How many 4 digit positive number are there which are divisible by 5 ?

Options

A. 1800
B. 1500
C. 2000
D. 1600

Answer

To find how many 4-digit positive numbers are divisible by 5, we can follow these steps:

### Step 1: Identify the range of 4-digit numbers
The smallest 4-digit number is 1000, and the largest is 9999.

### Step 2: Determine the criteria for divisibility by 5
A number is divisible by 5 if it ends in either 0 or 5.

### Step 3: Find the first and last 4-digit numbers divisible by 5
- The first 4-digit number divisible by 5 is 1000 (since it ends with 0).
- The last 4-digit number divisible by 5 is 9995 (since it ends with 5).

### Step 4: Establish the sequence of numbers divisible by 5
The sequence of 4-digit numbers divisible by 5 can be represented as:
1000, 1005, 1010, ..., 9995.

### Step 5: Identify the characteristics of the sequence
This sequence is an arithmetic progression (AP) where:
- First term (a) = 1000
- Common difference (d) = 5
- Last term (l) = 9995

### Step 6: Use the formula for the nth term of an AP
The nth term of an AP can be calculated using the formula:
\[ l = a + (n - 1) \cdot d \]
Substituting the known values:
\[ 9995 = 1000 + (n - 1) \cdot 5 \]

### Step 7: Solve for n
Rearranging the equation:
\[ 9995 - 1000 = (n - 1) \cdot 5 \]
\[ 8995 = (n - 1) \cdot 5 \]
Dividing both sides by 5:
\[ n - 1 = \frac{8995}{5} \]
\[ n - 1 = 1799 \]
Adding 1 to both sides:
\[ n = 1800 \]

### Conclusion
The total number of 4-digit positive numbers that are divisible by 5 is **1800**.

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