If the symbol "A" denotes "added to", the symbol "C" denotes "divided by", the symbol "D" denotes "multiplied by" and the symbol "B" denotes "subtracted from", then what is the value of the expression 72 C 9 D 2 B 6 A 10?

Difficulty: Easy

Correct Answer: 20

Explanation:


Introduction / Context:
This problem checks whether you can correctly interpret redefined arithmetic operators and still apply standard order of operations. Each symbol (A, B, C, D) stands for a different basic arithmetic operation. You must first translate the expression into normal arithmetic form and then evaluate it carefully.



Given Data / Assumptions:

  • "A" means "added to" → +.
  • "C" means "divided by" → /.
  • "D" means "multiplied by" → *.
  • "B" means "subtracted from" → −.
  • Expression: 72 C 9 D 2 B 6 A 10.
  • Standard BODMAS or operator precedence (multiplication and division before addition and subtraction) still applies after translation.


Concept / Approach:
First, replace each symbolic operator with the real operation it represents. After translation, we get a normal arithmetic expression like "72 / 9 * 2 - 6 + 10". Then we follow normal precedence: evaluate division and multiplication from left to right, then handle addition and subtraction.



Step-by-Step Solution:
Step 1: Translate each operator. C → /, D → *, B → −, A → +. So 72 C 9 D 2 B 6 A 10 becomes: 72 / 9 * 2 - 6 + 10. Step 2: Perform division and multiplication from left to right. 72 / 9 = 8. 8 * 2 = 16. Now the expression is 16 - 6 + 10. Step 3: Perform subtraction and addition from left to right. 16 - 6 = 10. 10 + 10 = 20.


Verification / Alternative check:
Re-check each symbol replacement carefully: A is addition, B is subtraction, C is division, D is multiplication. The only potential source of error is mixing up these definitions. Once corrected, the arithmetic itself is straightforward and leads to 20.



Why Other Options Are Wrong:
Answers like 25, 30, or 35 come from either treating the symbols as their usual meanings or from ignoring operator precedence and evaluating strictly left to right. Both approaches violate the conditions of the problem.



Common Pitfalls:
Many candidates forget that "subtracted from" means the second number minus the first in English. However, here the problem already gives the symbolic sequence, so you only need to replace B with minus. Another pitfall is to perform addition before finishing all multiplication and division operations.



Final Answer:
Under the redefined operations, the expression 72 C 9 D 2 B 6 A 10 evaluates to 20.

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