`3x26` a multiple of 6 ?

Options

A. `1, 4` or `7`
B. `2, 5` or `9`
C. `3, 5` or `7`
D. `3, 7` or `9`

Answer

To determine whether \(3x26\) is a multiple of 6, we need to check if it is divisible by both 2 and 3.

### Step-by-Step Solution:

**Step 1: Understand the conditions for divisibility by 6.**
- A number is a multiple of 6 if it is divisible by both 2 and 3.

**Step 2: Check divisibility by 2.**
- A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
- In the number \(3x26\), the last digit is 6, which is even.
- Therefore, \(3x26\) is divisible by 2.

**Step 3: Check divisibility by 3.**
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- The digits of \(3x26\) are \(3\), \(x\), \(2\), and \(6\).
- The sum of the digits is \(3 + x + 2 + 6 = 11 + x\).

**Step 4: Determine the values of \(x\) that make \(11 + x\) divisible by 3.**
- We will check each possible value of \(x\) (from 0 to 9):
- If \(x = 0\): \(11 + 0 = 11\) (not divisible by 3)
- If \(x = 1\): \(11 + 1 = 12\) (divisible by 3)
- If \(x = 2\): \(11 + 2 = 13\) (not divisible by 3)
- If \(x = 3\): \(11 + 3 = 14\) (not divisible by 3)
- If \(x = 4\): \(11 + 4 = 15\) (divisible by 3)
- If \(x = 5\): \(11 + 5 = 16\) (not divisible by 3)
- If \(x = 6\): \(11 + 6 = 17\) (not divisible by 3)
- If \(x = 7\): \(11 + 7 = 18\) (divisible by 3)
- If \(x = 8\): \(11 + 8 = 19\) (not divisible by 3)
- If \(x = 9\): \(11 + 9 = 20\) (not divisible by 3)

**Step 5: Compile the results.**
- The values of \(x\) that make \(11 + x\) divisible by 3 are \(x = 1\), \(x = 4\), and \(x = 7\).

### Conclusion:
- The values of \(x\) for which \(3x26\) is a multiple of 6 are \(1\), \(4\), and \(7\).