Wrong flaw. This establishes a necessary condition for students to excel at a particular school, then jumps to a prescriptive conclusions about what all schools should do. The stimulus makes a causal conclusion, not a prescriptive one.

This assumes that something causes a phenomenon merely because it’s generally a necessary condition for that phenomenon. The fact that crashes typically would not occur without carelessness does not prove that icy roads are not causing the crashes.

Wrong flaw. This assumes a causal relationship on the basis of a correlation observed in a potentially unrepresentative sample. The stimulus relies on a necessary condition—not a correlation—to infer its conclusion.

Wrong flaw. This amounts to a correlation-causation fallacy. Because certain good cooks happen to use butter, the author assumes that this is what all those who want to be good cooks should do. The stimulus relies on a necessary condition, rather than a correlation, to infer its conclusion.

Wrong flaw. This has mismatched variables that don’t link conditions together. Having an adequate understanding of algebra is not the same thing as doing good work. The stimulus’s flaw, in contrast, is assuming that a necessary condition for a phenomenon is the cause of that phenomenon.