solution: The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100.  Of these, the $\boxed{3}$ factors 10, 25 and 50 have two digits and are factors of 150 as well.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  How many positive two-digit integers are factors of both 100 and 150?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 3
extra_info.question: How many positive two-digit integers are factors of both 100 and 150?
extra_info.split: test