If `5432**7` is divisible by 9, then the digit in place of * is :

Options

A. 0
B. 1
C. 6
D. 9

Answer

To determine the digit represented by `*` in the number `5432*7` such that the entire number 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 of the number `5432*7` are:
- 5
- 4
- 3
- 2
- *
- 7

### Step 3: Calculate the sum of the known digits
First, we will sum the known digits:
- \(5 + 4 + 3 + 2 + 7 = 21\)

### Step 4: Include the unknown digit
Now, we include the unknown digit `*` in our sum:
- Total sum = \(21 + *\)

### Step 5: Set up the condition for divisibility
For the number to be divisible by 9, the total sum \(21 + *\) must be divisible by 9.

### Step 6: Find the possible values of `*`
We need to find a value for `*` such that \(21 + *\) is divisible by 9. We can check the next multiples of 9 after 21:
- The next multiple of 9 after 21 is 27.

### Step 7: Solve for `*`
Set up the equation:
- \(21 + * = 27\)
- Solving for `*`, we get:
\[ * = 27 - 21 = 6 \]

### Conclusion
The digit in place of `*` is **6**.