QUANTITATIVE REASONING · QUANTITATIVE COMPARISON

Prove the relation.
Or break the claim.

Two study objectives connect exact differences, safe bounds, complete domains, and admissible counterexamples. Solve only as far as the comparison requires.

Start the guided lesson →Build a comparison set ↗See both objectives ↓
1official topic
2study objectives
1guided lesson
0invented weights

Official scope

One named line.
No fabricated quota.

The ADA lists Quantitative Comparison within Mathematical Problems. It does not publish a separate item count or topic weight for this line.

DAT TRAIN’s two objectives and five-choice questions are original study organization. They do not predict ADA frequency, wording, order, difficulty, or scoring, and this route is not a calibrated form or score converter.

OFFICIAL HIERARCHY → STUDY SEQUENCE

One branch. Two outcomes.

Inspect the fixed-relation and counterexample outcomes, their evidence limits, common traps, representations, and source trail before beginning.

C1Quantitative Comparison2 objectives
Objective 1QR-MAT-QCO-01

Compare without over-solving

Compare two quantities by simplifying a difference or ratio, bounding values, or selecting valid test cases.

Must know
The sign of A − B directly identifies their order when it can be determined. Bounds and monotonic behavior can settle a comparison without exact values.
Evidence limit
Division-based comparisons require a known nonzero denominator and sign-aware reasoning.
Common trap
Exact numerical values are required before two quantities can be compared. Structure, bounds, or a sign test may determine the relationship directly.
Representations
comparison · equation · inequality
Objective 2QR-MAT-QCO-02

Prove indeterminacy with counterexamples

Choose admissible values that produce different comparison outcomes when the relationship cannot be determined.

Must know
One valid case can disprove an ‘always’ claim; two valid cases with different outcomes prove indeterminacy. Every test value must satisfy all stated restrictions.
Evidence limit
A counterexample outside the prompt’s domain is not evidence.
Common trap
If two convenient examples agree, the relationship is determined. Agreement among examples does not replace a proof; search boundary and sign-changing cases.
Representations
comparison · table · number line

ANSWER INTEGRITY

Fixed claims need proof.
Variation needs witnesses.

  1. 01Exact difference

    The sign of A−B is recomputed with rational arithmetic.

  2. 02Safe bounds

    Separated ranges prove order; overlapping ranges do not overclaim.

  3. 03Valid witnesses

    Counterexamples must satisfy every stated restriction and disagree.

  4. 04Unique match

    The computed conclusion must match exactly one semantic choice.

Free source ladder

Trace scope and instruction.

ADA DAT 2026 Candidate GuideSection count, timing, calculator, and administration policy. ↗ADA DAT User’s ManualMathematical-problem split and Quantitative Comparison line. ↗OpenStax Algebra and Trigonometry 2eFree instruction for equations, inequalities, signs, and bounds. ↗