solution: We have: $2 < \sqrt{t} < \frac{7}{2}$ so squaring the inequality (which we can do because all the terms in it are positive) gives us  $4 < t <\frac{49}{4}=12.25$.  Therefore, $t$ is an integer between 5 and 12 inclusive, which leaves us with $\boxed{8}$ possible integer values of $t$.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  The square root of $t$ is greater than $2$ and less than $3.5$. How many integer values of $t$ satisfy this condition?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 8
extra_info.question: The square root of $t$ is greater than $2$ and less than $3.5$. How many integer values of $t$ satisfy this condition?
extra_info.split: test