Question

If the symbols \(\alpha, \beta, \gamma,\) and \(\delta\) stand for ordinary arithmetical signs \(+\), \(-\), \(\times\), and \(\div\) respectively, then: \[ \frac{(48 \delta 4) \beta (8 \alpha 4)} {(4 \gamma 8) \beta (2 \gamma 16)+1} = ? \]

• A. \(16\)
• B. \(8\)
• C. \(4\)
• D. \(0\)

Hint:

In symbol replacement questions, always rewrite the entire expression using the actual operators before performing any calculations.

Answer 1

The Correct Option is D

Concept: In symbol substitution problems, each symbol represents a different arithmetic operation. The first step is to replace all symbols with their actual meanings and then simplify according to the BODMAS rule. Given: \[ \alpha=+ \] \[ \beta=- \] \[ \gamma=\times \] \[ \delta=\div \]

Step 1: Evaluate the numerator. The numerator is \[ (48 \delta 4)\beta(8\alpha4) \] Substituting the symbols: \[ (48\div4)-(8+4) \] First compute the bracket values: \[ 48\div4=12 \] and \[ 8+4=12 \] Therefore, \[ 12-12=0 \] Hence the numerator equals \[ 0 \]

Step 2: Evaluate the denominator. The denominator is \[ (4\gamma8)\beta(2\gamma16)+1 \] Substituting the symbols: \[ (4\times8)-(2\times16)+1 \] Now calculate: \[ 4\times8=32 \] \[ 2\times16=32 \] Therefore, \[ 32-32+1=1 \] Thus the denominator equals \[ 1 \]

Step 3: Compute the final value. \[ \frac{0}{1}=0 \] Hence, \[ \boxed{0} \]