Difficulty: Medium
Correct Answer: 20
Explanation:
Introduction / Context:
This is another operator coding problem where every arithmetic symbol is reassigned a new meaning. You must first decode the expression by replacing each symbol with its true operation and then evaluate the resulting normal arithmetic expression. Questions like this test attention to detail and understanding of operator precedence.
Given Data / Assumptions:
Concept / Approach:
The strategy is to translate the coded expression symbol by symbol. It is safer to write the decoded expression clearly on paper instead of doing mental substitution. Once decoding is done, you evaluate using the familiar rules: perform division and multiplication before resolving addition and subtraction from left to right.
Step-by-Step Solution:
Step 1: Start with 24 x 6 - 8 + 2.Step 2: Decode each symbol: "x" means "÷", "-" means "+", and "+" means "x". There is no "÷" in this particular expression.Step 3: The decoded expression is: 24 ÷ 6 + 8 x 2.Step 4: Apply precedence: 24 ÷ 6 = 4 and 8 x 2 = 16.Step 5: Now add the results: 4 + 16 = 20.
Verification / Alternative check:
Double check that the symbols were not misread. The original expression has one "x", one "-" and one "+", so after decoding we must have one division, one addition and one multiplication. No subtraction remains. Recomputing 24 ÷ 6 = 4 and 8 x 2 = 16 again gives the sum 20, confirming the result.
Why Other Options Are Wrong:
Common Pitfalls:
Typical errors include forgetting the new meanings of the symbols mid way through the calculation and ignoring operator precedence after decoding. Some candidates also decode only one symbol and then start calculating, which is risky. Always translate the entire expression first, then evaluate systematically.
Final Answer:
After decoding and simplifying, the value of the expression is 20.
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