Lesson 36 of 42 · Critical thinking
Excluding unsupported implications
Spot the plausible leaps a passage does not support (cause from correlation, a rule run backwards, sample to population) and keep the modest truths.
About 20 minutes
In this lesson
- Name the extra premise an attractive conclusion would need.
- Recognise the common leaps: correlation to cause, converse of a rule, sample to population, average to every member.
- Keep the implications that are fully supported, even when they look modest.
The idea
What an unsupported implication is
Many critical thinking statements sound like natural conclusions of a passage but need something the passage does not supply. Recognising these unsupported implications, and rejecting them however reasonable they sound, matters in both critical thinking formats Bocconi lists: the statement you must not choose is very often a plausible next step that goes one step too far.
The question to ask
For any candidate conclusion, ask: what would I have to add to the passage to make this certain? If the answer is "nothing", the conclusion is supported. If you need an extra premise, however modest ("and nothing else changed", "and the survey was representative", "and that is the only reason"), the conclusion cannot be deduced from the passage.
The usual leaps
| Leap | The passage gives | The unsupported conclusion |
|---|---|---|
| Correlation to cause | Provinces with more bank branches save more | Opening branches raises saving |
| Converse of a rule | Every applicant over the limit is refused | Every refused applicant was over the limit |
| Sample to population | 70% of one bank's surveyed customers never visit a branch | 70% of all bank customers never visit a branch |
| Average to every member | Average income in the town rose | Every household's income rose |
| Average of percentages to total | The departments' cuts average 15% | Total spending fell by 15% |
| Past to future | Prices rose in each of the last five years | Prices will rise next year |
| Some to most | Some exporters insure against currency risk | Most exporters insure |
Correlation and cause
When two things move together, several explanations are possible: one causes the other, the other causes the one, a third factor drives both, or the link is coincidence. In the bank-branch case, banks may open branches where people already save more. A passage that reports only the association does not establish any of these. A statement claiming a cause is not deducible unless the passage itself states the causal link.
Rules run one way
"If an applicant's repayments would exceed 35% of income, the loan is refused" tells you what happens to applicants over the limit. It says nothing about why other loans are refused; refusals can have many causes. The valid move in the other direction is the contrapositive: if a loan was approved, the repayments did not exceed 35%.
Averages and percentages hide the parts
An average can rise while some members fall. And percentage changes of parts of different sizes cannot be averaged into a total. If three departments that spend €50,000, €30,000 and €20,000 cut that spending by 0%, 10% and 35%, the average of the three cuts is 15%, but total spending falls by €10,000 out of €100,000, which is 10%.
What is supported
Rejecting leaps does not mean rejecting everything. Some implications are fully supported, and the test rewards spotting them too:
- If every part fell, the total fell.
- If an average fell, at least one member fell.
- If all A are B and X is an A, then X is B.
- If two groups from one total add up to more than the total, they overlap.
A well-built item often places one supported implication among several attractive leaps. The supported one tends to look modest; the leaps look interesting. Do not reject the modest statement because it seems too obvious to be the answer.
Worked examples
Example 1: Branches and saving
In a study of 40 provinces, those with more bank branches per resident had higher household saving rates.
Judge the statement: Opening more bank branches in a province raises its household saving rate.
Ask what must be added to make the statement certain: that the branches cause the saving, rather than the other way round or both being driven by something else.
Alternative 1: banks open branches where households already save more. Alternative 2: richer provinces both save more and attract more branches.
The passage reports only that the two go together. Each explanation fits it, so the causal claim is not established.
Answer
Cannot be deduced. The tempting verdict is true, because the causal story is plausible; but plausibility is an extra premise the passage does not give.
Example 2: Average cut against total cut
Three departments spent €50,000, €30,000 and €20,000 on travel in 2023. In 2024 they cut that spending by 0%, 10% and 35% respectively. By how much did their total travel spending fall?
The cuts in euros: ; ; .
Total cut: euros, out of a total of euros: 10%.
The simple average of the percentages is . It overstates the cut because the largest percentage cut fell on the smallest budget.
What is supported without the budgets: since no department increased its spending and some cut it, the total fell. Its size needs the budgets.
Answer
Total spending fell by 10%. "15%" is the unsupported implication: an average of percentages is not the percentage change of the total.
Example 3: A sample and its population
In a survey of 400 customers of an online bank, all of whom answered, 280 said they had not visited a bank branch in the past year.
Judge each statement: (1) 70% of the surveyed customers had not visited a branch in the past year. (2) Most of the country's bank customers no longer visit branches. (3) Fewer than half of the surveyed customers had visited a branch in the past year.
Statement 1: . True.
Statement 2 extends the result from one online bank's customers to all customers in the country. Online-bank customers may visit branches far less than others. Cannot be deduced.
Statement 3: had visited, which is 30%, fewer than half. True.
