Key takeaways
- The method is one habit: say the relationship between the first pair as a complete sentence, then substitute each option into that sentence and see which survives.
- Analogies are judged on shared relations, not shared attributes. Two things that look alike may be unrelated, and two things that look nothing alike may map perfectly.
- Direction is part of the relationship. If the first pair runs creator to work, the second must too, and an option that reverses the order is wrong however apt it seems.
- Distractors are usually built to match the surface — a word strongly associated with the third term, but not by the relation you identified.
- Number analogies are underdetermined by a single pair, because more than one rule fits any two numbers; a second worked pair is what fixes the rule.
- IQ Test & Brain Training Games, our own app, lists analogies among its logic games and ratios in its mental math practice, so the sentence-first habit and the arithmetic behind number analogies both have somewhere to be practised.
The method for analogy questions fits in one sentence: say the relationship between the first pair out loud as a complete sentence, then test each option by substituting it into that same sentence. Everything else in this article is elaboration on that, because the failures almost all come from skipping it — reading the options first, feeling a pull towards one, and reverse-engineering a relationship that justifies the pull.
An analogy in the classic form is written A : B :: C : D, read as "A is to B as C is to D". You are given three of the four terms and choose the fourth. What is being tested is whether you can identify a relation and carry it across to a new pair.
Relations, not resemblances
The single most useful idea in this subject is that analogies run on shared relations rather than shared attributes. The Stanford Encyclopedia of Philosophy's entry on analogical reasoning sets this out carefully: an analogical argument maps from a source domain to a target domain, and what gets mapped is a system of relations, not a list of properties. Two domains are similar when they share many attributes; they are analogous when they share few attributes but many relations.
The review of relational reasoning by Lindsey Richland and Hongyang Zhao in Behavioral Sciences makes the same point from the education side: relational alignment, not surface similarity, is what an analogy trades on. Items that look identical can be structurally unrelated, and items that look nothing alike can share a deep relational structure.
For a solver, this converts directly into a rule. When you write your sentence, write it about a relation — "a thermometer is the instrument that measures temperature" — not about a resemblance. "A thermometer and temperature go together" is not a sentence you can test anything against.
A taxonomy of relationship types
Most items draw on a short list. Recognising which family you are in narrows the search immediately.
| Relationship | Example | The sentence |
|---|---|---|
| Instrument and quantity | thermometer : temperature | X is the instrument that measures Y |
| Part and whole | petal : flower | X is a part of Y |
| Member and category | sparrow : bird | X is a kind of Y |
| Degree | warm : hot | X is a milder form of Y |
| Opposition | ascend : descend | X is the opposite of Y |
| Worker and tool | chef : knife | X characteristically works with Y |
| Creator and work | composer : symphony | X produces Y |
| Cause and effect | drought : famine | X can bring about Y |
The table is not exhaustive and is not meant to be memorised as a list. Its use is diagnostic: run down it, find the row whose sentence fits the first pair, and you have your test.
Worked through: thermometer : temperature :: odometer : ? The sentence is "X is the instrument that measures Y". An odometer measures distance travelled, so distance completes it. Compare sparrow : bird :: trout : ? — "X is a kind of Y" gives fish.
Direction, and the distractor built to exploit it
Relations have a direction, and an analogy must preserve it. "Composer is to symphony" runs creator to work. If the answer options include a pair that runs work to creator, it is wrong no matter how natural the pairing feels. Making the sentence explicit protects against this automatically, because a reversed pair produces a false sentence.
The other standard distractor is the surface match. Take hot : cold :: tall : ? The relation is opposition, so the answer is short. An option like height is strongly associated with tall and will exert a pull, but it does not survive the sentence: "tall is the opposite of height" is not true.
This is not accidental. Figural analogies are generated by software in precisely this way. The IMak package, described by Diego Blum and Heinz Holling in Frontiers in Psychology, builds items in the A : B :: C : ? form by applying rules such as rotation, reflection, segment removal and dot movement, and constructs the options by combining correct and incorrect outcomes for each rule. The correct option gets every rule right; each distractor gets at least one wrong while getting the rest right. That design is why a wrong option can feel three-quarters correct — it is.
Number analogies are underdetermined by one pair
Numerical analogies deserve separate treatment because they carry a problem that word analogies mostly avoid.
3 : 12 :: 5 : ?
Multiply by four gives 20. Add nine gives 14. Both rules fit the first pair exactly, and they disagree from the second pair onwards. Nothing in the item settles it, so any single answer is a guess dressed as reasoning.
Add a pair and the ambiguity evaporates. 3 : 12 :: 7 : 28 :: 5 : ? — adding nine would give 16 for the second pair, not 28, so the rule is multiplication by four and the answer is 20. This is the same underdetermination that afflicts short number sequences, treated at length in our guide to number sequence puzzles.
The other common numerical form is a straight ratio: 2 : 3 :: 8 : ? Here the relation is proportional rather than a rule applied to one number, and the answer is 12, because 8 is four times 2 and 12 is four times 3. Scaling both terms by the same factor is exactly the move that makes recipe adjustments and map scales tractable, and the arithmetic behind doing it quickly is covered in our mental math training guide.
Building the habit
The sentence-first method is a habit rather than a piece of knowledge, and habits install through repetition with feedback. Two things help. First, write the sentence down at the start; the act of committing to specific wording is what prevents the vague "they go together" formulation. Second, treat naming the relation as an encoding task in its own right — putting a relationship into your own words is a form of elaboration, which our guide to memory techniques that work covers as a general principle.
On our own app: IQ Test & Brain Training Games, built by Reign Creative, lists analogies among its logic games, alongside sequences, conditional reasoning and deduction, and its vocabulary games work on synonyms, antonyms and context clues — so the sentence-first habit has somewhere to be practised. Its listing does not say which relationship types or formats the analogy items use. Its mental math practice also covers ratios, the arithmetic that numerical analogies of the ratio form depend on. The app's IQ-style test covers logic, patterns and vocabulary too, and its Google Play listing describes the results as estimates based on app activities, not clinical or professional assessments. The app itself is described on the IQ Test & Brain Training Games app page.
If the figural version of this format is what you are after, the construction of grid items is dissected in how a matrix puzzle is built, and the wider question of what follows from what is the subject of deductive reasoning. The full set sits in the logic and pattern puzzles hub, alongside our other writing in the education and brain training section.
Good to know
Frequently asked questions
What is the best way to approach an analogy question?
Why does the wrong answer often feel right?
How do number analogies work?
Does the app have analogy puzzles?
Sources
- Analogy and Analogical Reasoning (opens in a new tab)Stanford Encyclopedia of Philosophy — accessed
- Relational Reasoning and Educational Applications (opens in a new tab)Behavioral Sciences, via PubMed Central — accessed
- Automatic Generation of Figural Analogies With the IMak Package (opens in a new tab)Frontiers in Psychology, via PubMed Central — accessed
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