Difficulty: Easy
Correct Answer: 8
Explanation:
Introduction / Context:
This coded-arithmetic problem replaces the usual symbols +, -, × and ÷ by letters. To solve it, we must first decode each letter into the correct basic operation, then rewrite the entire expression with normal symbols and finally evaluate it carefully using the standard order of operations.
Given Data / Assumptions:
Concept / Approach:
The strategy is straightforward: substitute each letter with its corresponding arithmetic symbol, simplify the expression step by step and ensure that we do not mix up the order of operations. Once we compute the numerical value of the left-hand side, we match it with the closest option provided.
Step-by-Step Solution:
Step 1: Replace M by minus, K by multiplication, L by division and J by plus.
Step 2: The coded expression 44 M 24 K 56 L 14 J 60 becomes 44 - 24 × 56 ÷ 14 + 60.
Step 3: First handle multiplication and division from left to right.
Step 4: Compute 24 × 56 = 1344.
Step 5: Then 1344 ÷ 14 = 96.
Step 6: Substitute back to get 44 - 96 + 60.
Step 7: Now perform the additions and subtractions from left to right: 44 - 96 = -52.
Step 8: Finally, -52 + 60 = 8.
Verification / Alternative check:
We can verify quickly by recomputing the core product and quotient: 24 × 56 = 1344 and 1344 ÷ 14 = 96, which is correct. This leads consistently to 44 - 96 + 60 = 8. No other arithmetic interpretation consistent with the given code gives a different value, so 8 is reliable.
Why Other Options Are Wrong:
The alternatives 16, 72 and 40 would require an error in decoding the letters or misapplying precedence, for example by adding 44 and 60 before subtracting 96, or by dividing in the wrong order. Any such mistake changes the intermediate steps and leads away from the correct value of 8.
Common Pitfalls:
Students sometimes misread 'subtracted from' and reverse the order of terms or forget that division and multiplication must be done before addition and subtraction. Another common error is to carry out division or multiplication mentally and slip on basic calculations. Writing down each intermediate result greatly reduces such mistakes.
Final Answer:
After decoding the letters and simplifying correctly, the value of 44 M 24 K 56 L 14 J 60 is 8, so option (c) is correct.
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