A made-up college has two ways of teaching a course, A and B, each with 300 students…

Step 1. A's passes. $0.5n + 0.95(300 - n) = 285 - 0.45n$.

Step 2. The condition. A's rate is below B's when $285 - 0.45n < 240$, so $0.45n > 45$ and $n > 100$.

Step 3. Check. At $n = 100$, A has $285 - 45 = 240$ passes, exactly equal to B. At $n = 101$, A has $239.55$, just below.

What it means. If more than a third of A's students are weak starters, A can lose overall while it may still win inside every group.