Question

In an imaginary language, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are substituted by a, b, c, d, e, f, g, h, i, and j, respectively. And 10 is written as ba. Then, the expression \[ \text{de} \times f - (bf - d) \times d \text{ is equal to:} \]

• A. abb
• B. abe
• C. bee
• D. bef

Hint:

When solving problems in imaginary languages, first convert the numbers into their corresponding characters and follow the arithmetic operations carefully.

Answer 1

The Correct Option is C

To solve the expression \( dc \times f - (bf - d) \times d \) in the given imaginary language, follow these steps: 1. **Understand the digit substitutions:** \begin{itemize} \item \( 0 \rightarrow a \) \item \( 1 \rightarrow b \) \item \( 2 \rightarrow c \) \item \( 3 \rightarrow d \) \item \( 4 \rightarrow e \) \item \( 5 \rightarrow f \) \item \( 6 \rightarrow g \) \item \( 7 \rightarrow h \) \item \( 8 \rightarrow i \) \item \( 9 \rightarrow j \) \end{itemize} 2. **Translate the expression to numerical values:** \begin{itemize} \item \( dc \rightarrow 32 \) \item \( f \rightarrow 5 \) \item \( bf \rightarrow 15 \) \item \( d \rightarrow 3 \) \end{itemize} 3. **Rewrite the expression with numerical values:** \[ 32 \times 5 - (15 - 3) \times 3 \] 4. **Evaluate the expression step by step:** \begin{itemize} \item First, calculate \( 32 \times 5 \): \[ 32 \times 5 = 160 \] \item Then, calculate \( 15 - 3 \): \[ 15 - 3 = 12 \] \item Next, calculate \( 12 \times 3 \): \[ 12 \times 3 = 36 \] \item Finally, subtract the second result from the first: \[ 160 - 36 = 124 \] \end{itemize} 5. **Translate the result back to the imaginary language:** \begin{itemize} \item \( 124 \rightarrow bee \) \end{itemize} 6. **Final Answer:** \[ \boxed{bee} \] Therefore, the correct option is C) bee.