Quantitative Battery: Number Analogies, Number Puzzles, and Number Series
The Quantitative battery of CogAT Level 11 tests reasoning with number relationships, not calculation speed. Its three subtests, Number Analogies, Number Puzzles and Number Series, reward one habit: find the rule, state it, then test it before you use it. Level 11 items use whole numbers, simple fractions and decimals, and the standard order of operations.
Number Analogies
Two complete pairs are shown, then a third pair with the second number missing, for example [3 to 12] [5 to 20] [7 to ?]. Derive a rule that works for both complete pairs, write it as an equation, and apply it. Many rules are two-step: n becomes 2n + 3, or n squared minus 1, or n divided by 2 plus 4. If a candidate rule fits the first pair but not the second, discard it.
Number Puzzles
One value is missing from an equation. Undo the operations in reverse order: if the missing number is multiplied and the result is then added to something, subtract first, then divide. Substitute your answer back into the original equation to check.
Number Series
Check differences first; if they are constant you are done. If not, look at second differences, at ratios, or at two interleaved sequences where positions 1, 3, 5 follow one rule and positions 2, 4, 6 follow another. Squares, cubes and 'double then add 1' rules are common at this level.
Worked example
6 + 3 x ? = 24 Multiplication comes before addition. Subtract 6 from both sides: 3 x ? = 18. Divide both sides by 3: ? = 6. Check: 6 + 3 x 6 = 6 + 18 = 24. Working left to right, (6 + 3) x ? = 24 gives about 2.67, and 24 divided by 3 gives 8; both are tempting wrong answers and both appear among the distractors.
Traps that cost marks
- Accepting a rule that fits only the first complete pair.
- Ignoring order of operations when a puzzle mixes multiplication and addition.
- Assuming a constant difference when the steps are actually growing.
- Missing an alternating series because the differences jump up and down.
- Reporting the last difference instead of the next term.