`5x2` a multiple of 11 ?

Options

A. `6`
B. `7`
C. `8`
D. `9`

Answer

To determine if \( 5x2 \) is a multiple of 11, we can follow these steps:

### Step 1: Understand the format of the number
The number \( 5x2 \) is a three-digit number where the first digit is 5, the second digit is \( x \), and the last digit is 2.

### Step 2: Apply the divisibility rule for 11
According to the divisibility rule for 11, a number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is either 0 or a multiple of 11.

For the number \( 5x2 \):
- The digits in odd positions are 5 (first position) and 2 (third position).
- The digit in the even position is \( x \) (second position).

### Step 3: Calculate the sums
- Sum of digits in odd positions: \( 5 + 2 = 7 \)
- Sum of digits in even position: \( x \)

### Step 4: Find the difference
Now, we calculate the difference:
\[ \text{Difference} = (5 + 2) - x = 7 - x \]

### Step 5: Check for values of \( x \)
We need to check for which values of \( x \) (from 0 to 9) the difference \( 7 - x \) is a multiple of 11.

- If \( x = 0 \): \( 7 - 0 = 7 \) (not divisible by 11)
- If \( x = 1 \): \( 7 - 1 = 6 \) (not divisible by 11)
- If \( x = 2 \): \( 7 - 2 = 5 \) (not divisible by 11)
- If \( x = 3 \): \( 7 - 3 = 4 \) (not divisible by 11)
- If \( x = 4 \): \( 7 - 4 = 3 \) (not divisible by 11)
- If \( x = 5 \): \( 7 - 5 = 2 \) (not divisible by 11)
- If \( x = 6 \): \( 7 - 6 = 1 \) (not divisible by 11)
- If \( x = 7 \): \( 7 - 7 = 0 \) (divisible by 11)
- If \( x = 8 \): \( 7 - 8 = -1 \) (not divisible by 11)
- If \( x = 9 \): \( 7 - 9 = -2 \) (not divisible by 11)

### Conclusion
The only value of \( x \) that makes \( 5x2 \) a multiple of 11 is \( x = 7 \). Therefore, \( 5x2 \) is a multiple of 11 when \( x = 7 \).