In a coded arithmetic notation, the following replacements are used:\n\nA denotes 'subtracted from', B denotes 'added to', C denotes 'divided by' and D denotes 'multiplied by'.\n\nUsing this code, which one of the following statements is numerically correct?

Introduction / Context:
Here the usual symbols +, -, × and ÷ are replaced by letter codes A, B, C and D. We must decode each option, translate it into an ordinary numerical expression and then check which equality holds. This tests both symbol-decoding skills and comfort with mixed operations.

Given Data / Assumptions:

• A means subtracted from (we treat it as ordinary minus in left to right form).
• B means added to (plus).
• C means divided by.
• D means multiplied by.
• We must test each of the four coded equations and identify the one that is numerically true.

Concept / Approach:
For each option we decode the letter symbols into their arithmetic counterparts and then evaluate the left-hand side step by step. We then compare the computed value with the number written on the right-hand side of the equality sign. The option where left and right match is the correct statement.

Step-by-Step Solution:
Step 1: Decode option (c): 13 C 13 A 13 B 13 D 13. Step 2: Replace C by ÷, A by -, B by + and D by ×. Step 3: This gives 13 ÷ 13 - 13 + 13 × 13. Step 4: Apply precedence: division and multiplication first. Step 5: Compute 13 ÷ 13 = 1. Step 6: Compute 13 × 13 = 169. Step 7: Substitute: 1 - 13 + 169. Step 8: Now perform addition and subtraction from left to right: 1 - 13 = -12, -12 + 169 = 157. Step 9: The left-hand side equals 157, which matches the right-hand side given in option (c).

Verification / Alternative check:
We can quickly test another option to see that it fails. For example, option (a) becomes 3 - 12 + 16 × 17 ÷ 1. This simplifies to 3 - 12 + 272, which is 263, not 163. Similar checks show that the other statements do not produce the claimed right-hand side values.

Why Other Options Are Wrong:
In option (a), the computed value is different from 163. In option (b), after decoding and calculating, the left-hand side is far from 294. In option (d), a correct decoding also leads to a number that is not 200. Therefore none of these equations is numerically consistent, and they must be rejected.

Common Pitfalls:
Learners may mishandle 'subtracted from' and reverse the order of numbers, or forget to apply multiplication and division before addition and subtraction. Another common pitfall is to decode correctly but then commit a small arithmetic mistake in squaring or dividing, which leads to rejecting the right answer. Stepwise evaluation and checking squares like 13 × 13 carefully helps avoid these issues.

Final Answer:
Only the decoded equation 13 ÷ 13 - 13 + 13 × 13 gives 157, so the correct coded statement is 13 C 13 A 13 B 13 D 13 = 157, corresponding to option (c).