Quantitative Comparisons: Which Quantity Is Bigger?
Master quantitative comparison questions on the ISEE and GRE — comparing two quantities, the four answer choices, and the plug-in strategy — with worked examples.
The Short Version
- You compare Quantity A and Quantity B and pick: A is greater, B is greater, they're equal, or it cannot be determined.
- Often you can compare without fully calculating — simplify both sides.
- With variables, plug in different numbers (try 0, 1, negatives, and fractions).
- If different test numbers give different results, the answer is cannot be determined. An ISEE and GRE format.
Most math questions ask "what is the value?" Quantitative comparison questions ask something different: "which of these two quantities is bigger — or can you even tell?" You're given Quantity A and Quantity B and four fixed answer choices. This format appears on the ISEE (Quantitative Reasoning) and the GRE, and it rewards a different mindset: you often don't need the exact values, just enough to compare — and you must stay alert to cases where the answer depends on unknown values.
This guide explains the format and the plug-in strategy, with worked and practice examples matched to real ISEE and GRE difficulty at Northside Tutoring.
Why This Format Matters
Quantitative comparison is a major question type on the ISEE's Quantitative Reasoning section and on the GRE. It tests number sense and efficiency more than computation, and a clear method makes it fast. (It is not used on the SSAT, SAT, or ACT, which use standard multiple choice.)
The Format & the Four Choices
You're shown two quantities and choose among four fixed options:
| Choice | Meaning |
|---|---|
| A | Quantity A is greater |
| B | Quantity B is greater |
| C | the two quantities are equal |
| D | cannot be determined from the information given |
The Core Strategy
You usually don't need exact values — just a comparison. Simplify both quantities as much as possible, and do the same operation to both sides (add, subtract, divide by a positive) to make them easier to compare without changing which is larger.
Plugging In Numbers
When variables are involved, test specific values. Crucially, don't stop at one easy number — try several different kinds: a positive, zero, a negative, and a fraction. If every value you try gives the same result, you can be confident; if results differ, that's information too (see below).
Try the tricky numbers
Always test 0, 1, a negative, and a fraction between 0 and 1. These are where comparisons flip — for example, squaring makes a number bigger if it's greater than 1 but smaller if it's between 0 and 1.
The 'Cannot Be Determined' Choice
This choice is what makes the format tricky. If plugging in different valid numbers makes Quantity A larger in one case and Quantity B larger (or equal) in another, then the comparison isn't fixed — the answer is cannot be determined. Whenever a problem has variables that aren't fully pinned down, consider this option seriously.
Comparing, Not Calculating
The efficient mindset: ask "do I actually need the values, or just which is bigger?" Often a quick estimate or a shared term you can cancel settles it instantly. Resist grinding out full calculations when a comparison will do.
Where You'll See This — Test by Test
Quantitative comparison is an ISEE and GRE format, not used on the SSAT, SAT, or ACT. It rewards number sense, the plug-in strategy, and watching for 'cannot be determined.'
ISEE
The ISEE Quantitative Reasoning section includes quantitative comparison questions.
Explore Admissions Test Prep → Graduate SchoolGRE
The GRE tests quantitative comparison heavily; the plug-in strategy is essential.
Explore GRE Tutoring → Independent School AdmissionsSSAT
The SSAT uses standard multiple-choice math, not quantitative comparisons.
Explore SSAT Tutoring → Every TestAll Standardized Tests
Our tutors teach the compare-don't-calculate mindset for the tests that use this format.
Explore Our Programs →Watch the Lesson
Sometimes a diagram needs a voice. In the short video below, one of our Northside tutors walks through the core idea and works through test-style problems in real time.
Quantitative Comparisons — In Plain English
A live walkthrough from our tutoring team.
— Featuring a Northside Tutoring instructor
Worked Example Problems
These problems are calibrated to the difficulty you'll actually see on test day. Try each one before opening the solution.
Quantity A: 3 + 5. Quantity B: 2 × 4. Which is greater?
Show solution
A = 8, B = 8. They're equal.
Quantity A: x². Quantity B: x. (No restriction on x.) Which is greater?
Show solution
Try x = 2: A = 4 > B = 2. Try x = 1/2: A = 1/4 < B = 1/2. Different results → cannot be determined.
Both quantities have '+ 7' added. Quantity A: 5 + 7. Quantity B: 9 + 7. Simplify the comparison.
Show solution
Subtract 7 from both: compare 5 vs. 9. B is greater.
Why test a fraction like 1/2 when plugging in?
Show solution
Because operations like squaring behave differently for fractions between 0 and 1 (squaring makes them smaller), which can flip a comparison.
Quantity A: the number of days in 3 weeks. Quantity B: 20. Which is greater?
Show solution
A = 3 × 7 = 21 > 20. A is greater.
Common Mistakes to Avoid
Three traps that catch students every year
- Testing only one number. Try positives, 0, negatives, and fractions — comparisons often flip.
- Overlooking 'cannot be determined.' If different valid values give different results, that's the answer.
- Over-calculating. You usually need only to compare — simplify or cancel rather than computing everything.
Practice Problems — You Try
Three problems below. Work each before checking the solution.
Quantity A: 1/4. Quantity B: 0.2. Which is greater?
Show solution
1/4 = 0.25 > 0.2. A is greater.
Quantity A: x + 1. Quantity B: x + 2. Which is greater (any x)?
Show solution
Subtract x from both: 1 vs. 2. B is always greater, regardless of x.
Quantity A: x. Quantity B: x³, where x can be any number. Which is greater?
Show solution
Try x = 2: A = 2 < B = 8. Try x = 1/2: A = 0.5 > B = 0.125. Try x = −2: A = −2 > B = −8. Results differ, so it cannot be determined.
The Northside Method — How We Teach This 1-on-1
Reading a blog is a great starting point. But there's a meaningful gap between understanding a concept and reflexively applying it under timed conditions. That gap is exactly what our tutors close.
Every Northside student works through a four-step framework:
- Assessment. We diagnose which specific skills are slowing your student down — not just whether they "get it" in the abstract.
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