Critical Reasoning
Verbal
7 min readResolve-the-paradox questions present two facts that seem to contradict each other. Your job is to choose the explanation that allows both facts to be true at the same time. The correct answer does not dispute either fact. It shows why they are compatible.
A paradox has two parts that appear inconsistent. For example: "A company raised its prices and its total revenue increased." At first, this seems odd because higher prices usually reduce sales. But the two facts can coexist if the price increase attracted customers who interpreted the higher price as a sign of quality, or if the company sold a premium product with inelastic demand.
The correct explanation usually introduces a factor that affects one side of the paradox without contradicting the other. It may explain why the expected result did not occur, or why the unexpected result did.
Both facts stay true. The answer explains how. If a choice denies one of the facts, it is not a resolution.
Identify the expectation and the outcome. The expectation is what would normally happen. The outcome is what the passage says happened. The tension lies between them. For the price example, the expectation is that higher prices reduce sales, and the outcome is that revenue rose. A resolution explains why the usual expectation did not hold.
Sometimes the passage states the expectation directly: "Although the drug is less effective in trials, doctors prescribe it more often." In that case, the tension is explicit. In other passages, you have to infer the expectation from common sense.
A good resolution is specific enough to explain the outcome and broad enough to leave the evidence intact. It often does one of the following:
Example. A city added more lanes to a highway, but traffic congestion became worse. Which explanation resolves the paradox?
A good resolution: the additional lanes attracted more drivers who had previously avoided the highway. The new capacity was used by new traffic, so congestion increased. This explains both facts without denying either one.
Some wrong answers explain one fact but ignore the other. A choice saying "the highway construction was expensive" explains the cost, but not why congestion worsened. A choice saying "drivers dislike construction" explains a temporary delay, but not a long-term increase in traffic. The correct answer must address the relationship between the two facts.
Other wrong answers introduce a factor that is too small to matter. A choice saying "a few drivers changed their route" does not explain a large increase in congestion. The explanation must be proportional to the effect described.
Numerical paradoxes often involve averages, percentages, or totals. A company can increase its average salary while reducing every employee's salary if it hires fewer highly paid workers or changes the mix of employees. A school can raise its graduation rate while producing fewer graduates if enrollment falls.
Example. A store's average sale per customer fell, but total revenue rose. How is this possible?
The store had many more customers. Even though each customer spent less on average, the larger number of customers produced higher total revenue. The resolution depends on the difference between an average and a total.
Behavioral paradoxes often involve incentives, information, or selection. A safety feature can lead people to take more risks. A warning label can make a product more attractive to a certain group. A policy can reduce one problem while increasing another. The correct answer identifies the behavioral link that makes the outcome possible.
For example, a mandatory seatbelt law may reduce deaths per accident but increase the number of accidents if drivers feel safer and drive less carefully. The resolution does not deny that seatbelts save lives in individual crashes. It explains why the total number of accidents could rise.
Some paradoxes arise because a group changes its composition. A company may report that average productivity rose even though every employee's productivity stayed the same. The explanation could be that the company laid off its least productive workers. The average of the remaining group is higher, but no individual improved.
Selection effects appear in many forms. A school may report higher average test scores after a new principal arrives, not because teaching improved, but because low-scoring students transferred out. A hospital may have a higher mortality rate than another hospital even though its treatment is better, because it handles more severe cases. The resolution identifies the change in the group, not a change in the individuals.
Example. A gym reports that the average fitness of its members improved after it introduced a new training program. However, the program was optional and only the most motivated members participated.
Resolution: the improvement may reflect the selection of motivated members rather than the program's effect. Both facts remain true, and the composition of the participating group explains the result.
A good resolution must be consistent with both facts and strong enough to explain the size of the effect. Test each choice by asking two questions. First, does it deny either fact? If so, eliminate it. Second, does it explain why the surprising result occurred? If it only describes a background condition, it is not enough.
Suppose a store's sales rose after it reduced its advertising budget. A resolution might be that the store also launched a viral social media campaign that reached more customers than the paid ads. This explains both the budget cut and the sales increase. A resolution saying that advertising is expensive does not explain why sales rose.
Some paradoxes depend on timing. A policy may produce a benefit after an initial cost, or a treatment may reduce long-term risk while increasing short-term side effects. The resolution can separate the short run from the long run. If the passage describes a result over one period, a choice about a different period may not resolve the tension unless the passage makes that connection.
The correct resolution often changes the unit of analysis. It may show that the two facts describe different groups, different time periods, or different measures. Look for that shift before choosing an answer.
| Paradox type | Common resolution |
|---|---|
| Price up, revenue up | Demand is inelastic or quality signal matters |
| More lanes, more traffic | New capacity attracts new drivers |
| Average down, total up | More customers or a change in composition |
| Safety feature, more accidents | Risk compensation or behavior change |
| Less effective drug, more prescriptions | Fewer side effects or lower cost |
The answer to a paradox question often feels like a small shift in perspective. It does not undo either fact. It shows that the two facts describe different groups, different time periods, or different measures.
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