step 8: Evaluate option D: 24 × 3 = 72 and 72 − 14 = 58, which matches the right side. So option D is the only correct equation.

Verification / Alternative check:
To quickly verify, we note that in option D the multiplication yields 72 and the subsequent subtraction by 14 gives 58. None of the other options can be adjusted or rearranged to match their claimed results without breaking operator precedence or altering the expression. Therefore, option D alone satisfies the equation exactly as written and decoded.

Why Other Options Are Wrong:
Option A gives 14 instead of 12, option B produces 32 instead of 31 and option C yields 7 instead of 6. These mismatches result from straightforward arithmetic after decoding and cannot be corrected without changing the operators or order of operations, which is not allowed. Hence they are included purely as distractors for candidates who miscalculate under time pressure.

Common Pitfalls:
Candidates sometimes ignore operator precedence and compute from left to right, which can accidentally make a wrong equation appear correct. Another frequent mistake is misreading which letter stands for which operation. Carefully rewriting each expression with standard symbols before calculating helps avoid these errors. Double checking the multiplication and division steps is especially important since small mistakes there propagate to the final result.

Final Answer:
After decoding the operations and evaluating all options, the only true equation is 24 C 3 B 14 = 58.