Difficulty: Medium
Correct Answer: 130
Explanation:
Introduction / Context:
This question belongs to the verbal reasoning topic of coding and decoding of mathematical operators. Instead of using the normal meaning of symbols such as plus, minus, multiply, and divide, the symbols are reassigned new meanings. The objective is to decode the expression by replacing each symbol with its correct operation and then evaluate the expression using standard arithmetic rules. It checks both understanding of operator precedence and the careful reading of symbol definitions.
Given Data / Assumptions:
Concept / Approach:
The key is to translate the encoded expression into a standard arithmetic expression. Every symbol in the given expression must be replaced with the operation it represents. After decoding, we must apply the usual order of operations: perform multiplication and division first, followed by addition and subtraction from left to right. Many errors occur when candidates either decode incorrectly or ignore operator precedence and simply compute from left to right without regard for multiplication and division priority.
Step-by-Step Solution:
Step 1: Note that minus stands for addition, plus stands for multiplication, and division stands for subtraction in this specific code.Step 2: The given coded expression is 15 - 5 + 25 ÷ 10.Step 3: Replace each symbol with its real operation: minus becomes plus, plus becomes multiplication, and division becomes subtraction. So the expression becomes 15 + 5 * 25 - 10.Step 4: Apply operator precedence. First evaluate the multiplication: 5 * 25 = 125.Step 5: Substitute this result: 15 + 125 - 10.Step 6: Perform the addition and subtraction from left to right: 15 + 125 = 140, then 140 - 10 = 130.Step 7: Therefore the decoded value of the original coded expression is 130.
Verification / Alternative check:
As a quick verification, we can plug the answer back and mentally confirm each step. The original coded form 15 - 5 + 25 ÷ 10, once translated, becomes 15 plus 5 times 25 minus 10. There is only one multiplication and one subtraction after decoding. No brackets are involved, so the only potential source of variance is operator precedence. Recomputing 5 times 25 gives 125, then adding 15 and subtracting 10 yields exactly 130, confirming that the final answer is consistent.
Why Other Options Are Wrong:
The option 22 could result from incorrectly replacing symbols and then simply performing addition and subtraction without multiplication precedence. The value minus 4 may arise if division is performed first as 25 divided by 10 and then misapplied with incorrect symbolic meanings. The option 17 can come from evaluating strictly left to right without performing the multiplication first, which is not mathematically correct. The distractor 40 is another possible miscalculation where the intermediate multiplication or subtraction step is handled wrongly. None of these match the correctly decoded and evaluated value of 130.
Common Pitfalls:
Many learners rush and forget to decode all the symbols consistently, leaving one or more operations with their original meaning. Another frequent issue is ignoring the standard hierarchy of operations, especially in questions where multiplication appears after addition or subtraction. Writing the translated expression explicitly and underlining multiplication and division before computing helps avoid mistakes. It is also wise to recheck the mapping rules at least once before final evaluation.
Final Answer:
After decoding the operators and applying normal arithmetic precedence, the value of the coded expression 15 - 5 + 25 ÷ 10 is 130.
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