(A) is wrong because it swaps the stimulus’ second premise and its conclusion. In (A), there are two requirements for good piano playing (excellent ear or* manual dexterity). To match our stimulus, (A)’s next premise should say Paul meets those two requirements, and its conclusion should claim Paul is good at piano. But those two claims are swapped. Here’s the formal logic:

P1: Piano → Ear or* Dexterity
P2: _PaulPiano
________
C: _PaulEar and _PaulDexterity

*That or is sus too, since the terms in our stimulus are connected by an and.

Like the stimulus, (B) confuses sufficiency and necessity. It establishes two conditions (language 1 and language 2) that are both necessary for a sufficient condition (effective teacher), then reasons that because someone has met both requirements, the sufficient condition follows. Here’s the formal logic:

P1: Effective → Language 1 and Language 2
P2: _YessiosLanguage 1 and _YessiosLanguage 2
________
C: _YessiosEffective

You may have noticed she also meets a third requirement – language 3 – which doesn’t have a direct counterpart in the stimulus. That’s fine since (B) preserves the stimulus’ core flaw.

(C) demonstrates valid reasoning. Apprenticeships are necessary to get a license, so if someone has a license they must have done an apprenticeship. Here’s the logic:

P1: License → Apprenticeship
P2: _MartinLicense
________
C: _MartinApprenticeship

(D) doesn’t confuse sufficiency and necessity. It sets up two conditions (national affairs and international affairs) that are both necessary for a sufficient condition (effective mayor*), then affirms the sufficient condition* instead of affirming the necessary conditions. Here’s the logic:

P1: Effective* → National and International
P2: _LerouxEffective*
________
C: _LerouxNational and _LerouxInternational

*The structural mismatch above is what you should use to eliminate (D), but you may also have noticed the domain shift from “mayor of a major industrial seaport” to just “mayor.” That’s a real thing – what if Leroux is the effective mayor of a tiny rural town? – and it makes (D)’s reasoning invalid. But that flaw doesn’t match the flaw in the stimulus.

(E) demonstrates valid reasoning. Fresh vegetables are necessary for a delicious soup, so if a soup is delicious, it must contain fresh vegetables. Here’s the logic:

P1: Delicious → Fresh Veggies
P2: _{This Soup}Delicious
________
C: _{This Soup}Fresh Veggies