solution: The first $N$ positive odd integers are 1, 3, $\dots$, $2N - 1$.  The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms, so the sum of the first $N$ positive odd integers is \[\frac{1 + (2N - 1)}{2} \cdot N = N^2.\]If $N^2 = 121$, then $N = \boxed{11}$.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  The sum of the first $N$ positive odd numbers is 121. What is the value of $N$?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 11
extra_info.question: The sum of the first $N$ positive odd numbers is 121. What is the value of $N$?
extra_info.split: test