Quantitative Reasoning
Quantitative Reasoning tests number sense and pattern logic, not just calculation. On CogAT Level 9 (Grade 3) the Quantitative Battery has three subtests: Number Analogies, Number Puzzles, and Number Series. Items use whole numbers and the four operations, with simple fractions and place value appearing at this level. Answer choices are numbers.
Number Analogies
Two pairs are shown: the first is complete, and the second has a missing number. Find the rule that turns the first number into its partner, then apply the same rule to the first number of the second pair. Rules may be one step (multiply by 4) or two steps (add 2, then multiply by 3). Test your rule on the complete pair before using it.
Number Puzzles
An equation has a missing value, often shown inside a shape. Use inverse operations: if ? + 7 = 15, subtract 7. If 4 x ? = 24, divide by 4. Always substitute your answer back into the puzzle to check that both sides balance.
Number Series
Look at how the numbers change. Check differences first: 2, 5, 8, 11 adds 3 each time. If the differences are not constant, check whether the numbers double or halve, or whether two patterns alternate, such as add 4, subtract 1, add 4, subtract 1.
Worked example
Analogy: 3 -> 12, 5 -> 20, 7 -> ? 3 x 4 = 12 and 5 x 4 = 20, so the rule is "multiply by 4." Apply it: 7 x 4 = 28. Check: 28 makes the pair 7 -> 28 consistent with both earlier pairs. Choosing 11 would just add 4, which fits 3 -> 7 but not the completed pairs, so it fails.
Traps that cost marks
- Using addition when the completed pair shows multiplication.
- Assuming every series adds the same number.
- Missing a two-step rule and stopping after the first operation.
- Solving for the wrong side of the equation in a puzzle.
- Not checking the answer in the original equation.