Quantitative Reasoning
What the Quantitative battery measures
The Quantitative battery of CogAT Form 7 assesses numerical reasoning through Number Analogies, Number Series, and Number Puzzles. The items are designed so that arithmetic alone is not enough: you must infer the rule that generates the numbers and apply it.
Core rules and concepts
- Number Analogies: Two complete pairs establish a rule; apply the same rule to the third pair. The rule can be one step (add 4, multiply by 3) or two steps (add 2, then double). Check the rule on both complete pairs before using it.
- Number Series: A sequence follows a consistent pattern. First look at differences; if they are not constant, look at ratios, alternating patterns (two interleaved sequences), square numbers, or differences that themselves change in a pattern.
- Number Puzzles: An equation has one missing element-a number or an operation sign. Use inverse operations or fact families, and check whether the blank is in the position of an operator.
Worked example
6 → 18, 4 → 12, 9 → ? Test the first pair: 6 × 3 = 18. Test the second: 4 × 3 = 12. The rule is “multiply by 3.” Apply it to 9: 9 × 3 = 27. Answer: 27. If the choices include 12 or 18, they are distractors built from the input numbers or a partial rule.
Traps that cost marks
- Assuming the first operation you notice is the whole rule; always verify it on the second complete pair.
- In Number Series, stopping after first differences when the sequence actually uses second-order differences, doubling differences, or two alternating rules.
- In Number Puzzles, solving for a missing number when the blank is an operation sign-check the form of the answer choices.
- Rushing because the numbers look simple; distractors often come from common calculation slips or from applying the rule only once.