If "#" means subtraction, "&" means division, "@" means addition and "%" means multiplication, then what is the value of 132 & 3 # 10 @ 20 % 2 under this coded operation system?

Introduction / Context:
This verbal reasoning question tests your ability to interpret coded arithmetic operators. Instead of using the usual symbols for addition, subtraction, multiplication, and division, the question uses special symbols like "#", "&", "@", and "%". Your task is to decode what each symbol really stands for and then evaluate the mixed expression correctly by applying standard arithmetic rules such as the order of operations.

Given Data / Assumptions:
- "#" means subtraction (minus).
- "&" means division.
- "@" means addition (plus).
- "%" means multiplication.
- The coded expression is 132 & 3 # 10 @ 20 % 2.
- After decoding, normal arithmetic precedence rules apply: division and multiplication first, then addition and subtraction from left to right.

Concept / Approach:
The key idea is to convert the coded expression into a normal arithmetic expression using the given mappings. Once that is done, you simply follow the usual BODMAS or PEMDAS rules. It is important not to mix up the printed symbol with its actual meaning. For example, "&" looks unfamiliar in arithmetic, but here it clearly stands for division. Only after complete decoding should you start numerical calculations.

Step-by-Step Solution:
Step 1: Write the coded expression clearly: 132 & 3 # 10 @ 20 % 2. Step 2: Replace each code with its real operation using the mapping. Step 3: "&" becomes division, "#" becomes subtraction, "@" becomes addition, "%" becomes multiplication. Step 4: The decoded expression is 132 ÷ 3 - 10 + 20 * 2. Step 5: Apply precedence. First evaluate division and multiplication: 132 ÷ 3 = 44, and 20 * 2 = 40. Step 6: Now evaluate the remaining operations left to right: 44 - 10 + 40 = 34 + 40 = 74.

Verification / Alternative check:
We can quickly confirm each step. The mapping is clearly stated in the question, so there is no ambiguity in decoding the symbols. Recomputing 132 ÷ 3 gives 44, and 20 * 2 gives 40. Subtracting 10 from 44 results in 34, and adding 40 leads to 74. No other interpretation of the mapping produces a simpler or more consistent result, so the answer 74 is firmly supported by the data.

Why Other Options Are Wrong:
- Option 91 would result from incorrect arithmetic, for example by adding instead of subtracting 10 or ignoring precedence rules.
- Option 69 might come from partial mistakes, such as incorrect intermediate results during subtraction or addition.
- Option 76 could arise if one of the operations were mis-decoded or if a small calculation error was made when combining the numbers.

Common Pitfalls:
Common errors include carrying out the operations strictly from left to right without applying division and multiplication first or accidentally using the printed symbols with their usual meaning instead of the coded meaning given in the question. Another frequent mistake is to decode some operators correctly but forget to decode others, leading to a mixed and incorrect expression. Always rewrite the entire expression clearly in standard arithmetic form before calculating.

Final Answer:
After decoding the operators and evaluating the expression with proper precedence, the value of 132 & 3 # 10 @ 20 % 2 is 74.