`5x555` a multiple of 9 ?

Options

A. `5`
B. `6`
C. `7`
D. `8`

Answer

To determine if the number \( 5x555 \) is a multiple of 9, we need to check the divisibility rule for 9. According to this rule, a number is divisible by 9 if the sum of its digits is divisible by 9.

### Step-by-Step Solution:

1. **Identify the digits**: The number \( 5x555 \) consists of the digits \( 5, x, 5, 5, 5 \).

2. **Calculate the sum of the digits**: The sum of the digits can be expressed as:
\[ 5 + x + 5 + 5 + 5 = 20 + x \]

3. **Check for divisibility by 9**: We need to find values of \( x \) (where \( x \) can be any digit from 0 to 9) such that \( 20 + x \) is divisible by 9.

4. **Test each value of \( x \)**:
- For \( x = 0 \): \( 20 + 0 = 20 \) (not divisible by 9)
- For \( x = 1 \): \( 20 + 1 = 21 \) (not divisible by 9)
- For \( x = 2 \): \( 20 + 2 = 22 \) (not divisible by 9)
- For \( x = 3 \): \( 20 + 3 = 23 \) (not divisible by 9)
- For \( x = 4 \): \( 20 + 4 = 24 \) (not divisible by 9)
- For \( x = 5 \): \( 20 + 5 = 25 \) (not divisible by 9)
- For \( x = 6 \): \( 20 + 6 = 26 \) (not divisible by 9)
- For \( x = 7 \): \( 20 + 7 = 27 \) (divisible by 9)
- For \( x = 8 \): \( 20 + 8 = 28 \) (not divisible by 9)
- For \( x = 9 \): \( 20 + 9 = 29 \) (not divisible by 9)

5. **Conclusion**: The only value of \( x \) that makes \( 20 + x \) divisible by 9 is \( x = 7 \). Therefore, \( 5x555 \) is a multiple of 9 when \( x = 7 \).

### Final Answer:
Yes, \( 5x555 \) is a multiple of 9 when \( x = 7 \).

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