In a coded expression, the symbols have special meanings: α denotes subtracted from, β denotes multiplied by, θ denotes added to and δ denotes divided by. Evaluate the expression 10 θ 8 β 4 δ 8 α 9 under these meanings.

Difficulty: Medium

Correct Answer: 5

Explanation:


Introduction / Context:
This verbal reasoning question uses Greek symbols to represent standard mathematical operations. We must replace each symbol with its correct operation and then evaluate the resulting expression using normal arithmetic rules. The challenge lies in decoding correctly and respecting operator precedence.


Given Data / Assumptions:

  • α denotes subtracted from.
  • β denotes multiplied by.
  • θ denotes added to.
  • δ denotes divided by.
  • Expression: 10 θ 8 β 4 δ 8 α 9.
  • Use normal precedence: multiplication and division before addition and subtraction.


Concept / Approach:
We treat θ as plus, β as times, δ as division, and α as minus in the usual left-to-right expression. The phrase subtracted from signals a minus type operation, and in standard exam practice for such coding questions, we simply substitute the operators and use normal order of operations. This gives a straightforward arithmetic expression to evaluate.


Step-by-Step Solution:
Rewrite the coded expression by replacing symbols with operations. 10 θ 8 β 4 δ 8 α 9 becomes 10 + 8 × 4 ÷ 8 − 9. According to precedence, handle × and ÷ first from left to right. Compute 8 × 4 = 32. Then 32 ÷ 8 = 4. Now the expression reduces to 10 + 4 − 9. Next perform addition and subtraction from left to right. 10 + 4 = 14. 14 − 9 = 5.


Verification / Alternative check:
Double-checking the steps: there is exactly one multiplication and one division segment, 8 × 4 ÷ 8, which simplifies neatly to 4. Substituting back, we see that 10 plus 4 minus 9 unambiguously equals 5. No other reading of the coded operators is consistent with the instructions and standard exam conventions.


Why Other Options Are Wrong:
Values 7, 9 and 11 would arise only if some operation were misread, such as adding instead of subtracting 9, or ignoring precedence and computing strictly left to right. Since our evaluation follows the given meanings and correct order of operations, those alternatives are incorrect.


Common Pitfalls:
Many learners confuse subtracted from and treat it as reversing the order of the numbers throughout the expression, which is not how such coded-operator questions are usually handled. Another error is to perform addition before completing all multiplication and division operations, which leads to wrong results.


Final Answer:
The value of the coded expression 10 θ 8 β 4 δ 8 α 9 is 5.

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