How many times the keys of a typewriter have to be pressed in order to write numbers from 121 to 1346

Options

A. 3675
B. 4018
C. 4021
D. 4025

Answer

To find out how many times the keys of a typewriter have to be pressed in order to write numbers from 121 to 1346, we can break the problem down into steps.

### Step-by-Step Solution

1. **Identify the Range of Numbers**:
We need to write numbers from 121 to 1346. This includes both 3-digit and 4-digit numbers.

2. **Count the 3-Digit Numbers**:
The 3-digit numbers range from 121 to 999.
- To find the total number of 3-digit numbers, we calculate:
\[ \text{Total 3-digit numbers} = 999 - 121 + 1 = 879 \]

3. **Count the 4-Digit Numbers**:
The 4-digit numbers range from 1000 to 1346.
- To find the total number of 4-digit numbers, we calculate:
\[ \text{Total 4-digit numbers} = 1346 - 1000 + 1 = 347 \]

4. **Calculate Key Presses for 3-Digit Numbers**:
Each 3-digit number requires 3 key presses.
- Therefore, the total key presses for 3-digit numbers is:
\[ \text{Key presses for 3-digit numbers} = 879 \times 3 = 2637 \]

5. **Calculate Key Presses for 4-Digit Numbers**:
Each 4-digit number requires 4 key presses.
- Therefore, the total key presses for 4-digit numbers is:
\[ \text{Key presses for 4-digit numbers} = 347 \times 4 = 1388 \]

6. **Calculate Total Key Presses**:
Now, we add the key presses for both 3-digit and 4-digit numbers:
\[ \text{Total key presses} = 2637 + 1388 = 4025 \]

### Final Answer
The total number of times the keys of the typewriter have to be pressed to write numbers from 121 to 1346 is **4025**.