Paradox questions (officially called "Resolve the Paradox" or "Explain the Discrepancy" in Critical Reasoning) trip up a lot of people, and I think it's because most students try to "explain away" one of the two facts instead of holding both as true simultaneously.
The key mental shift: both statements in the stimulus ARE true. Your job is not to challenge either one — it is to find the answer choice that makes both facts coexist logically.
Here's the framework I used during my prep:
Step 1 — Identify the two conflicting facts explicitly. Write them out as "Fact A: ___" and "Fact B: ___." Most students read the paradox and vaguely sense the tension but never articulate it precisely.
Step 2 — Ask yourself: "What kind of hidden information would make both facts simultaneously true?" This is your target answer profile before you look at the choices.
Step 3 — Scan choices for ones that introduce a third variable or context that bridges the gap. Wrong answers typically explain one fact but ignore the other, or introduce information that's irrelevant to the tension.
Example of what goes wrong: If the stimulus says "Drug X reduces disease X, but people who take Drug X have higher rates of disease X," a trap answer might say "Drug X is very expensive" — that explains why few take it, but does nothing to explain why takers still get the disease. The correct answer should explain why drug-takers still get the disease despite the drug's effectiveness (e.g., "people who take Drug X already had disease X before starting treatment").
One concrete technique: before checking answer choices, complete this sentence: "Both facts are true because ____." Any answer that doesn't fill that blank cleanly is wrong.
You're not alone on this — Paradox is one of the trickier CR subtypes because it requires holding two contradictory ideas in your head without resolving the tension prematurely. With practice on 20-30 official questions and deliberate pre-answer profiling, accuracy tends to jump noticeably.