The value of k if k35624 is divisible by 11 :

Options

A. 2
B. 5
C. 7
D. 6

Answer

To find the value of \( k \) such that the number \( k35624 \) is divisible by 11, we will use the divisibility rule for 11. According to this rule, we need to find the difference between the sum of the digits at odd positions and the sum of the digits at even positions. This difference must be 0 or a multiple of 11.

### Step 1: Identify the positions of the digits
The number \( k35624 \) has the following positions:
- Position 1: \( k \) (odd)
- Position 2: \( 3 \) (even)
- Position 3: \( 5 \) (odd)
- Position 4: \( 6 \) (even)
- Position 5: \( 2 \) (odd)
- Position 6: \( 4 \) (even)

### Step 2: Sum the digits at odd positions
The digits at odd positions are \( k, 5, \) and \( 2 \). Therefore, the sum is:
\[ \text{Sum of odd positions} = k + 5 + 2 = k + 7 \]

### Step 3: Sum the digits at even positions
The digits at even positions are \( 3, 6, \) and \( 4 \). Therefore, the sum is:
\[ \text{Sum of even positions} = 3 + 6 + 4 = 13 \]

### Step 4: Set up the equation for divisibility by 11
According to the divisibility rule, we need to find the absolute difference:
\[ |(\text{Sum of odd positions}) - (\text{Sum of even positions})| = |(k + 7) - 13| \]
This simplifies to:
\[ |k + 7 - 13| = |k - 6| \]

### Step 5: Solve for \( k \)
For \( k35624 \) to be divisible by 11, the expression \( |k - 6| \) must be 0 or a multiple of 11.

1. **Case 1:** \( k - 6 = 0 \)
\[ k = 6 \]

2. **Case 2:** \( k - 6 = 11 \) (not possible since \( k \) must be a single digit)
3. **Case 3:** \( k - 6 = -11 \) (not possible since \( k \) must be a single digit)

Thus, the only valid solution is:
\[ k = 6 \]

### Final Answer
The value of \( k \) is \( 6 \).

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