How to solve number analogies
Number analogies: find the operation
One hidden operation links each pair. Test simple operations in a fixed order and confirm on every pair shown.
Updated
'6 : 13 :: 9 : ?' hides one operation (here ×2+1). The failure mode is fixating on the first relation you spot — 6+7=13 — without checking whether it's the only one that fits. Items with two example pairs exist precisely to pin the operation down; use both.
The operation bank
In rising order of exoticness: add/subtract a constant · multiply by a constant · multiply then add/subtract · square (± a constant) · halve then add. On tests, if plain adding and plain multiplying both fail, try 'multiply then adjust' before anything fancier.
The strategy
- Compute b−a and b÷a for the first pair. Integer ratio? Suspect multiplication. Neither clean? Try ×k±m.
- Confirm the candidate operation on the second example pair if one is shown — a rule that fits only one pair is a guess.
- Apply the confirmed operation to the query number, predict, then match options.
- Sanity-check magnitude: if your answer is wildly larger or smaller than the pattern suggests, you picked the wrong operation.
Common traps
- 2 : 4 fits both +2 and ×2 — single-pair items on good tests choose numbers where only one operation works; if two work, re-read the pair.
- Sign slips on subtract-then-multiply variants.
- The options contain the result of the simpler but wrong operation. Confirmation beats speed here.
Speed · ~35s/item: The bank is small: testing it exhaustively takes under 40 seconds, which is faster than staring and hoping.
Try it yourself: 4 practice questions
Pick an answer, then reveal it. Nothing is recorded, there is no clock, and none of these questions is ever used in a test.
What comes next in the series?
Reveal the answer
The answer is A — 7.
Show why — the worked reasoning
What comes next in the series?
Reveal the answer
The answer is D — 3.
Show why — the worked reasoning
What comes next in the series?
Reveal the answer
The answer is B — 13.
Show why — the worked reasoning
What comes next in the series?
Reveal the answer
The answer is E — -3.
Show why — the worked reasoning
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Questions people ask
Will number analogies questions be on the free test?
Maybe. The free test gives numerical reasoning 5 of its 20 questions, spread across 13 different question types, so any one test may or may not include this kind.