Difficulty: Medium
Correct Answer: 0
Explanation:
Introduction / Context:
This arithmetic reasoning question involves operator coding and order of operations. The usual meanings of the symbols "+", "-", "x", and "÷" are changed to new meanings. You must first translate the given expression using the new definitions and then evaluate it using standard arithmetic precedence rules. This tests both symbol substitution skills and understanding of the correct order of operations.
Given Data / Assumptions:
Concept / Approach:
The key steps are: (1) carefully substitute each operator in the expression with its new meaning; (2) obtain a new expression involving the usual operators +, -, x, and ÷; and (3) evaluate this new expression using standard arithmetic rules. It is important not to change the order of the numbers, only the meanings of the operators. This type of problem punishes careless substitution or ignoring operator precedence.
Step-by-Step Solution:
Step 1: Start with the original coded expression: 24 - 4 ÷ 6 x 3 + 4.
Step 2: Replace each operator with its true meaning:
"-" means "÷", so 24 - 4 becomes 24 ÷ 4 as the first operation symbol.
"÷" means "+", so 4 ÷ 6 becomes 4 + 6.
"x" means "-", so 6 x 3 becomes 6 - 3.
"+" means "x", so 3 + 4 becomes 3 x 4.
Step 3: After substitution, the entire expression becomes: 24 ÷ 4 + 6 - 3 x 4.
Step 4: Apply normal precedence rules. First perform division and multiplication from left to right, then addition and subtraction.
Step 5: Compute 24 ÷ 4 = 6. The expression now is 6 + 6 - 3 x 4.
Step 6: Next do multiplication: 3 x 4 = 12. The expression becomes 6 + 6 - 12.
Step 7: Finally, perform addition and subtraction from left to right: 6 + 6 = 12, and 12 - 12 = 0.
Verification / Alternative check:
If you prefer, you can recompute the entire process carefully to confirm. Rewriting the sequence of operations and recalculating yields the same final expression 6 + 6 - 12 and the same result 0. Since both passes lead to 0, the answer is consistent and correct.
Why Other Options Are Wrong:
Options 1, 2, and 3 would arise only if the substitution of operators or the order of operations were handled incorrectly, such as evaluating operations strictly left to right without honoring precedence, or forgetting that "+" has been recoded to mean multiplication. None of these options matches the properly evaluated result.
Common Pitfalls:
The most common mistakes are to substitute operators incorrectly, to change numbers by accident when recoding, or to evaluate the transformed expression strictly from left to right, ignoring the standard rule that division and multiplication must be handled before addition and subtraction. Writing the substituted expression clearly and then applying arithmetic rules step by step helps avoid these errors.
Final Answer:
The value of the coded expression is 0.
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