You can solve almost any deductive reasoning question with the same four moves: restate the premises in plain words, draw them, test every answer option against the drawing, and eliminate what fails. The test for each option is a single question: do the premises force it? Anything that merely sounds sensible is out.
Set up the problem
Step 1: treat the statements as a closed world
Read the instruction line before you read the statements, because "must be true", "could be true" and "cannot be true" call for different answers. Then read the statements as the only facts that exist. If you catch yourself reasoning from something you know that is not on the page, stop and delete that thought.
Mark the small words that carry the logic: all, no, some, if, only if, unless, either, not. Those words are where the traps live.
Step 2: restate each premise in neutral shorthand
Rewrite every premise using letters in place of topics. "All members of the audit team are reviewed by a manager" becomes "All A are R". "If the budget is cut, hiring stops" becomes "If B then H".
The letters do real work. Experiments on belief bias, such as the 1983 study by Jonathan Evans, Julie Barston and Paul Pollard, found that how believable a conclusion sounds affects whether people accept it. Letters have no believability, so they strip that influence out.
Draw it, test it, eliminate
Step 3: draw it, and draw every possibility
Pick the picture that suits the statements.
- All, no and some: overlapping circles, one per group.
- If-then rules: arrows, written both ways, so "P to Q" is always paired with "not-Q to not-P".
- Ordering and ranking: a line with names placed along it, leaving room for names whose position is not fixed yet.
- Either-or: a small box listing the allowed cases.
In an experiment on diagrams and deduction, Malcolm Bauer and Philip Johnson-Laird found that diagrams helped people reason faster and reach more valid conclusions when the diagram made the alternative possibilities explicit. A preliminary version that did not do this had no effect. So do not draw one tidy scenario. Draw everything the premises allow.
Step 4: try to break each option
For each answer option, search the drawing for a picture in which every premise holds and the option fails. If you find one, the option does not follow. If you cannot find one after a real attempt, it follows.
Searching for a breaker goes against the grain, because people tend to look for cases that confirm what they already think. Raymond Nickerson's review of confirmation bias describes that tendency in detail, and the counterexample hunt is the deliberate remedy.
Step 5: eliminate, then decide
Cross off the options you have broken. If two survive, re-read the quantifiers, because "all" and "some" are the usual difference. If none survive, check whether you smuggled in an outside fact or misread an "if".
When the format offers "cannot be determined", you should be able to draw one picture where the conclusion holds and another where it fails. That is what "cannot be determined" means, and having both pictures protects you from guessing.
Two worked examples
A short worked example
Statements: "Every report from the audit team is reviewed by a manager. Some reviewed documents are returned for changes. No document returned for changes is filed this week." Which option follows?
- A. Some audit reports are returned for changes. Draw it: the returned documents that were reviewed might all be other kinds of document. A can fail, so it does not follow.
- B. Some reviewed documents are not filed this week. Some reviewed documents are returned, and no returned document is filed this week, so those documents are not filed this week. B follows.
- C. No audit report is filed this week. An audit report that is never returned is not covered by the third statement, so it could be filed. C can fail.
The answer is B. Notice that B was the only option you could prove, not the only one that sounded sensible.
A second example: ranking
Statements: "Five runners finished a race, with no ties. Ana finished ahead of Ben. Ben finished ahead of Cleo. Dev finished ahead of Ana. Eli finished ahead of Cleo." Which is certain? A: Dev finished first. B: Cleo finished last. C: Ana finished ahead of Eli.
Draw two chains: Dev, Ana, Ben, Cleo, and separately Eli, Cleo. Cleo is behind all four of the others, so B is certain.
Eli can slot in anywhere above Cleo. Put Eli first and A fails. Put Eli between Dev and Ana and C fails. The drawing shows the loose ends at a glance, and loose ends are where "cannot be determined" lives.
Habits that save time and points
- Read the question stem again after you read the options.
- Be suspicious of strong words in options. An option saying "all" or "no" needs strong premises, while "some" needs far less.
- Do not re-derive a drawing you already have. Check new options against the picture.
- If a question is eating your time, mark it and move on. The next guide, deductive reasoning test pacing tips, shows how.
For more problems with the reasoning written out step by step, see deductive reasoning examples with answers.
Try the method
The JobCannon Deductive Reasoning Test is a good place to practise these steps, because its questions are built around "follows / does not follow" conclusions from a set of statements, with syllogisms, if-then rules and ranking puzzles. JobCannon's older logical reasoning test is a broader mix that adds analytical puzzles. The questions are written in-house, so use the result as practice feedback.