Replace * by the smallest digit so that: 52*721 is divisible by 9

Options

A. `1`
B. `2`
C. `3`
D. `4`

Answer

To solve the problem of replacing * in the number 52*721 so that it 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 52*721 are:
- 5
- 2
- *
- 7
- 2
- 1

### Step 3: Calculate the sum of the known digits
Let's add the known digits:
- 5 + 2 + 7 + 2 + 1 = 17

### Step 4: Include the unknown digit (*)
Now, we include the unknown digit represented by * in the sum:
- Total sum = 17 + *

### Step 5: Find the smallest digit for * that makes the sum divisible by 9
We need to find the smallest digit (0-9) that, when added to 17, results in a sum that is divisible by 9.

- The nearest multiple of 9 greater than 17 is 18.
- Therefore, we set up the equation:
- 17 + * = 18
- * = 18 - 17
- * = 1

### Step 6: Conclusion
The smallest digit that can replace * to make 52721 divisible by 9 is **1**.

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