Quantitative Reasoning: Analogies, Series, and Puzzles
The Quantitative Reasoning battery tests how you reason with number and quantity. Calculation speed is not the point: the arithmetic is kept easy so that the pattern, not the computation, is what separates answers. Form 7/8 uses Number Analogies, Number Series, and Number Puzzles; K–2 versions present the same reasoning with picture-supported items. Results are reported as a Standard Age Score with a mean of 100 and a standard deviation of 16, plus a stanine from 1 to 9.
The three item types
- Number analogy: two pairs governed by the same rule. Find the rule on the complete pair, then apply it to the incomplete one. Rules may be one step (×3) or two (×2 then +1).
- Number series: a list following a rule; supply the next or missing term.
- Number puzzle: a short statement or equation with a missing value; translate it into an equation, or back-solve from the answer choices.
Rules that decide the answer
- Test the simplest rule first on all terms; if it breaks, escalate to a two-step rule.
- Write the differences between consecutive terms. If the differences change, look at how they change.
- When terms alternate high/low, check for two interleaved sequences.
- Back-solving from choices is often faster and safer than algebra under time pressure.
Worked example
3, 6, 11, 18, 27, ? Differences: 3, 5, 7, 9 - increasing by 2 each time, so the next difference is 11 and the term is 38. Confirm with a second rule: each term equals n² + 2 for n = 1, 2, 3, 4, 5, giving 3, 6, 11, 18, 27; the sixth term is 36 + 2 = 38. Two independent rules agreeing is strong evidence.
Traps
- Committing to a constant difference after seeing only one pair of terms.
- Off-by-one counting: the number of integers from 12 to 30 inclusive is 30 − 12 + 1 = 19, not 18.
- Reversing a comparison: "how many more than" is not "how many fewer than".
- Dropping a remainder in division items or ignoring units.
- Order of operations in puzzles: 4 + 3 × 5 = 19, not 35.