Quantitative Comparison is the signature question format of the GRE Quantitative Reasoning section. You are given two quantities and must decide which is greater, whether they are equal, or whether the relationship cannot be determined. When the underlying math involves arithmetic — percents, rates, exponents, integer properties, and sequences — specific patterns and traps recur with remarkable consistency. This guide breaks down the seven most common QC arithmetic patterns, walks you through two interactive worked examples, and gives you six practice questions drawn from an official-style question bank.
What Are Quantitative Comparison Arithmetic Questions?
Arithmetic QC questions present two quantities — Quantity A and Quantity B — where the comparison hinges on core arithmetic concepts: percentage calculations, ratio and rate problems, exponent and root relationships, absolute value, integer properties such as divisibility and primes, sequences, and decimal or fraction manipulation. Additional information (constraints, given values, or context) may appear above the two quantities. Your job is to select exactly one of the four fixed answer choices: (A) Quantity A is greater, (B) Quantity B is greater, (C) The two quantities are equal, or (D) The relationship cannot be determined from the information given.
These questions split into two categories. In fully determined comparisons, all values are fixed and you can compute a definite answer — A, B, or C. In variable-dependent comparisons, one or more unknowns appear with constraints, and you must test whether the comparison always goes one way or whether it can flip. The variable-dependent type frequently produces answer D, especially when exponential expressions with different bases are involved.
Format reminder: Every QC question on the GRE uses the same four answer choices — A, B, C, D — in the same order. There is no option E and no partial credit. If there are no variables in the problem, the answer is never D. Use this structural fact as a built-in sanity check.
7 Patterns You'll See
Nearly every QC arithmetic question on the GRE falls into one of seven recurring patterns. Learning to recognize these patterns instantly tells you what approach to use and which traps to watch for.
1
Percent Markup / Discount Comparison
A word problem describes a purchase, markup, or percent change. One quantity is the computed result; the other is a benchmark number. The key move is to compute the actual value and compare directly.
2
Rate / Work Comparison
Two machines or workers produce at different rates. You compare their outputs over different time periods. Convert each to a common unit (e.g., units per minute), multiply by time, then compare.
3
Exponent Comparison with Integer Variable
Compare exponential expressions with different bases. Because growth rates eventually cross over, the answer is often D. Always test at least two values of the variable.
4
Symmetric Percent Change on Dimensions
Dimensions change by +p% and −p%. The product changes by −(p2/100)%. A 10% increase and 10% decrease yields 0.99 of the original, not 1.00. Larger percentages produce larger losses.
5
Set Counting / Integer Properties
Count integers satisfying conditions (not perfect squares, not multiples of X, etc.). Use inclusion-exclusion and check boundary cases carefully — the count is always a fixed number.
6
Sequence and Pattern
Compare terms or sums of arithmetic or geometric sequences. Express all terms in terms of a single variable and simplify algebraically before computing.
7
Prime Number Identification
Identify primes in a specific range and compare. These are straightforward once you recall your primes — the challenge is speed and avoiding careless inclusion of composites like 27 or 51.
How to Solve QC Arithmetic Step by Step
These five strategies cover every QC arithmetic pattern. Apply them in order and you will handle each question efficiently while sidestepping the most common errors.
For percent and ratio problems, use benchmarks like 10%, 25%, 50%, or 100% to quickly estimate quantities. You do not need exact values — just enough precision to determine which side is larger. For example, if something is 40% more than $102, estimate: 40% of $100 is $40, so the result is roughly $142. Compare that to the other quantity and move on.
In a rate problem, you do not need the actual number of units produced — you only need to compare two rates multiplied by their respective times. If one side gives 6x and the other gives 5x with x greater than 0, stop computing: 6x is always greater than 5x. The GRE rewards strategic laziness.
When the problem involves expressions like af(x) versus bg(x) where a and b differ, plug in at least two values of x: a small value (e.g., x = 2) and a larger value (e.g., x = 5 or x = 10). If the comparison flips, the answer is D. Never stop after a single test case for exponent problems.
