The problem presents two loops: a 'while' loop and a 'repeat until' loop. We need to determine the final values of the variables `count_x` and `count_y` after the execution of each loop, respectively.

1. Problem Description

The problem presents two loops: a 'while' loop and a 'repeat until' loop. We need to determine the final values of the variables `count_x` and `count_y` after the execution of each loop, respectively.

2. Solution Steps

First, let's analyze the 'while' loop:

`count_x = 1`

`while count_x <= 10`

` count_x = count_x + 2`

`end while`

The loop starts with `count_x = 1`. The loop continues as long as `count_x` is less than or equal to

1

0. Inside the loop, `count_x` is incremented by 2 in each iteration.

Let's trace the values of `count_x`:

- Initial: `count_x = 1`

- 1st iteration: `count_x = 1 + 2 = 3`

- 2nd iteration: `count_x = 3 + 2 = 5`

- 3rd iteration: `count_x = 5 + 2 = 7`

- 4th iteration: `count_x = 7 + 2 = 9`

- 5th iteration: `count_x = 9 + 2 = 11`

Now `count_x = 11`. The condition `count_x <= 10` (i.e., $11 <= 10$) is false, so the loop terminates.

Therefore, the final value of `count_x` is

1

1.

Next, let's analyze the 'repeat until' loop:

`count_y = 1`

`repeat`

` count_y = count_y + 2`

`until count_y <= 10`

The loop starts with `count_y = 1`. The loop executes at least once, and then continues until `count_y` is less than or equal to

1

0. Inside the loop, `count_y` is incremented by 2 in each iteration.

Let's trace the values of `count_y`:

- Initial: `count_y = 1`

- 1st iteration: `count_y = 1 + 2 = 3`

- 2nd iteration: `count_y = 3 + 2 = 5`

- 3rd iteration: `count_y = 5 + 2 = 7`

- 4th iteration: `count_y = 7 + 2 = 9`

- 5th iteration: `count_y = 9 + 2 = 11`

Now `count_y = 11`. The condition `count_y <= 10` (i.e., $11 <= 10$) is false, so the loop terminates.

Therefore, the final value of `count_y` is

1

1.

3. Final Answer

The final values of `count_x` and `count_y` are 11 and 11 respectively. So the answer is (4) 11 and 11.