To find the numbers between 1 to 200 that are divisible by 3 but not by 7, we can use the concepts of divisibility and counting.

Step 1: Find the numbers divisible by 3
To find the numbers divisible by 3, we need to check if each number between 1 and 200 is divisible by 3. We can do this by dividing each number by 3 and checking if the remainder is 0.

Step 2: Find the numbers divisible by 7
Similarly, we need to check if each number between 1 and 200 is divisible by 7. If the remainder is 0 when dividing a number by 7, it is divisible by 7.

Step 3: Find the numbers divisible by 3 but not by 7
To find the numbers that are divisible by 3 but not by 7, we need to find the numbers that are divisible by 3 but have a remainder when divided by 7.

Step 4: Count the numbers
Finally, we count the numbers that meet the criteria of being divisible by 3 but not by 7.

Now, let's break down the steps and solve the problem.

Step 1: Find the numbers divisible by 3
To find the numbers divisible by 3, we divide each number between 1 and 200 by 3 and check if the remainder is 0.

Step 2: Find the numbers divisible by 7
To find the numbers divisible by 7, we divide each number between 1 and 200 by 7 and check if the remainder is 0.

Step 3: Find the numbers divisible by 3 but not by 7
To find the numbers that are divisible by 3 but not by 7, we look for numbers that have a remainder when divided by 7.

Step 4: Count the numbers
Finally, we count the numbers that meet the criteria of being divisible by 3 but not by 7.

The correct answer is option 'C' which states that there are 57 numbers between 1 and 200 that are divisible by 3 but not by 7.