The difference between the greatest and the least four digit numbers that begin with 3 and ends with 5 is

Options

A. a) 999
B. b) 900
C. c) 990
D. d) 909

Answer

To solve the problem of finding the difference between the greatest and least four-digit numbers that begin with 3 and end with 5, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Format of the Numbers**:
We need to find four-digit numbers that start with 3 and end with 5. The format of these numbers will be:
**3 _ _ 5**
Here, the underscores represent the two middle digits.

2. **Find the Greatest Four-Digit Number**:
To find the greatest four-digit number in this format, we should maximize the two middle digits. The highest digit we can use is 9. Therefore, the greatest number will be:
**3 9 9 5**
This equals **3995**.

3. **Find the Least Four-Digit Number**:
To find the least four-digit number in this format, we should minimize the two middle digits. The smallest digit we can use for the second digit is 0, and for the third digit, it can also be 0. Therefore, the least number will be:
**3 0 0 5**
This equals **3005**.

4. **Calculate the Difference**:
Now, we will find the difference between the greatest and the least four-digit numbers:
\[ \text{Difference} = \text{Greatest Number} - \text{Least Number} = 3995 - 3005 \]
Performing the subtraction:
\[ 3995 - 3005 = 990 \]

5. **Conclusion**:
The difference between the greatest and least four-digit numbers that begin with 3 and end with 5 is **990**.