Find out the unit digit in the following expression ? `31xx37xx36xx46xx89`

Options

A. 2
B. 8
C. 6
D. 1

Answer

To find the unit digit of the expression \(31 \times 37 \times 36 \times 46 \times 89\), we can simplify the problem by focusing only on the unit digits of each number involved in the multiplication.

### Step-by-Step Solution:

1. **Identify the Unit Digits**:
- The unit digit of \(31\) is \(1\).
- The unit digit of \(37\) is \(7\).
- The unit digit of \(36\) is \(6\).
- The unit digit of \(46\) is \(6\).
- The unit digit of \(89\) is \(9\).

2. **Write Down the Unit Digits**:
- We can represent the expression using only the unit digits:
\[ 1 \times 7 \times 6 \times 6 \times 9 \]

3. **Multiply the Unit Digits Step by Step**:
- First, multiply \(1\) and \(7\):
\[ 1 \times 7 = 7 \]
- Next, multiply the result by \(6\):
\[ 7 \times 6 = 42 \quad \text{(unit digit is } 2\text{)} \]
- Now, multiply the result by \(6\):
\[ 2 \times 6 = 12 \quad \text{(unit digit is } 2\text{)} \]
- Finally, multiply the result by \(9\):
\[ 2 \times 9 = 18 \quad \text{(unit digit is } 8\text{)} \]

4. **Conclusion**:
- The unit digit of the entire expression \(31 \times 37 \times 36 \times 46 \times 89\) is \(8\).

### Final Answer:
The unit digit of the expression is \(8\).