What is the maximum difference between the number formed by 7 various numerals and 6 various numerals?

Options

A. 9774198
B. 35802
C. 38502
D. 999998

Answer

To find the maximum difference between the number formed by 7 various numerals and the number formed by 6 various numerals, we can follow these steps:

### Step 1: Identify the largest 7-digit number
The largest number that can be formed using 7 different digits (0-9) is by using the largest digits available. The largest 7 different digits are 9, 8, 7, 6, 5, 4, and 3. Arranging these in descending order gives us:
- **Largest 7-digit number = 9876543**

### Step 2: Identify the smallest 6-digit number
To form the smallest 6-digit number using different digits, we should use the smallest digits available. The smallest 6 different digits are 0, 1, 2, 3, 4, and 5. However, since we want a 6-digit number, we cannot start with 0. Therefore, we start with 1 and arrange the remaining digits in ascending order:
- **Smallest 6-digit number = 102345**

### Step 3: Calculate the difference
Now, we can find the difference between the largest 7-digit number and the smallest 6-digit number:
- **Difference = 9876543 - 102345**

### Step 4: Perform the subtraction
Let's perform the subtraction:
```
9876543
- 102345
-----------
9876208
```

### Final Answer
The maximum difference between the number formed by 7 various numerals and 6 various numerals is:
- **9876208**