Quantitative Reasoning
The Quantitative battery tests number sense and pattern detection rather than memorized formulas. Its three subtests are Number Analogies, Number Puzzles, and Number Series. Level 12 items use whole numbers with some fractions and decimals, and most rules combine two operations rather than one, so the first rule that comes to mind is frequently a trap.
Number analogies
You get two complete pairs plus a third pair with one missing value. Find a rule that holds for both complete pairs; a rule that fits only the first pair is not the rule. State it with numbers - 'multiply by 3, then subtract 1' - and apply it in the same order to the third pair. If your rule needs an exception to work on the second pair, discard it and look again.
Number puzzles
An equation hides one value, for example 8 × ? = 60 − 12. Simplify the side that is already complete first (60 − 12 = 48), then undo operations in reverse order (48 ÷ 8 = 6). Substitute your answer back into the original equation to confirm it.
Number series
Start with first differences. If they do not settle into a pattern, look at second differences. Also test alternating rules on odd and even positions, combined operations such as ×2 + 1, perfect squares and near-squares, and digit-based rules. Confirm any rule against at least two consecutive steps before extending it.
Worked example
4, 9, 19, 39, ?
First differences are 5, 10, 20 - each doubles - so the next difference is 40 and the answer is 79. Verify with a second rule: ×2 + 1 gives 4→9→19→39→79. Two independent rules agreeing on the same value is strong confirmation that you have the intended pattern.
Traps that cost marks
- Assuming a constant difference when the series is actually multiplicative.
- Extending a rule that fits only the final step but fails on earlier terms.
- In puzzles, undoing an operation before simplifying the side that is already complete, or applying inverses in the wrong order.
- Applying a single rule to every term of an alternating series instead of splitting odd and even positions.
- Silent arithmetic slips: write down the one operation you are performing at each step.