Zachary did 19 push-ups in gym class today. David did 39 more push-ups than Zachary. John did 13 push-ups less than david. How many push-ups did David do?
: 

Zachary did 19 push-ups. 
David did more than Zachary, so he must have done at least 20 push-ups. 
John did 13 push-ups less than David, so he must have done at least 6 push-ups. 

Now we have a few possibilities: 

David could have done 21 push-ups, in which case John would have done 7. 
David could have done 22 push-ups, in which case John would have done 8. 
David could have done 23 push-ups, in which case John would have done 9, and so on. 

The answer is that David did at least 20 push-ups, and John did at least 6.