If 31 x 5 is a multiple of 9, where x is a digit, then the value of x will be

Options

A. 1
B. 3
C. 6
D. 9

Answer

To solve the problem, we need to find the digit \( x \) such that the number \( 31x5 \) is a multiple of 9. According to the divisibility rule for 9, a number is divisible by 9 if the sum of its digits is also divisible by 9.

### Step-by-Step Solution:

1. **Identify the digits of the number**: The number \( 31x5 \) has the digits 3, 1, \( x \), and 5.

2. **Calculate the sum of the known digits**:
\[ 3 + 1 + 5 = 9 \]

3. **Include the unknown digit \( x \)**:
\[ \text{Sum of digits} = 9 + x \]

4. **Set up the condition for divisibility by 9**:
For \( 31x5 \) to be a multiple of 9, the sum \( 9 + x \) must be divisible by 9.

5. **Determine possible values for \( x \)**:
Since \( 9 + x \) must be divisible by 9, we can analyze the possible values of \( x \):
- If \( x = 0 \), then \( 9 + 0 = 9 \) (divisible by 9)
- If \( x = 1 \), then \( 9 + 1 = 10 \) (not divisible by 9)
- If \( x = 2 \), then \( 9 + 2 = 11 \) (not divisible by 9)
- If \( x = 3 \), then \( 9 + 3 = 12 \) (not divisible by 9)
- If \( x = 4 \), then \( 9 + 4 = 13 \) (not divisible by 9)
- If \( x = 5 \), then \( 9 + 5 = 14 \) (not divisible by 9)
- If \( x = 6 \), then \( 9 + 6 = 15 \) (not divisible by 9)
- If \( x = 7 \), then \( 9 + 7 = 16 \) (not divisible by 9)
- If \( x = 8 \), then \( 9 + 8 = 17 \) (not divisible by 9)
- If \( x = 9 \), then \( 9 + 9 = 18 \) (divisible by 9)

6. **Conclusion**: The possible values for \( x \) that make \( 31x5 \) a multiple of 9 are \( 0 \) and \( 9 \). However, since \( x \) must be a single digit, the only valid option from the given choices is \( 9 \).

Thus, the value of \( x \) is:
\[ \boxed{9} \]