The sum of predecessor and successor of the smallest five digit number formed from the digits 1 , 4 , 0 , 2 , 5 (each digit used only once) is _____ .

Options

A. 20490
B. 20480
C. 2490
D. 20508

Answer

To solve the problem step by step, we need to find the sum of the predecessor and successor of the smallest five-digit number formed from the digits 1, 4, 0, 2, and 5, using each digit only once.

### Step 1: Identify the smallest five-digit number
To form the smallest five-digit number using the digits 1, 4, 0, 2, and 5, we need to ensure that the first digit is not zero (as it would make it a four-digit number).

- The smallest digit we can start with is **1**.
- After **1**, we can use **0** (since it is the next smallest digit), followed by the remaining digits in ascending order.

Thus, the smallest five-digit number is:
**10245**

### Step 2: Find the predecessor
The predecessor of a number is obtained by subtracting 1 from it.

- So, we calculate:
\[ 10245 - 1 = 10244 \]

### Step 3: Find the successor
The successor of a number is obtained by adding 1 to it.

- So, we calculate:
\[ 10245 + 1 = 10246 \]

### Step 4: Sum the predecessor and successor
Now, we need to find the sum of the predecessor and successor.

- We add:
\[ 10244 + 10246 \]

Let's perform the addition:
- Align the numbers:
```
10244
+ 10246
-------
```
- Starting from the rightmost digit:
- 4 + 6 = 10 (write down 0, carry over 1)
- 4 + 4 + 1 (carry) = 9
- 2 + 2 = 4
- 0 + 0 = 0
- 1 + 1 = 2

So, the sum is:
**20490**

### Final Answer
The sum of the predecessor and successor of the smallest five-digit number formed from the digits 1, 4, 0, 2, and 5 is **20490**.

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