If the symbol "A" denotes "added to", "B" denotes "divided by", "C" denotes "multiplied by" and "D" denotes "subtracted from", then what is the value of the coded expression 116 B 29 C 6 A 24 D 45 ?

Introduction / Context:
This coded arithmetic expression replaces the usual operators plus, minus, multiplication and division with letters. The challenge is to translate each symbol back into its corresponding operation and then evaluate the expression step by step while respecting standard precedence rules. Such questions are common in reasoning sections to check clarity about operations and the order in which they should be applied.

Given Data / Assumptions:

• "A" means added to, so A corresponds to plus.
• "B" means divided by, so B corresponds to division.
• "C" means multiplied by, so C corresponds to multiplication.
• "D" means subtracted from, used here as the minus operation between the operands.
• The expression to evaluate is 116 B 29 C 6 A 24 D 45.
• Standard precedence applies: division and multiplication before addition and subtraction.

Concept / Approach:
First decode the entire expression by replacing the letters with their mathematical operators. Then simplify it step by step, starting with division and multiplication. Only after these are completed do we perform addition and subtraction in order from left to right. Keeping the correct sequence of operations is the key to avoiding errors and obtaining the correct final value.

Step-by-Step Solution:
Step 1: Replace each coded symbol with its corresponding operator. Step 2: 116 B 29 C 6 A 24 D 45 becomes 116 ÷ 29 × 6 + 24 − 45. Step 3: Perform the division 116 ÷ 29 first. Since 29 × 4 = 116, this quotient is 4. Step 4: Now perform the multiplication 4 × 6 = 24. Step 5: Substitute back to get 24 + 24 − 45. Step 6: Add 24 + 24 = 48. Step 7: Subtract 45 from 48: 48 − 45 = 3. Step 8: Therefore, the value of the coded expression is 3.

Verification / Alternative check:
We can verify by quickly recomputing with mental arithmetic. Once simplified, the expression is 116 ÷ 29 × 6 + 24 − 45. Recognizing that 116 ÷ 29 is exactly 4, the rest becomes 4 × 6 + 24 − 45. That is 24 + 24 − 45 = 48 − 45 = 3. Since this recomputation matches our previous result, the answer is confirmed.

Why Other Options Are Wrong:
Answers 4, 5 and 6 result from various mistakes such as ignoring operator precedence, reversing the subtraction or miscomputing 116 ÷ 29 or 4 × 6. Because the intermediate calculations yield clear integers and combine to 3, any other value must arise from an arithmetic slip or misinterpretation of the coded operators.

Common Pitfalls:
Candidates sometimes treat "subtracted from" as reversing the order of subtraction or they perform addition and subtraction before finishing multiplication and division. Another source of error is misreading 29 as 30 or miscalculating the quotient 116 ÷ 29. Careful reading of the operator definitions and stepwise calculation prevent such issues.

Final Answer:
After decoding and evaluating the expression, we find that 116 B 29 C 6 A 24 D 45 equals 3.