If in a certain code language A denotes multiplied by, B denotes subtracted from, C denotes added to and D denotes divided by, then what is the value of 8 B 31 C 49 D 7 A 16?

Introduction / Context:
This problem uses letter symbols to represent the four basic operations. We are given an expression in these symbols and must decode it to find its numerical value. Such questions appear frequently in competitive exams to test attention to definitions and the ability to evaluate an expression with altered symbols accurately.

Given Data / Assumptions:

• A means multiplied by.
• B means subtracted from.
• C means added to.
• D means divided by.
• Expression: 8 B 31 C 49 D 7 A 16.
• After decoding, standard arithmetic precedence holds.

Concept / Approach:
We replace each letter by its corresponding arithmetic operation. B becomes subtraction, C becomes addition, D becomes division, and A becomes multiplication. The decoded expression is then evaluated with the usual rule that division and multiplication are performed before addition and subtraction. A careful, stepwise evaluation prevents errors due to misordered operations or misapplied symbol meanings.

Step-by-Step Solution:
Step 1: Replace B with subtraction, C with addition, D with division, and A with multiplication.Step 2: The coded expression 8 B 31 C 49 D 7 A 16 becomes 8 − 31 + 49 ÷ 7 × 16.Step 3: Evaluate division and multiplication first. Compute 49 ÷ 7 = 7.Step 4: Then compute 7 × 16 = 112.Step 5: Substitute this back into the expression, which is now 8 − 31 + 112.Step 6: Perform subtraction first: 8 − 31 = −23.Step 7: Add 112: −23 + 112 = 89.

Verification / Alternative check:
Rechecking is straightforward. The only high priority part is 49 divided by 7 times 16, which yields 112. The remaining low priority operations are 8 minus 31 plus 112, which equals 89. No alternative grouping or different interpretation of the symbols is allowed, so 89 is stable as the correct value.

Why Other Options Are Wrong:
The answer 98 might result from treating the subtraction in 8 B 31 as 31 minus 8, which is not what the problem specifies. The options 102 and 11 could arise from miscalculating the product 7 times 16 or failing to include the negative sign after 8 minus 31. The distractor 79 is another possible result of misordered addition and subtraction. None of these match the properly decoded and evaluated value of 89.

Common Pitfalls:
Misinterpreting B as meaning 31 minus 8 instead of 8 minus 31 is a classic error, because the words subtracted from sometimes reverse operand order in other problems. Here, however, the notation is positional, and 8 B 31 simply means 8 minus 31. Another error is to perform 49 divided by 7 and divide by 16 instead of multiplying, which flips the meaning of A. Reading the definitions carefully and writing the standard expression clearly helps avoid these issues.

Final Answer:
After decoding and evaluating the expression 8 B 31 C 49 D 7 A 16, the correct value is 89.