In a coded arithmetic system, letters stand for operations as follows: A denotes division (/), B denotes multiplication (x), C denotes addition (+) and D denotes subtraction (-). Which one of the following coded statements is mathematically true when decoded?

Introduction / Context:
This question mixes coding of operators with verification of equations. Each letter stands for a basic arithmetic operation, and we are given several candidate equations written in this coded form. Our task is to decode each equation into normal arithmetic, evaluate the left hand side and see which equation is actually true. This combines understanding of operator mapping with ordinary numerical calculation and the use of precedence rules.

Given Data / Assumptions:

• A denotes division (/).
• B denotes multiplication (x).
• C denotes addition (+).
• D denotes subtraction (-).
• We have four main candidates:
• 1) 11B34A17D8A3 = 38/3
• 2) 6B18D26A13C7 = 173/13
• 3) 32C8A16D4 = -3/4
• 4) 9C9A9D9B9 = -71
• We must find which equality holds true after decoding and correct evaluation.

Concept / Approach:
The method is straightforward but requires care. For each option, we replace A, B, C and D with /, ×, + and - respectively and write the resulting arithmetic expression. Then we evaluate the left hand side using standard precedence rules, and compare it with the right hand side value. The option where both sides match exactly is the correct answer. It is often efficient to start with the simplest looking expression to check for correctness quickly.

Step-by-Step Solution:
Step 1: Decode option D, which is shorter: 9C9A9D9B9 = -71. Step 2: Substitute operators: C → +, A → /, D → -, B → ×. Step 3: The left side becomes 9 + 9 / 9 - 9 × 9. Step 4: Apply precedence. First 9 / 9 = 1 and 9 × 9 = 81. Step 5: Substitute these results: 9 + 1 - 81. Step 6: Now evaluate from left to right: 9 + 1 = 10. Step 7: Then 10 - 81 = -71, which matches the right hand side exactly. Step 8: Therefore, option D is a true equation after decoding. Step 9: Briefly check that other options fail. For example, option A decodes to 11 × 34 / 17 - 8 / 3 which simplifies to 22 - 8/3 = 58/3, not 38/3. Step 10: Option B decodes to 6 × 18 - 26 / 13 + 7, which equals 108 - 2 + 7 = 113, not 173/13. Step 11: Option C decodes to 32 + 8 / 16 - 4, which equals 32.5 - 4 = 28.5, not -3/4.

Verification / Alternative check:
Recomputing the arithmetic for option D confirms that 9 / 9 is 1 and 9 × 9 is 81, and that 9 + 1 - 81 is indeed -71. The right hand side of the equation is -71, so the equality holds exactly. Because all other options give left hand sides that do not match their right hand side values, option D is uniquely correct. There is no alternative interpretation of the operator mapping that would change this conclusion.

Why Other Options Are Wrong:
In option A, the difference between 22 and 8/3 is 58/3, which does not equal 38/3. In option B, the left side equals 113, while the right side is a fraction around 13.3. Option C's left side is 28.5, not -0.75. Option E is an extra distractor that would decode to a different false equation. Since these values do not match their claimed right hand sides, they cannot be correct in this coded system.

Common Pitfalls:
A common error is to misremember the mapping of letters to operations, for instance swapping A and B or confusing C with D. Another is to ignore operator precedence and evaluate from left to right, which will change the result. To avoid this, it is helpful to rewrite each coded expression slowly with the proper symbols and type it mentally as an ordinary arithmetic expression before evaluating it step by step.

Final Answer:
The only coded equation that is true after decoding and evaluation is 9C9A9D9B9 = -71.