Lesson 34 of 42 · Critical thinking
True, false or cannot be deduced
Judge an assertion against a short passage with the two-scenario test, and keep "false" apart from "not stated" and "true" apart from "likely".
About 20 minutes
In this lesson
- Define the three verdicts precisely and apply them to a statement about a passage.
- Use the two-scenario test, with invented figures where the passage has numbers.
- Keep outside knowledge and likely-but-unstated conclusions out of the verdict.
The idea
The format
One of the two critical thinking formats Bocconi lists for the standard test gives a short passage followed by an assertion, and you judge whether the assertion is true, false, or cannot be deduced from the passage. These items have only three options, and Bocconi scores a wrong answer to a three-option critical thinking item at −0.33 rather than the −0.2 used elsewhere; a correct answer still scores 1 and a blank 0.
The three verdicts, defined
Everything depends on using the three labels precisely.
| Verdict | Means | Test |
|---|---|---|
| True | The passage guarantees the statement | No situation consistent with the passage makes it false |
| False | The passage guarantees the opposite | No situation consistent with the passage makes it true |
| Cannot be deduced | The passage allows both | One situation consistent with the passage makes it true, another makes it false |
"True" does not mean "probably true", "reasonable" or "what usually happens". It means the passage leaves no alternative. "False" does not mean "not mentioned"; it means the passage rules the statement out. Everything in between is "cannot be deduced".
The two-scenario test
The most reliable way to decide is to try to build situations.
- Accept everything the passage says, and nothing else.
- Try to describe a situation that fits the passage and makes the statement true.
- Try to describe a situation that fits the passage and makes the statement false.
If only the first is possible, the answer is true. If only the second, false. If both, cannot be deduced. With numbers, the situations can be concrete: invent figures that satisfy the passage and see what happens to the statement. One pair of invented figures that goes each way settles a "cannot be deduced".
Only the passage counts
Your own knowledge stays out. If a passage about an invented bank says nothing about its interest rates, a statement about those rates cannot be deduced, however predictable it seems. Equally, a statement you know to be true in the real world is not "true" here unless the passage supports it.
What you may, and must, use is the ordinary meaning of words and simple arithmetic. If the passage says revenue rose by 10% and costs by 12%, you are entitled to work out what that does to costs as a share of revenue.
Words that change the verdict
- Some means at least one, and possibly all. "Some managers work remotely" does not imply that some do not.
- All is contradicted by a single exception, so the opposite of "all" is "not all", not "none".
- Every A is B does not mean every B is A. If every night-shift worker gets a supplement, a day worker might get it too, for another reason.
- Most means more than half.
- Only, unless and if set conditions that run in one direction; the lesson on quantifiers and conditionals covers them.
A sensible order of work
Read the passage carefully once, because each word may matter. Then, for each statement:
- find the sentence or sentences of the passage it relates to;
- decide whether the statement adds anything those sentences do not give;
- run the two-scenario test.
If the statement restates, combines or follows arithmetically from the passage, it is true. If it contradicts the passage, it is false. If it goes beyond the passage in any way, it cannot be deduced.
Guessing with three options
With three options, a blind guess has a one-in-three chance of +1 and a two-in-three chance of −0.33, an expected value of about +0.11 points. Once you can rule out one verdict with confidence, a guess between the other two is worth about a third of a point on average. The lesson on negative marking and guessing works through the numbers.
Worked examples
Example 1: Three statements, three verdicts
All the cooperatives in the Lavine valley sell their wine through a single distributor, Vinaria. Vinaria also sells wine from producers outside the valley. Cantina Rossa is a cooperative in the Lavine valley.
Judge each statement: (1) Cantina Rossa sells its wine through Vinaria. (2) Every wine Vinaria sells comes from the Lavine valley. (3) Some producers outside the valley are cooperatives.
Statement 1 combines two sentences: all valley cooperatives sell through Vinaria, and Cantina Rossa is a valley cooperative. No situation fitting the passage makes it false. True.
Statement 2 is contradicted by the second sentence: Vinaria sells wine from producers outside the valley. False.
Statement 3: the passage says nothing about whether producers outside the valley are cooperatives. A situation where some are and one where none are both fit the passage. Cannot be deduced.
Answer
True, false, cannot be deduced. Statement 3 is the one people get wrong, by marking it false because the passage never says so; "not stated" is not "false".
Example 2: Using invented figures
In 2025 a bakery's revenue rose by 10% and its costs rose by 12%.
Judge each statement: (1) The bakery's profit fell in 2025. (2) The bakery's costs as a share of its revenue rose in 2025.
Statement 1, first situation: revenue 100 rises to 110, costs 50 rise to . Profit goes from 50 to 54: it rose.
Second situation: revenue 100 rises to 110, costs 95 rise to . Profit goes from 5 to 3.6: it fell.
Both situations fit the passage, so statement 1 cannot be deduced.
