If 2794p561 is divisible by 9, then the value of p is:

Options

A. 3
B. 2
C. 0
D. 4

Answer

To determine the value of \( p \) such that the number \( 2794p561 \) is divisible by 9, we can follow these steps:

### Step 1: Understand the divisibility rule for 9
A number is divisible by 9 if the sum of its digits is divisible by 9.

### Step 2: Write down the digits of the number
The digits in the number \( 2794p561 \) are:
- 2, 7, 9, 4, \( p \), 5, 6, 1

### Step 3: Calculate the sum of the known digits
First, we calculate the sum of the known digits:
\[ 2 + 7 + 9 + 4 + 5 + 6 + 1 = 34 \]

### Step 4: Include \( p \) in the sum
Now, we include \( p \) in the sum:
\[ 34 + p \]

### Step 5: Set up the condition for divisibility by 9
We need \( 34 + p \) to be divisible by 9. To find suitable values for \( p \), we can check the nearest multiples of 9 around 34.

### Step 6: Find the nearest multiples of 9
The nearest multiples of 9 around 34 are:
- \( 27 \) (not applicable since it's less than 34)
- \( 36 \) (the next multiple of 9)

### Step 7: Solve for \( p \)
To find \( p \), we set up the equation:
\[ 34 + p = 36 \]
Solving for \( p \):
\[ p = 36 - 34 = 2 \]

### Step 8: Verify the solution
Now we check if substituting \( p = 2 \) makes the sum divisible by 9:
\[ 34 + 2 = 36 \]
Since \( 36 \) is divisible by 9, our solution is correct.

### Final Answer
Thus, the value of \( p \) is \( \boxed{2} \).

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