If 46N is divisible by 18, then what is the value of N?

Options

A. 2
B. 4
C. 7
D. 8

Answer

To find the value of \( N \) such that \( 46N \) is divisible by 18, we can follow these steps:

### Step 1: Understand the divisibility rule for 18
A number is divisible by 18 if it is divisible by both 2 and 9.

### Step 2: Check divisibility by 2
For a number to be divisible by 2, it must be even. Therefore, \( N \) must be an even digit. The possible even digits are:
- 0
- 2
- 4
- 6
- 8

### Step 3: Check divisibility by 9
For a number to be divisible by 9, the sum of its digits must be divisible by 9. The digits of the number \( 46N \) are 4, 6, and \( N \). Therefore, the sum of the digits is:
\[ 4 + 6 + N = 10 + N \]

### Step 4: Set up the equation for divisibility by 9
We need \( 10 + N \) to be divisible by 9. We can find the values of \( N \) that satisfy this condition by checking each even digit:

- If \( N = 0 \): \( 10 + 0 = 10 \) (not divisible by 9)
- If \( N = 2 \): \( 10 + 2 = 12 \) (not divisible by 9)
- If \( N = 4 \): \( 10 + 4 = 14 \) (not divisible by 9)
- If \( N = 6 \): \( 10 + 6 = 16 \) (not divisible by 9)
- If \( N = 8 \): \( 10 + 8 = 18 \) (divisible by 9)

### Step 5: Conclusion
The only even digit \( N \) that makes \( 10 + N \) divisible by 9 is \( N = 8 \).

Thus, the value of \( N \) is:
\[ \boxed{8} \]