Difficulty: Medium
Correct Answer: 2
Explanation:
Introduction / Context:
This is another coded operations question where the familiar operators do not carry their usual meanings. To solve it, we must first translate each symbol into its true operation in this code language, then simplify the resulting expression using standard arithmetic precedence. These questions sharpen precision in symbol handling and logical reasoning.
Given Data / Assumptions:
Concept / Approach:
We must decode the entire expression before doing any arithmetic. Each symbol is replaced according to the mapping, but the numbers remain in the same order. Once the expression is rewritten in terms of real operations, we evaluate it step by step, starting with multiplication and division, followed by addition and subtraction from left to right.
Step-by-Step Solution:
Step 1: Decode each operator.
"+" represents "−", so 5 + 10 becomes 5 − 10.
"×" represents "+", so 10 × 21 becomes 10 + 21.
"÷" represents "×", so 21 ÷ 5 becomes 21 × 5.
"−" represents "÷", so − 15 becomes ÷ 15.
Putting these together, the entire expression becomes:
5 − 10 + 21 × 5 ÷ 15.
Step 2: Evaluate multiplication and division.
First compute 21 × 5 = 105.
Then compute 105 ÷ 15 = 7.
The expression now reduces to: 5 − 10 + 7.
Step 3: Perform addition and subtraction from left to right.
5 − 10 = −5.
Then −5 + 7 = 2.
Verification / Alternative check:
We can verify quickly by reconfirming our decoding. The final expression 5 − 10 + 7 is simple, and a mental recomputation shows that it indeed equals 2. Any alternate decoding, such as reading "+" as addition or "−" as subtraction, would give a completely different and inconsistent result. Since the calculated value matches one of the answer options exactly, the solution is consistent.
Why Other Options Are Wrong:
The answers 49, 20, and 34 would require incorrect handling of one or more of the coded symbols or ignoring operator precedence. For instance, if someone treated "×" as multiplication and "÷" as division in the usual sense, the intermediate products would be much larger, leading to an answer far from 2. Because our decoding strictly follows the code language specified in the question, only 2 emerges as the correct value.
Common Pitfalls:
Common mistakes include decoding only part of the expression, mixing coded and real operations halfway through, or performing operations from left to right without giving priority to multiplication and division. Writing down the decoded expression clearly and then simplifying it is the safest strategy.
Final Answer:
Under the given code language, the expression 5 + 10 × 21 ÷ 5 − 15 evaluates to 2.
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