When dimensions change by +p% and −p%, the product changes by −(p2/100)% of the original. For +10% and -10%, the product is 0.99 of the original (a 1% loss). For +20% and -20%, the product is 0.96 of the original (a 4% loss). This formula is faster than computing both products individually.
For consecutive integer or consecutive odd/even problems, express all terms in terms of one variable (let the first term be n, then the next is n+2, etc.) and simplify both quantities. The variable often cancels entirely, giving you a direct numerical comparison.
Pro tip: Before doing any arithmetic, check whether the problem contains a variable. If it does, your first instinct should be to test two different values. If both values give the same winner, consider whether algebra can prove the result holds universally. If the values give different winners, the answer is D and you are done in under 30 seconds.
Worked Example: Comparing Fractions
Work through each step below. You must answer each mini-challenge correctly to unlock the next step. If you get stuck, a second wrong attempt will reveal the answer so you can keep going.
Interactive Walkthrough0/4 steps
Comparing Fractions with Different Operations
No additional constraints are given.
Quantity A
Quantity B
73+52
73×25
Quantity A is greater
Quantity B is greater
The two quantities are equal
Cannot be determined
1
Step 1: Compute Quantity A
Find a common denominator for 73+52. The LCD is 35. What is 3515+3514?
2
Step 2: Estimate Quantity A
3
Step 3: Compute Quantity B
4
Step 4: Compare the quantities
Worked Example: Powers of Negative Numbers
This example demonstrates how even and odd powers of negative numbers behave differently. Work through each step to see why the sign of each power determines the comparison.
Interactive Walkthrough0/5 steps
Comparing Powers of Negative Numbers
n=−3.
Quantity A
Quantity B
n4
n3+n2
Quantity A is greater
Quantity B is greater
The two quantities are equal
Cannot be determined
1
Step 1: Compute n⁴
(−3)4=(−3)(−3)(−3)(−3). What is the value?
2
Step 2: Compute n³
3
Step 3: Compute n²
4
Step 4: Compute Quantity B
5
Step 5: Compare the quantities
Practice Questions
Now apply what you have learned. Each question presents Quantity A and Quantity B for you to compare. After you submit your answer, click through the solution walkthrough one step at a time to compare against your own reasoning.
Practice 1 — Integer Properties: Divisibility Sets
Of the integers from 1 to 360, inclusive, let S be the number of integers that are divisible by 4 but not by 6, and let T be the number of integers that are divisible by 6 but not by 4.
Quantity A
Quantity B
S
T
Select one answer:
Practice 2 — Rate and Speed
A car travels the first 200 kilometers of a 300-kilometer journey at a constant speed of 60 km/h and the remaining 100 kilometers at a constant speed of 90 km/h.
Quantity A
Quantity B
The car's average speed for the entire 300-km journey, in km/h
75
Select one answer:
Practice 3 — Percent Change
A retailer increases the price of an item by 30 percent and then increases the new price by an additional 20 percent.
Quantity A
Quantity B
50 percent of the item's original price
The total dollar amount of the increase from the original price to the final price
Select one answer:
Practice 4 — Interest Comparison
A bank account earns simple interest at an annual rate of 8 percent on a principal of $5,000 for 3 years. A second bank account earns interest at an annual rate of 8 percent compounded annually on a principal of $5,000 for 3 years.
Quantity A
Quantity B
The total interest earned by the first account
The total interest earned by the second account
Select one answer:
Practice 5 — Units Digit Patterns
n is a positive integer.
Quantity A
Quantity B
The units digit of 7n
The units digit of 3n
Select one answer:
Practice 6 — Integer Properties: Consecutive Digits
N is a three-digit positive integer whose digits are three consecutive integers in decreasing order from left to right (for example, 876 or 321). N is divisible by 8.
Quantity A
Quantity B
The units digit of N
The arithmetic mean of the three digits of N
Select one answer:
Common Traps
The GRE question writers exploit the same cognitive shortcuts again and again. Here are the three arithmetic traps that catch the most test-takers on QC questions.
