Back to the on-screen lesson ·
Explain how two surprising observations can coexist by identifying a missing distinction or mechanism.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
Choose an explanation that makes both given observations understandable without denying either one.
Weakening questions invite evidence against an inference. A resolution question presents two observations that seem difficult to combine and asks what makes them compatible. Treat both observations as facts to explain rather than choosing one to discard.
| Term | What it means |
|---|---|
| Apparent paradox | Observations that seem surprising together because of an unstated expectation. |
| Rate | An amount per unit, which can change differently from a total. |
| Composition | The mix of groups or cases contributing to an overall result. |
| Detection | The process by which actual events become recorded observations. |
An apparent paradox is often a clash between an expectation and an observation, not a strict logical contradiction. Lower prices might suggest lower revenue, but revenue also depends on quantity sold. More recorded defects might suggest worse production, but recorded defects also depend on detection. An added fact can reveal the missing variable and make the combination unsurprising.
Write the two observations separately. Then ask why a reader might expect one to rule out the other. That expectation usually contains an unstated assumption: quantity stayed constant, the groups were comparable, reporting rates did not change, or the same population was measured. A good resolution supplies a relevant distinction or mechanism that relaxes the assumption while preserving both observations.
The answer need not prove that the explanation is the only possible one. It must help explain how the reported results can occur together. An option that denies the price change or denies the attendance increase is not a resolution. An option describing a true but unrelated detail leaves the surprise untouched.
Another way: picture
Put the two observations side by side. Add a third box for the hidden assumption that made them seem incompatible. A resolving fact changes that assumption, not either observation.
Another way: steps
State both facts; locate the expectation creating tension; identify a missing variable or distinction; add each candidate; check that both facts remain true and become easier to understand.
Total revenue equals price times quantity. A lower price can coexist with greater revenue if enough additional units are sold. Total resource use similarly depends on use per person and the number of people. A lower total with higher individual use can result when the number of users falls substantially. Identify which quantity each statement describes.
You do not always need exact arithmetic, but the direction and relative size must make sense. A tiny increase in sales may not offset a large price reduction. An answer saying quantity rose enough supplies the relevant relation; one saying both quantity and price fell would move the total in the wrong direction. Check the proposed mechanism rather than selecting any answer that mentions a number.
An overall average combines groups that may have very different starting values. If a delivery company stops serving its longest routes, average journey time can fall even while each retained route takes longer. The cases contributing to the average have changed. Comparing only the retained routes misses that compositional effect.
The same pattern can occur with customer mix, class enrollment or product categories. State which population is included before and after. A resolution based on changed membership is relevant only if the removed or added group's values point in the needed direction and have enough weight. Merely saying the population changed is weaker than explaining how the change affects the reported result.
A reported count depends on both how many events occur and how many are detected or reported. Easier complaint procedures can produce more recorded complaints while actual service failures fall. Improved screening can find more defects among a better-quality batch because the earlier process missed many defects.
Do not conclude that records are useless. The distinction tells you what additional information would make comparisons meaningful. If detection is stable, recorded trends may track actual trends more closely. If detection changes, a resolution should specify how. An answer about a new logo does not explain a recording change unless the passage connects it to reporting behavior.
A policy can create several effects at once. Higher admission prices may discourage visits while a highly attractive exhibition encourages them more strongly. The final attendance reflects the combined influences. A resolution often identifies the omitted effect that outweighs the expected one.
Be careful with the conclusion's scope. Showing that an attraction increased attendance does not establish that higher prices themselves increased attendance. The resolving explanation may preserve the ordinary negative price effect while adding a larger positive attraction effect. Distinguish explaining the net result from reversing every causal relationship that initially seemed relevant.
Two statements may refer to different periods. A repair can increase short-term cost while reducing long-term cost. A program can increase the number of applications while reducing the proportion accepted. A word such as success may refer to completing a process in one statement and achieving a later outcome in another. Preserve the definitions before declaring a contradiction.
A candidate that changes the comparison group can also resolve a puzzle. More visitors at one museum and fewer at another need not reflect price alone when exhibitions and access differ. Identify the comparison the surprising expectation assumes. The added fact should explain why that assumed comparison is incomplete rather than simply announce that institutions differ.
An option may explain why revenue rose while failing to accommodate the stated price reduction. Another may explain why some complaints exist without explaining why their count increased as failures decreased. Read the two-fact requirement after every candidate.
A useful check is a short combined account: although one factor moved in the expected direction, another relevant factor changed enough to produce the reported result. If you cannot complete that account without denying a premise or inventing another fact, the option has not resolved the discrepancy. Do not demand a complete history of the event, but require the supplied fact to do the connecting work rather than relying on a story you added yourself.
When a report gives two apparently conflicting trends, label the measures before deciding that one must be wrong. Ask whether they concern totals, rates, averages, different groups or different stages of measurement. A count of complaints is not automatically a count of all failures, and a changing average does not describe every individual.
The practice questions supply the facts needed to compare explanations. They do not ask you to invent unsupported rescue stories. Review an incorrect answer by stating which observation it contradicted or which missing variable it failed to address. The automatic records verify your choice among the supplied explanations and your identification of the task. They do not validate a real causal investigation. On later practice, retrieve the two observations first, then test whether the added fact actually makes their coexistence understandable.
