How many multiples of 5 are there from 1 to 200 which are not multiple of 4?

Options

A. 40
B. 30
C. 25
D. 35

Answer

To solve the problem of finding how many multiples of 5 are there from 1 to 200 that are not multiples of 4, we can follow these steps:

### Step 1: Find the multiples of 5 from 1 to 200
To find how many multiples of 5 are there from 1 to 200, we can divide 200 by 5.

\[ \text{Number of multiples of 5} = \frac{200}{5} = 40 \]

### Step 2: Find the multiples of both 5 and 4
Next, we need to find the multiples of both 5 and 4. The least common multiple (LCM) of 5 and 4 is 20. Now we will find how many multiples of 20 are there from 1 to 200.

\[ \text{Number of multiples of 20} = \frac{200}{20} = 10 \]

### Step 3: Calculate the multiples of 5 that are not multiples of 4
Now, we subtract the number of multiples of 20 from the total number of multiples of 5 to find the multiples of 5 that are not multiples of 4.

\[ \text{Multiples of 5 that are not multiples of 4} = \text{Multiples of 5} - \text{Multiples of 20} = 40 - 10 = 30 \]

### Conclusion
Thus, the number of multiples of 5 from 1 to 200 that are not multiples of 4 is **30**.

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