Find the difference between the smallest 5-digit number and the greatest 5-digit number formed by using the digits `6, 8, 2, 5 and 9` (using each digit only once).

Options

A. 27936
B. 72963
C. 56293
D. 39576

Answer

To solve the problem of finding the difference between the smallest 5-digit number and the greatest 5-digit number formed by the digits 6, 8, 2, 5, and 9, we will follow these steps:

### Step 1: Identify the digits
The digits we have are: 6, 8, 2, 5, and 9.

### Step 2: Form the smallest 5-digit number
To form the smallest 5-digit number, we need to arrange the digits in ascending order.
- Arranging the digits: 2, 5, 6, 8, 9
- Therefore, the smallest 5-digit number is **25689**.

### Step 3: Form the greatest 5-digit number
To form the greatest 5-digit number, we need to arrange the digits in descending order.
- Arranging the digits: 9, 8, 6, 5, 2
- Therefore, the greatest 5-digit number is **98652**.

### Step 4: Calculate the difference
Now, we will find the difference between the greatest and the smallest number.
- Difference = Greatest number - Smallest number
- Difference = 98652 - 25689

### Step 5: Perform the subtraction
Now, we will perform the subtraction step by step:

```
98652
- 25689
_________
```

1. Start from the rightmost digit:
- 2 - 9: We cannot subtract, so we borrow 1 from the 5 (which becomes 4), making it 12 - 9 = 3.

2. Next digit:
- 4 - 8: We cannot subtract, so we borrow 1 from the 6 (which becomes 5), making it 14 - 8 = 6.

3. Next digit:
- 5 - 6: We cannot subtract, so we borrow 1 from the 8 (which becomes 7), making it 15 - 6 = 9.

4. Next digit:
- 7 - 5 = 2.

5. Last digit:
- 9 - 2 = 7.

Putting it all together, we have:
```
98652
- 25689
_________
72963
```

### Final Result
The difference between the smallest 5-digit number and the greatest 5-digit number formed by the digits 6, 8, 2, 5, and 9 is **72963**.

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