Statement 2: the ratio costs ÷ revenue is multiplied by , which is greater than 1, whatever the starting figures. So the share rose. True.
Answer
Statement 1 cannot be deduced; statement 2 is true. Marking statement 1 true ("costs grew faster, so profit fell") is the tempting error: it holds only if costs were already a large part of revenue.
Example 3: Some, and the rest
Some of the firm's managers work remotely.
Judge the statement: Some of the firm's managers do not work remotely.
"Some" means at least one, and possibly all.
Situation 1: three of ten managers work remotely; then some do not, and the statement is true.
Situation 2: all ten work remotely; "some work remotely" is still true, and the statement is false.
Answer
Cannot be deduced. In conversation "some" hints "not all", but the passage does not say so.
Common traps
Not mentioned is not false
A statement about something the passage does not discuss feels wrong, so it is marked false. False requires the passage to rule it out. If the passage is simply silent, the verdict is cannot be deduced.
Likely is not true
A statement that would usually follow in real life (costs grew faster, so profit fell) is marked true. True requires that no situation fitting the passage makes it false. Try to build one; if you can, it is not true.
Reading "every A is B" backwards
"Every night-shift worker gets the supplement" is read as "only night-shift workers get it". The rule says nothing about anyone else. Keep the direction of the rule.
Bringing in the real world
Your knowledge of how banks, firms or markets usually behave fills a gap in the passage. On these items the passage is the whole world. Use only its statements, ordinary word meanings and arithmetic.
Check yourself
Answer each question before you open its answer.
Question 1: Does Marta get the supplement?
Critical thinking
Every employee of Orsa Logistics who works night shifts receives a 15% pay supplement. Some employees at Orsa's north depot work night shifts. No employee at Orsa's south depot works night shifts. Marta is an employee at the south depot.
Is the following statement true, false, or can it not be deduced from the passage? Marta does not receive a 15% pay supplement.
- A.True
- B.False
- C.Cannot be deduced
Show the answer
Answer: C. Cannot be deduced
Working
Marta works at the south depot, where no one works night shifts, so the night-shift rule does not apply to her. But the rule runs one way: night-shift work guarantees the supplement; the passage does not say that the supplement is paid only for night shifts. A situation where Marta receives a 15% supplement for some other reason fits the passage, and so does one where she receives none. The statement cannot be deduced.
Why the other options are wrong
- A. Assumes that only night-shift workers receive the supplement. The passage says every night-shift worker receives it, not that no one else does.
- B. Nothing in the passage says Marta receives the supplement; she works at a depot with no night shifts, so the rule does not give it to her.
What carries over
"Every A is B" says nothing about those who are not A.
Question 2: Night shifts at the south depot
Critical thinking
Every employee of Orsa Logistics who works night shifts receives a 15% pay supplement. Some employees at Orsa's north depot work night shifts. No employee at Orsa's south depot works night shifts. Marta is an employee at the south depot.
Is the following statement true, false, or can it not be deduced from the passage? At least one employee at the south depot works night shifts.
- A.True
- B.False
- C.Cannot be deduced
Show the answer
Answer: B. False
Working
The third sentence says "No employee at Orsa's south depot works night shifts." The statement claims at least one does, which is the exact opposite. No situation consistent with the passage makes it true, so it is false.
Why the other options are wrong
- A. Perhaps confuses the depots: it is the north depot where some employees work night shifts.
- C. The passage is not silent here: it says no employee at the south depot works night shifts, which rules the statement out.
What carries over
A statement is false only when the passage rules it out, as "no employee" rules out "at least one employee".
Question 3: Up 20%, then down 20%
Critical thinking
A firm's sales in 2024 were 20% higher than in 2023. Its sales in 2025 were 20% lower than in 2024.
Is the following statement true, false, or can it not be deduced from the passage? The firm's sales in 2025 were lower than its sales in 2023.
- A.True
- B.False
- C.Cannot be deduced
Show the answer
Answer: A. True
Working
Let 2023 sales be . Then 2024 sales are and 2025 sales are . Whatever is (sales are positive), . The statement follows from the passage by arithmetic alone, so it is true.
Why the other options are wrong
- B. Assumes a 20% rise and a 20% fall cancel, or that the fall leaves sales higher. They do not cancel: the fall is taken of the larger 2024 figure.
- C. No extra data is needed: the result holds for every starting value, because 2025 sales are always 96% of 2023 sales.
What carries over
Arithmetic on the passage’s own figures is allowed; if a result holds for every starting value, the statement is true.
Key points
True means the passage leaves no alternative; false means it rules the statement out; anything else cannot be deduced.
Test with two situations: if one fits the passage and makes the statement true and another makes it false, it cannot be deduced.
"Not mentioned" is not false, and "likely" is not true.
Use only the passage, the ordinary meaning of words and arithmetic.
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.