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Home » Thus, the minimum value is \(\boxed\frac32\). - Portal da AcÃºstica

Thus, the minimum value is \(\boxed\frac32\). - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 So 39 is valid and the largest.

📌 Hence, the largest possible total duration is $ oxed{39} $.

📌 Question: A deep learning model processes patient data in batches, each batch size a multiple of 11, and the total dataset size is a multiple of 9. If the model must process at least 100 but fewer than 200 patients, what is the smallest possible batch size (in patients) that allows full utilization of both constraints?

📌 Solution: We are to find the smallest batch size $ B $ such that:

📌 $ B $ is a multiple of 11

📌 There exists a dataset size $ D $ with $ 100 \leq D < 200 $ and $ D \equiv 0 \pmod{9} $

📌 $ D = B \cdot k $ for some integer $ k \geq 1 $ (full utilization of batches, but $ k $ can vary)

📌 But the key is: $ B $ must divide some multiple of 9 in the range [100, 199], i.e., $ B \mid D $ for some $ D \in [100,199] \cap 9\mathbb{Z} $

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