Trap 1: Symmetric percent changes are not neutral. A 10% increase followed by a 10% decrease yields 1.1×0.9=0.99, not 1.00. The larger the percentage, the bigger the loss: 1.2×0.8=0.96 (a 4% loss). Students who assume "+10% then -10% = no change" will choose C when the correct answer is A or B. Remember the shortcut: the product drops by (p2/100)% of the original.
Trap 2: Exponential growth rates are deceptive. Expressions like 3x+1 versus 4x may seem to favor one side for small x, but exponential growth with a larger base eventually dominates. Students who test only one value of x and generalize will choose A or B when the correct answer is D. Always test at least two values — one small, one large — for any exponent comparison with a variable.
Trap 3: Average speed is not the average of speeds. If a car travels 200 km at 60 km/h and 100 km at 90 km/h, the average speed is total distance divided by total time = 67.5 km/h, not (60 + 90)/2 = 75 km/h. The arithmetic mean of speeds equals the true average speed only when equal time — not equal distance — is spent at each speed. More time at the slower speed pulls the average below the arithmetic mean.
Recognition / When to Apply
The table below maps the keywords and structural cues you will see in a QC problem to the specific arithmetic pattern and recommended strategy. Use it as a quick-reference during practice sessions until pattern recognition becomes automatic.
Matching QC Arithmetic Cues to Strategies
Cue in the Problem
Pattern
Strategy
Markup, discount, percent more/less than
Percent Markup/Discount
Estimate with benchmark values; compute only if close
Machine, worker, rate, produces x units in y minutes
Rate / Work
Convert to common rate unit, multiply by time, compare
Exponent expressions with a variable (e.g., ax vs. bx)
Exponent Crossover
Test 2+ values of the variable; expect answer D
Dimensions increased by p% and decreased by p%
Symmetric Percent Change
Apply the −(p2/100)% shortcut directly
Count of integers, multiples, non-perfect-squares
Set Counting
Use inclusion-exclusion; list and count systematically
Consecutive integers, arithmetic sequence, sum of terms
Sequence / Pattern
Express all terms with one variable; simplify algebraically
Greatest/least prime in a range
Prime Identification
List primes in the range; compare directly
One structural shortcut deserves special emphasis: if there is no variable in the problem, the answer is never D. The moment you confirm that both quantities are fixed numbers, you can eliminate choice D immediately and focus on computing whether A is greater, B is greater, or the two are equal.
Study Checklist
QC Arithmetic Mastery0/8 complete
Frequently Asked Questions
How many Quantitative Comparison Arithmetic questions appear on the GRE?
Each Quantitative Reasoning section contains roughly 7-8 Quantitative Comparison questions in total. Of those, 2-4 typically involve arithmetic topics such as percents, rates, exponents, and integer properties. The exact distribution varies by adaptive section, but arithmetic is one of the most heavily tested content domains in the QC format.
What are the four answer choices for every QC question?
Every QC question uses the same four fixed choices: (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. There is no option E, and the wording never changes. Memorize them so you can focus entirely on the math.
When should I choose answer D on a QC question?
Choose D when different valid values of the variable or variables produce different comparison outcomes. For example, if plugging in x = 2 makes Quantity A greater but x = 5 makes Quantity B greater, the answer is D. You need at least two test cases that give opposite results. Importantly, D is only possible when the problem contains a variable — if both quantities are fixed numbers, eliminate D immediately.
Is it possible to get answer D when there are no variables in the problem?
No. If both quantities are fixed numerical values with no unknowns, the comparison is fully determined and the answer must be A, B, or C. Answer D applies only when a variable or unknown is present and the relationship changes depending on its value. This is a powerful structural shortcut: no variables means you can cross out D before computing anything.
What is the most common arithmetic trap in QC questions?
The most common trap involves symmetric percent changes. Students assume that a 10% increase followed by a 10% decrease returns to the original value, but 1.1 times 0.9 equals 0.99, not 1.00. This causes students to select C (equal) when the correct answer is A or B. The shortcut to remember is that symmetric percent changes always reduce the product by (p2/100)% of the original — so a 20% increase paired with a 20% decrease yields a 4% net loss.