DAT Quantitative Reasoning: The Quantitative Comparison Answer System

DAT High-Yield Concept

The Fixed Four Choices: Every Quantitative Comparison (QC) prompt uses four unchanged answer choices: Choice A (Quantity A is greater), Choice B (Quantity B is greater), Choice C (The two quantities are equal), or Choice D (The relationship cannot be determined).
Relative Focus: Evaluate strictly whether Quantity A is larger, smaller, or equal to Quantity B—never waste time calculating standalone magnitudes unless required for comparison.
The Pure Numbers Rule: Choice D ("Cannot be determined") is never correct if both columns contain only pure numerical constants with no variables.
Universal Shared Context: Any centered information, figure, or variable restriction presented above the two columns applies simultaneously to both Quantity A and Quantity B.

1. The Four Fixed Answer Choices

Quantitative Comparison (QC) questions on the DAT test efficiency and mathematical reasoning. Every QC problem presents two quantities in side-by-side columns labeled Quantity A and Quantity B. Unlike standard multiple-choice questions or Data Sufficiency questions (which use a fixed five-choice framework covered in depth in its own lesson), QC prompts strictly rely on four fixed options:

(A) Quantity A is greater.
(B) Quantity B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined from the information given.

Core Distinction: Your goal is solely to determine the relative relationship between Quantity A and Quantity B. You do not need to determine how large either quantity is individually on its own. Avoid performing long absolute calculations when algebraic reduction or qualitative estimation yields the relationship.

2. Assessing Relative Relationship vs. Absolute Magnitude

A common mistake on the DAT is calculating exact decimal or integer values for both columns. Optimization requires simplifying the expressions comparatively. You can add, subtract, multiply, or divide both columns by positive terms—just like manipulating an inequality—without changing their relative order.

Worked Example: Relative Exponent Comparison

Question: Compare the two quantities.

Quantity A: A = $2^{100}$
Quantity B: B = $3^{75}$

Step-by-Step Reasoning:

Calculating $2^{100}$ or $3^{75}$ directly is impossible without a scientific calculator. Instead, analyze their base-exponent structure using power rules.
Notice that both exponents are multiples of $25$ . Rewrite both quantities using the exponent rule $x^{a \times b} = (x^a)^b$ :
$Quantity\ A = 2^{100} = (2^4)^{25} = 16^{25}$
$Quantity\ B = 3^{75} = (3^3)^{25} = 27^{25}$
Because both quantities now share the positive exponent $25$ , compare their bases directly: $16 < 27$ . Thus, $16^{25} < 27^{25}$ .
Therefore, Quantity B is greater than Quantity A.

Answer: (B)

Common Exam Trap: Trying to compute exact magnitudes rather than rewriting expressions into a shared exponent power base.

3. The "Pure Numbers" Rule for Choice (D)

Choice (D), "The relationship cannot be determined from the information given," means that different valid inputs yield conflicting relative relationships (e.g., Quantity A is larger for one value, but Quantity B is larger for another).

However, pure numbers containing no unknown variables are mathematical constants on the real line. Their relationship is fixed and immutable. Therefore, Choice D can NEVER be the correct answer when both columns contain only pure numbers.

Worked Example: Comparing Pure Radical Numbers

Question: Compare the two quantities.

Quantity A: $\frac{\sqrt{50}}{2}$
Quantity B: $\frac{7}{2}$

Step-by-Step Reasoning:

Identify that both columns contain only pure numbers and zero variables. Instantly rule out Choice (D).
Because both columns share a positive denominator of $2$ , multiply both columns by $2$ :
Quantity A becomes $\sqrt{50}$ , while Quantity B becomes $7$ .
Express $7$ as a radical to compare directly: $7 = \sqrt{49}$ .
Compare the radicals: $\sqrt{50} > \sqrt{49}$ . Therefore, Quantity A is greater than Quantity B.

Answer: (A)

Common Exam Trap: Selecting Choice (D) out of confusion when encountering complex fractions or roots, forgetting that pure numbers must have a fixed, deterministic answer (A, B, or C).

4. Shared Context Given Above the Columns

Centered text, equations, constraints, or geometric diagrams provided above the columns set the stage for the entire problem. This shared information applies equally and simultaneously to both Quantity A and Quantity B. Never evaluate one column under the given premise while ignoring it for the other.

Worked Example: Shared Variable Constraint

Centered Information: Given that $x$ is a negative integer ( $x \in \mathbb{Z}^-$ ).

Quantity A: $x^2 + 1$
Quantity B: $(x - 1)^2$

Step-by-Step Reasoning:

Expand Quantity B algebraically: $(x - 1)^2 = x^2 - 2x + 1$ .
Subtract the common terms $x^2 + 1$ from both columns:
$Quantity\ A: (x^2 + 1) - (x^2 + 1) = 0$
$Quantity\ B: (x^2 - 2x + 1) - (x^2 + 1) = -2x$
Now apply the shared constraint given above the columns: $x$ is negative ( $x < 0$ ).
If $x < 0$ , then multiplying $x$ by $-2$ yields a strictly positive value: $-2x > 0$ .
Because $-2x > 0$ , Quantity B is greater than Quantity A ( $0$ ) for all negative integers.

Answer: (B)

Common Exam Trap: Forgetting the constraint $x < 0$ from the shared heading, testing a positive number like $x = 2$ (where Quantity A = $5$ and Quantity B = $1$ ), and incorrectly picking Choice (D).

5. Quantitative Comparison Decision Rules

Answer Choice	Mathematical Meaning	Key Testing Strategy
(A) Quantity A is greater	Quantity A $>$ Quantity B for all valid conditions.	Prove true across all constrained variable domains.
(B) Quantity B is greater	Quantity B $>$ Quantity A for all valid conditions.	Simplify algebraically or test extremes (fractions, negative values, zero).
(C) The quantities are equal	Quantity A $=$ Quantity B universally.	Algebraic reduction yields identical expressions.
(D) Cannot be determined	The relationship changes depending on chosen valid inputs.	Never pick for pure numbers. Pick when plugging in different valid numbers gives conflicting results (e.g., A is bigger for $x=2$ , but B is bigger for $x=0$ ).

Memory Aid — The "P-U-R-E" QC Checklist:

P — Pure numbers? Rule out Choice D immediately!
U — Universal context? Apply centered information above the columns to BOTH quantities.
R — Relative comparison! Do not compute standalone magnitudes if relative reduction works.
E — Evaluate boundary cases! If variables are present, test $0$ , $1$ , negative numbers, and fractions before deciding.

Critical Thinking Questions

If Quantity A is $\sqrt{x^2}$ and Quantity B is $x$ , under what centered constraint above the columns would Choice C be correct? Under what constraint would Choice A be correct?
Why is Choice D automatically ruled out for the comparison between $\pi^2$ and $9.86$ , even though $\pi$ is an irrational number?
When simplifying two algebraic expressions in Quantity A and Quantity B, why is multiplying both sides by an unknown variable $x$ a dangerous move unless centered information specifies $x > 0$ ?

References

Sources returned by Google Search grounding during lesson verification.

GRE Quantitative Comparison Questions - Manhattan Review — manhattanreview.com
GRE Quantitative Comparison Questions: Complete Strategy Guide - Test Ninjas — testninjas.com

The Quantitative Comparison Answer System

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