If the symbol minus denotes multiplication, the symbol x denotes addition, the symbol plus denotes division and the symbol division sign denotes subtraction, then what is the value of the coded expression 40 x 12 + 3 - 6 ÷ 60 ?

Introduction / Context:
This is a coded arithmetic question where familiar operators are replaced by different symbols. The goal is to decode the expression correctly and then evaluate it using standard arithmetic precedence. Such questions are common in verbal reasoning because they test both symbol interpretation and careful calculation rather than direct application of formulas.

Given Data / Assumptions:

• The symbol minus stands for multiplication.
• The symbol x stands for addition.
• The symbol plus stands for division.
• The division sign stands for subtraction.
• The coded expression is 40 x 12 + 3 - 6 ÷ 60.
• We must decode this to a normal arithmetic expression and then evaluate using normal precedence rules.

Concept / Approach:
The method is to map every coded symbol to its real arithmetic meaning, then rewrite the expression using the usual plus, minus, multiplication and division signs. After decoding, we must apply correct precedence: multiplication and division first, followed by addition and subtraction, working from left to right at each level. This avoids common errors where operations are done strictly from left to right without respecting priority.

Step-by-Step Solution:
Step 1: Replace x by addition. So 40 x 12 becomes 40 + 12 in actual arithmetic. Step 2: Replace plus by division. So the symbol between 12 and 3 represents division, which gives 12 ÷ 3. Step 3: Replace minus by multiplication. Between 3 and 6 the symbol minus represents a multiplication, but in the coded expression it already appears as a minus sign between 3 and 6, so we interpret it as the coded multiplication sign, which becomes × in real arithmetic. Step 4: Replace the division sign by subtraction. Thus ÷ 60 becomes − 60 in real arithmetic. Step 5: The fully decoded expression is 40 + 12 ÷ 3 × 6 − 60. Step 6: Apply precedence. First compute 12 ÷ 3 = 4. Step 7: Then multiply 4 × 6 = 24. Step 8: Now the expression becomes 40 + 24 − 60. Step 9: Perform addition and subtraction from left to right: 40 + 24 = 64, and 64 − 60 = 4.

Verification / Alternative check:
We can verify by recomputing the operations quickly. After decoding, the only nontrivial part is 12 ÷ 3 × 6. Using precedence gives 4 × 6 = 24. Substituting back, 40 + 24 − 60 yields 4 again, so the result is stable and there is no arithmetic slip. Any other answer would require either decoding a symbol incorrectly or ignoring operator precedence.

Why Other Options Are Wrong:
Values 7, 16 and 44 typically arise from errors such as performing addition before division and multiplication or misreading which symbol stands for which operation. For example, if multiplication is done incorrectly or the final subtraction is mishandled, the result moves away from 4. Since 4 is the only value that matches the correctly decoded and evaluated expression, the other options are all distractors.

Common Pitfalls:
Learners often rush and treat x as multiplication out of habit instead of reading the new meaning carefully. Another frequent mistake is to convert symbols correctly but then compute from left to right without doing division and multiplication first. Writing the decoded expression fully and then solving step by step is the safest way to avoid such errors in exam conditions.

Final Answer:
Once the coded symbols are translated and the correct arithmetic precedence is applied, the expression evaluates to 4.