If in a certain code language S denotes multiplied by, V denotes subtracted from, M denotes added to and L denotes divided by, then what is the value of 11 V 9 M 88 L 11 S 9?

Difficulty: Medium

Correct Answer: 74

Explanation:


Introduction / Context:
This is another symbolic operation question in the coding decoding topic. Each of the letters S, V, M, and L stands for one of the four basic arithmetic operations. After decoding these symbols, we must compute the value of the given expression with standard precedence. These problems reinforce careful substitution and methodical evaluation.



Given Data / Assumptions:

  • S denotes multiplied by.
  • V denotes subtracted from.
  • M denotes added to.
  • L denotes divided by.
  • Expression: 11 V 9 M 88 L 11 S 9.
  • Standard arithmetic precedence holds after decoding.


Concept / Approach:
We replace V with subtraction, M with addition, L with division, and S with multiplication, resulting in a normal arithmetic expression. Then we evaluate it in the usual way, giving priority to division and multiplication. The correctness of the answer relies on translating each symbol properly and maintaining the correct order of operations.



Step-by-Step Solution:
Step 1: Translate the coded expression using the defined meanings.Step 2: The expression 11 V 9 M 88 L 11 S 9 becomes 11 − 9 + 88 ÷ 11 × 9.Step 3: Evaluate the division first: 88 ÷ 11 = 8.Step 4: Next, multiply 8 × 9 = 72.Step 5: Substitute this back so the expression is 11 − 9 + 72.Step 6: Perform the subtraction: 11 − 9 = 2.Step 7: Add 72 to get 2 + 72 = 74.


Verification / Alternative check:
The process can be rechecked quickly: 88 divided by 11 equals 8, times 9 equals 72. Then 11 minus 9 is 2, plus 72 is 74. Since we have only one division and one multiplication, there is little room for alternative interpretations, and the arithmetic is simple, confirming that 74 is the correct value.



Why Other Options Are Wrong:
The option 66 might appear if one incorrectly subtracts 11 from 9 or miscomputes the product 8 times 9 as 64. The value minus 70 is far from the correct result and would require a sign inversion of the 72 term. The option 72 would be chosen if someone ignores the 11 minus 9 part and only computes the 88 divided by 11 times 9 portion. The distractor 70 could result from partial calculations or rounding errors. Only 74 matches the correct decoding and careful evaluation.



Common Pitfalls:
Misinterpreting V as 9 minus 11 instead of 11 minus 9 is one source of errors, as is forgetting that the multiplication of 8 and 9 must be computed before handling the addition and subtraction. Another common issue is to misread the sequence and accidentally calculate 11 minus (9 plus 72) instead of (11 minus 9) plus 72. Writing and simplifying stepwise prevents such mistakes.



Final Answer:
After decoding S, V, M, and L and performing the operations with correct precedence, the value of 11 V 9 M 88 L 11 S 9 is 74.


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