Inference questions: what must be true

A different job

In most Critical Reasoning questions the passage contains an argument with a gap, and you work on the gap. Inference questions turn this round. The passage is usually a set of facts with no conclusion, and you must choose the conclusion they support. Typical stems:

• "If the statements above are true, which of the following must also be true?"
• "The statements above, if true, most strongly support which of the following?"
• "Which of the following can be properly inferred from the information above?"

Treat every statement in the passage as true, and nothing else. Your own knowledge, however reasonable, is not evidence here.

The standard of proof

"Must be true" is strict: the right answer cannot be false if the statements are true. "Most strongly supported" is a little looser: the right answer is the one the statements make most likely, but in practice it is almost always something that follows with near certainty. In both cases the test for each option is the same: can I imagine the statements all being true while this option is false? If you can, reject the option.

This is the reverse of everyday reading. In conversation, "most of the club's members voted" suggests that some did not, and "the drug reduced symptoms" suggests it worked well. In an inference question, "most" means only "more than half", and could even be all; "reduced" means only "made smaller".

Combining statements

The best answers usually join two statements. If every member who entered the tournament won a game, and no one who won a game had played in a tournament before, then every member who entered was new to tournaments. Neither statement alone says this. When the passage has several facts, look for a shared term that lets you chain them:

$$\text{A} \rightarrow \text{B}, \quad \text{B} \rightarrow \text{C} \quad \text{so} \quad \text{A} \rightarrow \text{C}$$

Quantifiers

Statement	What follows	What does not follow
All A are B	Any particular A is B	All B are A (the converse)
No A are B	No B are A	Anything about things that are not A
Some A are B	Some B are A	Some A are not B
Most A are B	At least one A is B	Most B are A

The converse ("all B are A") is the single most common wrong answer in inference questions. "Every household with solar panels received the grant" does not mean every household that received the grant has solar panels.

Numbers, rates and shares

Numerical inference questions reward working from the definition. A share is a part divided by a whole, so a share and a number can move differently when the whole changes. If the part-time share of a workforce rises while the workforce shrinks, the number of part-time workers might rise or fall; but the full-time share has fallen and the whole has fallen, so the number of full-time workers must have fallen. When in doubt, try two sets of numbers that fit the statements: if the option is true in one and false in the other, it is not a "must be true".

Wrong-answer patterns

1. Goes one step too far. It adds a reason, a prediction or a recommendation. "Higher-income households cannot afford panels" gives a reason the passage never offers.
2. Converse. It reverses an "all" statement.
3. Strengthened quantifier. It turns "some" into "most", or "most" into "all".
4. Possible but not required. It could be true, and might even be likely, but the statements allow it to be false.
5. Contradicts the passage. Surprisingly common, and easy to fall for if you read the passage quickly.

Modest answers win

Because the right answer must survive every situation consistent with the statements, it tends to be cautious: "at least some", "not all", "was lower than". Strong, sweeping options are not automatically wrong, but they need strong support in the passage, and usually it is not there.

A routine

1. Read every statement, noting quantifiers and measures (number, share, average).
2. Look for a shared term that lets you combine two statements.
3. For each option, try to build a situation where the statements hold and the option fails.
4. Choose the option for which you cannot build one.