Answer:
The answer would be C) swimmed. 
Explanation:
If you put each answer into the sentence, you can see if it does or doesn't make sense. Ex:
Lets try A first:
At the motel, we used the exercise room and <u>swammed </u>in  the outdoor pool. 
Although saying "swammed" might be fun, this does not make sense, therefore the answer cannot be A. 
Lets try B next!
At the motel, we used the exercise room and <u>swum </u>in  the outdoor pool.
Again, this might be fun to say and all, but this does not make sense, so we should try C next. 
At the motel, we used the exercise room and <u>swimmed </u>in  the outdoor pool.
This one makes sense and works! We should still try the last answer, D, though (you never know!)
At the motel, we used the exercise room and <u>swam </u>in  the outdoor pool.
At first glance, this may seem correct, but if you say this out loud, it doesn't make sense. The answer must be C) swimmed. 
Hope this helped! :)