What should come in place of '_' so that te number `8432_(harr)96` must be divisible by 8 ?

Options

A. 7
B. 2
C. 3
D. 5

Answer

To determine what digit should replace the underscore in the number `8432_(harr)96` so that it is divisible by 8, we will follow these steps:

### Step-by-Step Solution:

1. **Understand the Rule for Divisibility by 8**:
A number is divisible by 8 if the number formed by its last three digits is divisible by 8. In this case, the last three digits of our number are `_(harr)96`.

2. **Identify the Last Three Digits**:
The last three digits of the number can be represented as `d96`, where `d` is the digit we need to find.

3. **List the Options**:
The options provided for `d` are 7, 2, 8, 3, and 5. We will check each option to see if `d96` is divisible by 8.

4. **Check Each Option**:
- **Option 1: d = 7** → Last three digits = 796
- Check if 796 is divisible by 8:
\[ 796 \div 8 = 99.5 \quad (\text{not divisible}) \]
- **Option 2: d = 2** → Last three digits = 296
- Check if 296 is divisible by 8:
\[ 296 \div 8 = 37 \quad (\text{divisible}) \]
- **Option 3: d = 8** → Last three digits = 896
- Check if 896 is divisible by 8:
\[ 896 \div 8 = 112 \quad (\text{divisible}) \]
- **Option 4: d = 3** → Last three digits = 396
- Check if 396 is divisible by 8:
\[ 396 \div 8 = 49.5 \quad (\text{not divisible}) \]
- **Option 5: d = 5** → Last three digits = 596
- Check if 596 is divisible by 8:
\[ 596 \div 8 = 74.5 \quad (\text{not divisible}) \]

5. **Conclusion**:
The options that make the last three digits divisible by 8 are 2 and 8. However, since the question asks for what should come in place of `_`, we will choose the first correct option found, which is `2`.

### Final Answer:
The digit that should replace `_` is **2**.