Reject answers that deny a given observation, explain only one side, or confuse a total with a rate. A resolution can be plausible without being the sole possible explanation. Check whether the proposed change is large enough and points in the right direction; naming a relevant variable without the needed relationship may leave the original tension unresolved.
Read the passage and question.
A shop lowered the price of each notebook, yet total notebook revenue increased during the same period.
Which fact best explains how both results occurred?
Keep the lower unit price and the higher total revenue; inspect quantity sold.
Compare the five proposed answers.
1: The number of notebooks sold more than doubled while the price fell only slightly. 2: The shop actually raised the notebook price. 3: Customers never bought notebooks. 4: The shop sells pencils too. 5: The notebooks have blue covers.
Apply the question's test to each option; do not choose solely by shared vocabulary.
Explain the best answer.
The number of notebooks sold more than doubled while the price fell only slightly.
The quantity increase can outweigh the modest price reduction in total revenue.
Account for every rejected answer.
2: This rejects a given fact instead of reconciling it. 3: That cannot explain an increase in notebook revenue. 4: Other products do not explain notebook revenue without an added connection. 5: Color alone does not connect price and quantity.
Each rejection identifies a specific mismatch with the passage or task.
Read the passage and question.
A town used less water in total during a hotter summer, although each occupied household used more water than before.
Which fact best resolves the apparent discrepancy?
The number of occupied households is separate from use per occupied household.
Compare the five proposed answers.
1: Many households were unoccupied that summer, more than offsetting higher use in the occupied ones. 2: Every household used less water. 3: Summer weather never changes. 4: The town painted its water tower. 5: Water is useful for gardens.
Apply the question's test to each option; do not choose solely by shared vocabulary.
Explain the best answer.
Many households were unoccupied that summer, more than offsetting higher use in the occupied ones.
A smaller number of users can lower the total despite a higher amount per remaining user.
Account for every rejected answer.
2: That contradicts the given higher usage per occupied household. 3: This denies the given contrast and does not explain the totals. 4: No connection to occupied-household counts or usage is supplied. 5: A general use does not explain the observed combination.
Each rejection identifies a specific mismatch with the passage or task.
Read the passage and question.
After a factory improved its screening, more defective units were recorded even though production quality improved.
Which fact best reconciles the findings?
Recorded defects depend on screening sensitivity as well as actual defects.
Compare the five proposed answers.
1: The new screening detects many defects that the old screening missed. 2: The factory stopped recording defects. 3: Actual quality did not improve. 4: The factory changed its logo. 5: No unit was ever screened.
Apply the question's test to each option; do not choose solely by shared vocabulary.
Explain the best answer.
The new screening detects many defects that the old screening missed.
Recorded defects can rise because detection improves even while actual defect frequency falls.
Account for every rejected answer.
2: That conflicts with the increase in recorded defects. 3: This discards rather than explains the given finding. 4: The logo does not connect screening and recording. 5: This contradicts the screening premise.
Each rejection identifies a specific mismatch with the passage or task.
Check the difficult boundary.
More detected defects does not by itself show that actual defect frequency increased.
This last check preserves the exact strength and scope of the answer rather than turning it into a broader claim.
Preserve both observations.
A course's average score rose, although every returning student scored slightly lower.
The average may include more than the returning students.
Supply a relevant composition change.
A large group of new students earned scores well above the previous average.
The new group's contribution can outweigh the small declines among returners.
State what the explanation does not claim.
A museum raised admission prices but received more visitors, while a nearby museum with unchanged prices received fewer visitors. Which fact most helps reconcile these outcomes?
A delivery service's average journey time fell even though every route it kept operating took longer than before. Which fact explains how this could happen?
A bakery lowered the price of every loaf but earned more total bread revenue. Which fact best explains both results?
A city's water use per household fell, but total residential water use rose. Which information best resolves the discrepancy?
After a clinic improved screening, the recorded number of a condition's cases increased, although an independent survey found its prevalence unchanged. Which explanation best fits?
A train's scheduled trip time increased, yet its average passenger arrival delay decreased. Which explanation fits both statements?
A forest plot had fewer mature trees after a storm, yet more canopy cover two years later than just before the storm. Which finding best explains this?
A school reduced the number of books borrowed per student while its total number of borrowed books increased. Which fact best explains both results?
A theater's ticket revenue rose this season even though it sold fewer tickets than last season. Its manager says these facts are entirely compatible and do not require assuming an accounting mistake. Which additional fact best explains how both reported changes could occur?
A performance group sold 1100 tickets last year and 20 percent fewer this year, but its ticket revenue rose. The accounts include only ticket sales, and both reported changes are accurate. Which fact would explain the apparent discrepancy?
A cinema sold fewer tickets in June than in May, yet its total ticket revenue was higher in June. Both totals cover the same cinema and count only ticket sales. Which fact best resolves the apparent discrepancy?
Answer three reserved questions without hints. These cases are separate from lesson practice.
A shop served fewer customers but sold more items this week than last week. Which fact best resolves the apparent conflict?
A survey reports that average commute distance increased while average commute time decreased. Which finding best explains both changes?
After a town simplified its complaint process, recorded complaints increased even though an independent inspection found fewer service failures. Which statement best reconciles the findings?
Tomorrow, recall a total-versus-rate explanation and an actual-versus-recorded explanation. State both observations before seeking a resolution. Next: describe what an argument does rather than whether its conclusion is true.
16. Explain a changing average, step 3
The account does not deny the returning students' declines.
A resolution keeps the observations it was asked to reconcile.