Quantitative Reasoning
What the quantitative battery measures
The Quantitative battery on CogAT Levels 13–18 has three subtests: Number Analogies, Number Puzzles, and Number Series. The arithmetic is deliberately simple - the score reflects how reliably you find the underlying rule, not how fast you compute. Battery results are reported as a Standard Age Score (mean 100, standard deviation 16) and an age stanine (1–9); the three battery scores also combine into a composite and an ability profile letter (A = flat profile, B = one score deviating, C = two, E = two deviating in opposite directions).
Number Analogies
Two complete pairs establish a rule; apply it to the third pair. The rule must hold for both given pairs, so always verify on the second pair before answering. Common rules: add or subtract a constant, multiply or divide, square or cube, 2n + 3, digit sum, reverse the digits.
Number Puzzles
An equation with one missing value, e.g. 4 × ? − 6 = 22. Work backwards with inverse operations in reverse order: add 6 to get 28, divide by 4 to get 7. Or substitute answer choices, starting with the middle value. Watch grouping symbols and negative numbers.
Number Series
Take first differences. If they are not constant, look at second differences, ratios, alternating subsequences (two interleaved series), square or cube patterns, or a two-step rule such as 'multiply by 2, then add 1.'
Worked example
2, 5, 11, 23, 47, ? Differences: 3, 6, 12, 24 - each doubles, so the next difference is 48 and the answer is 47 + 48 = 95. Cross-check with a multiplicative rule: 2×2+1 = 5, 5×2+1 = 11, 11×2+1 = 23, 23×2+1 = 47, 47×2+1 = 95. Two independent rules agreeing is strong confirmation.
Traps that cost marks
- Locking onto a constant difference after two terms; geometric or combined rules are common at this level.
- Fitting a rule to one pair without checking it against the second.
- Order-of-operations slips: 4 × ? − 6 is not 4 × (? − 6).
- Stopping at the first workable rule - series can be ambiguous, so test it on every term.
- Misreading which term is requested; some items ask for a middle term, not the next one.