The given problem requires us to find the total number of 3-digit numbers whose greatest common divisor (GCD) with 36 is 2. Let's break down the problem into smaller steps to better understand and solve it.

Step 1: Finding the GCD of a number with 36
To find the GCD of a number with 36, we need to determine the common factors between the number and 36. In this case, we are specifically interested in numbers that have a GCD of 2 with 36.

Step 2: Divisibility of a number by 2
A number is divisible by 2 if its units digit is even (0, 2, 4, 6, or 8). Since we are looking for 3-digit numbers, the first digit can only be 1, 2, 3, 4, 5, 6, 7, 8, or 9.

Step 3: Divisibility of a number by 36
For a number to have a GCD of 2 with 36, it should be divisible by both 2 and 36. Since 36 is a multiple of 2, any number divisible by 2 will also be divisible by 36. Therefore, we don't need to worry about the divisibility by 36, as it will already be satisfied by the divisibility by 2.

Step 4: Counting the numbers
Now that we know the first digit can be any of 1, 2, 3, 4, 5, 6, 7, 8, or 9, and the second and third digits can be any even number (0, 2, 4, 6, or 8), we can calculate the total count.

- For the first digit, we have 9 options.
- For the second digit, we have 5 options (since it must be even).
- For the third digit, we also have 5 options.

By the multiplication principle, the total count is 9 * 5 * 5 = 225.

However, we need to consider that the problem asks for 3-digit numbers. Therefore, any number starting with 0 as the first digit will be excluded. As a result, we need to subtract the count of numbers starting with 0.

- For the second digit, we have 5 options (since it must be even).
- For the third digit, we also have 5 options.

By the multiplication principle, the count of numbers starting with 0 is 1 * 5 * 5 = 25.

Finally, the total count of 3-digit numbers whose GCD with 36 is 2 is 225 - 25 = 200.

Therefore, the correct answer is 200, not 150 as stated.