What should come in place of '_', so that the number 8432_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_96 so that the entire number is divisible by 8, we can follow these steps:

### Step 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 represented as "_96".

### Step 2: Identify the Last Three Digits
We need to consider the last three digits of the number, which are "_96". This means we will be checking the numbers 096, 196, 296, 396, 496, 596, 696, 796, 896, and 996 (where the underscore can be replaced by any digit from 0 to 9).

### Step 3: Check Each Possibility
We will check each of these combinations to see which one is divisible by 8:

1. **096**: \( 96 \div 8 = 12 \) (divisible)
2. **196**: \( 196 \div 8 = 24.5 \) (not divisible)
3. **296**: \( 296 \div 8 = 37 \) (divisible)
4. **396**: \( 396 \div 8 = 49.5 \) (not divisible)
5. **496**: \( 496 \div 8 = 62 \) (divisible)
6. **596**: \( 596 \div 8 = 74.5 \) (not divisible)
7. **696**: \( 696 \div 8 = 87 \) (divisible)
8. **796**: \( 796 \div 8 = 99.5 \) (not divisible)
9. **896**: \( 896 \div 8 = 112 \) (divisible)
10. **996**: \( 996 \div 8 = 124.5 \) (not divisible)

### Step 4: List the Valid Digits
From our checks, the valid digits that can replace the underscore to make the number divisible by 8 are:
- 0 (for 096)
- 2 (for 296)
- 4 (for 496)
- 6 (for 696)
- 8 (for 896)

### Conclusion
The digits that can replace the underscore in 8432_96 to make it divisible by 8 are **0, 2, 4, 6, or 8**.