Answer
Statements 1 and 3 are true; statement 2 cannot be deduced. The supported statements are dull restatements; the unsupported one is the interesting headline.
Common traps
The reasonable story
A causal explanation is so natural that it feels stated. Ask whether the passage says one thing causes the other, or only that they occur together. Without the causal claim in the passage, the statement cannot be deduced.
Running the rule backwards
"Over the limit, so refused" becomes "refused, so over the limit". The first is a rule; the second needs the extra premise that the limit is the only reason for refusal.
The interesting conclusion
Options that generalise (to the whole country, to every member, to next year) are more interesting than restatements, and catch readers who expect the answer to say something new. Check scope: same group, same period, same measure.
Rejecting the modest truth
A statement that only restates or combines the passage looks too easy to be right. If it follows with no added premise, it is supported, and in a "must be true" item it is the answer.
Check yourself
Answer each question before you open its answer.
Question 1: Ring roads and town centres
Critical thinking
Over the past ten years, the towns in a province that built a ring road saw retail employment in their centres fall by an average of 8%, while the towns that did not build one saw it rise by an average of 2%.
Which of the following can be deduced from the information?
- A.Building a ring road reduces retail employment in a town's centre.
- B.In at least one town that built a ring road, retail employment in the centre fell over the period.
- C.Every town without a ring road gained retail jobs in its centre.
- D.Total retail employment in the province fell over the period.
Show the answer
Answer: B. In at least one town that built a ring road, retail employment in the centre fell over the period.
Working
If the average change across the ring-road towns was a fall of 8%, the towns cannot all have had a rise or no change; at least one must have fallen. That needs no added premise. The causal claim needs the premise that the ring road, not something else, explains the difference; the claim about every town confuses an average with each member; the claim about the province needs town sizes and jobs outside centres, which are not given.
Why the other options are wrong
- A. The passage reports an association, not a cause. Towns whose centres were already declining might have been the ones to build ring roads.
- C. An average rise of 2% is compatible with some of those towns losing jobs while others gained more.
- D. The figures cover only town centres and are averages of towns of unknown sizes; jobs outside the centres are not mentioned at all.
What carries over
If an average fell, at least one member fell; nothing more about individual members or causes follows.
Question 2: A refused mortgage
Critical thinking
A bank approves a mortgage only if the monthly repayments would be no more than 35% of the applicant's net monthly income. Paolo applied to the bank for a mortgage and was refused.
Is the following statement true, false, or can it not be deduced from the passage? Paolo's monthly repayments would have been more than 35% of his net monthly income.
- A.True
- B.False
- C.Cannot be deduced
Show the answer
Answer: C. Cannot be deduced
Working
"Approved only if repayments are at most 35%" means every approved mortgage met the limit. It does not say that every mortgage meeting the limit is approved. Paolo's refusal fits a situation where his repayments exceeded 35%, and also one where they were within the limit but he was refused for another reason. Both fit the passage, so the statement cannot be deduced.
Why the other options are wrong
- A. Treats the 35% condition as the only reason for refusal. The passage makes it necessary for approval, not sufficient, so Paolo may have met it and been refused for another reason.
- B. Nothing in the passage says his repayments were within the limit. He may have been refused precisely because they were not.
What carries over
A necessary condition explains some refusals, not all of them; a refusal does not tell you which condition failed.
Question 3: Three departments cut spending
Critical thinking
Compared with 2023, three departments of a firm cut their travel spending in 2024 by 5%, 10% and 30% respectively.
Is the following statement true, false, or can it not be deduced from the passage? Together, the three departments spent less on travel in 2024 than in 2023.
- A.True
- B.False
- C.Cannot be deduced
Show the answer
Answer: A. True
Working
Each department spent less in 2024 than in 2023. A sum of three smaller amounts is smaller than the sum of the three larger ones, whatever the budgets were. So total travel spending fell, and the statement is true. What cannot be deduced is the percentage fall of the total, which depends on the budgets.
Why the other options are wrong
- B. Perhaps reacts against the unknown size of the total cut. The size is unknown, but every part fell, so the total must have fallen.
- C. The size of the total cut cannot be deduced, because the budgets are not given; but the statement asks only about the direction, and that is fixed.
What carries over
If every part fell, the total fell; separate what is fixed (direction) from what is not (size).
Key points
Ask what you would have to add to the passage to make a conclusion certain; if anything, it is not deducible.
Association is not cause, and a rule does not run backwards.
Averages hide their members, and percentages of different bases cannot be averaged into a total.
Modest restatements and combinations are often the supported answer; do not reject them for being obvious.
All questions here are original and written for UniExamer; none comes from the test maker.
Written by the UniExamer team with AI assistance. Every worked example and check question was re-solved by an independent checker before publication. No subject expert has reviewed this lesson yet. If you find a mistake, write to support@uniexamer.com.