If xAy means `x + y , xSy` mean `x - y, xMy` means `x xx y` and `xDy` means `x div y`. Then the value of `4D2S3M6A12` is :

Options

A. `-4`
B. `18`
C. `(-47)/4`
D. None of these

Answer

To solve the expression \( 4D2S3M6A12 \) using the given operations, we will follow the order of operations, which is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

### Step-by-Step Solution:

1. **Identify the operations**:
- \( D \) means division
- \( S \) means subtraction
- \( M \) means multiplication
- \( A \) means addition

2. **Rewrite the expression**:
- \( 4D2S3M6A12 \) translates to \( 4 \div 2 - 3 \times 6 + 12 \).

3. **Perform the division first**:
- Calculate \( 4 \div 2 \):
\[ 4 \div 2 = 2 \]
- Now the expression is \( 2 - 3 \times 6 + 12 \).

4. **Next, perform the multiplication**:
- Calculate \( 3 \times 6 \):
\[ 3 \times 6 = 18 \]
- Now the expression is \( 2 - 18 + 12 \).

5. **Now perform the subtraction**:
- Calculate \( 2 - 18 \):
\[ 2 - 18 = -16 \]
- Now the expression is \( -16 + 12 \).

6. **Finally, perform the addition**:
- Calculate \( -16 + 12 \):
\[ -16 + 12 = -4 \]

### Final Result:
The value of \( 4D2S3M6A12 \) is \( -4 \).

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