ISEE quantitative comparisons confuse most students the first time they see the Column A vs Column B layout, but the format is actually one of the easiest places on the test to bank quick points. This guide breaks down the four answer choices, the simplify and plug-in techniques, and the three rules for choosing (D) — so you can move through 14 to 17 of these questions in under 30 seconds each.
ISEE quantitative comparisons sit inside the broader Quantitative Reasoning section, which is the second of the four scored ISEE sections. On the Middle Level and Upper Level tests, the section gives you 37 questions to finish in 35 minutes — and roughly 14 to 17 of those questions are quantitative comparisons rather than traditional word problems. No calculator is allowed.
A quantitative comparison shows you two quantities side by side: one labeled Column A and one labeled Column B. Sometimes there is a constraint listed above the columns, like "x > 0" or "a > b > c > d." Your job is not to compute either column to a final number — your job is to decide how the two columns relate. That single shift in mindset, from solving to comparing, is what unlocks fast points in this section.
Quantitative comparisons appear only on the Middle Level (grades 7–8 entry) and Upper Level (grades 9–12 entry) ISEE. The Lower Level Quantitative Reasoning section is made entirely of word problems, so if you are taking the Lower Level test you can skip the QC techniques in this guide and focus on word problem strategy instead.
The full Quantitative Reasoning section runs 35 minutes. Of the 37 questions, 32 are scored and 5 are unscored experimental items — but you cannot tell which is which, so treat every question as if it counts. That works out to about 57 seconds per question on average. Quantitative comparisons can usually be answered faster than word problems if you know the strategy, so a smart pacing plan is to bank time on QCs and spend it on word problems.
| Detail | Middle Level | Upper Level |
|---|---|---|
| Includes Quantitative Comparisons? | Yes | Yes |
| Total Quantitative Reasoning questions | 37 | 37 |
| Approximate QC questions | 14-17 | 14-17 |
| Approximate word problems | 18-21 | 18-21 |
| Time for the section | 35 minutes | 35 minutes |
| Calculator allowed? | No | No |
Every ISEE quantitative comparison Column A Column B question uses the exact same four answer choices in the exact same order. Memorize them once and you stop reading them on test day, which buys you several seconds on every QC question.
| Choice | Meaning | Pick When |
|---|---|---|
| (A) | The quantity in Column A is greater | Every test value you try shows Column A larger than Column B. |
| (B) | The quantity in Column B is greater | Every test value you try shows Column B larger than Column A. |
| (C) | The two quantities are equal | Both columns simplify to the same expression or number, no matter what. |
| (D) | The relationship cannot be determined | Two valid test values give different relationships — and only when at least one column has a variable. |
The first move on almost every quantitative comparison is to simplify. Treat the two columns like an inequality where you do not yet know which way the operator points. Anything you do to keep the columns balanced — adding, subtracting, multiplying or dividing both sides by the same positive number — preserves the unknown relationship between them. The ISEE quantitative comparison strategy here is identical to algebra, just with one twist about variables.
If both columns share a term, subtract that term from both sides. The relationship between the columns does not change, but the math gets cleaner. If Column A is x + 7 and Column B is 7 + 2, subtract 7 from both columns — now you are comparing x to 2, which is much easier to think about.
Multiplying both columns by a positive constant scales the expressions without changing which one is bigger. The danger is multiplying or dividing by a variable. If the variable could be negative, the inequality flips. If the variable could be zero, the comparison becomes meaningless. Only multiply or divide by a variable when the problem guarantees that variable is positive.
When both columns are sums of similar parts, look for matching pieces you can drop instead of computing. The worked example below uses commutative addition — both columns are the same three numbers in a different order — so the comparison is settled before you do any arithmetic at all.
Worked Example
Setup: Column A: 47 + 88 + 19. Column B: 88 + 19 + 47. Compare the two quantities.
When a quantitative comparison contains a variable, the right move is almost always to plug in concrete numbers for that variable. The trick is picking values that expose the trap. Most students plug in 1, 2, and 3, which often gives the same relationship every time and locks you into a wrong answer. The five-value cycle below catches the cases ISEE QC questions like to exploit.
These three values are the cheapest stress test you have. Negative one catches sign flips: if your column has a variable raised to an odd power or multiplied by another variable, the negative reverses the result. Zero catches edge cases — anything times zero is zero, division by zero is undefined. One reveals whether multiplication does anything meaningful at all (since multiplying by 1 is the identity).
Squaring a number greater than 1 makes it bigger, but squaring a fraction between 0 and 1 makes it smaller. That single behavior trips up more students than any other plug-in trap. Always include 1/2 in your test values whenever the columns involve squares, square roots, or any power.
Some relationships hold for small numbers but break at scale, especially when one column grows linearly and the other grows polynomially. If the small integers all give the same answer, swap in a 6, a 10, or a 100 and re-check. If the relationship still holds, you can commit. If it changes, the answer is (D).
Worked Example
Setup: Given x is a real number. Column A: x squared. Column B: x. Compare the two quantities.
| Value | Why You Try It | What It Catches |
|---|---|---|
| -1 | Tests negative behavior | Sign flips when columns multiply by the variable. |
| 0 | Tests the zero edge case | Anything times zero is zero; division by zero is undefined. |
| 1 | Tests the multiplicative identity | Reveals whether multiplying changes the column at all. |
| 1/2 (a fraction between 0 and 1) | Tests squaring direction | Squaring shrinks fractions in this range — the opposite of what whole numbers do. |
| A value greater than 5 | Tests size effects | Catches relationships that hold for small values but break at scale. |
Answer (D) is the trickiest of the four choices. Picking it too eagerly or refusing to pick it at all are both common ways to lose points. Three rules cut through the confusion.
Quantitative comparison questions are loosely ordered easier-to-harder, and the early questions almost always have a clean computable answer. If you find yourself wanting to pick (D) on the very first QC, double-check your work — odds are you missed a simpler approach.
Two fixed numbers always have a definite relationship. If both Column A and Column B contain only specific numerical values — no variables, no unknowns — then the answer must be (A), (B), or (C). Eliminate (D) before you even start computing.
If two valid test values give different relationships between the columns, you've proven the relationship is not fixed. That is what (D) is for. The plug-in cycle from Strategy 2 is your tool for finding this — when -1, 0, 1, or 1/2 give you a different answer than the small positive integers, (D) is locked in.
ISEE quantitative comparison questions ask which column is bigger, not what either column equals. That distinction is your opening for estimation. Decimal arithmetic without a calculator burns the clock; rounding and rough size comparisons settle most QCs in seconds.
Before reaching for any pencil work, scan the columns for an obvious size mismatch. If Column A is in the hundreds and Column B is in the tens, you do not need to compute either side — you already have your answer. This is the lazy-but-correct first move on every QC.
Three benchmarks, 0, 1/2, and 1, are enough to settle most fractional comparisons. A fraction with a denominator twice the numerator is about 1/2. A fraction with the numerator close to the denominator is close to 1. Round each fraction to its nearest benchmark, then compare benchmarks.
Lock in 10%, 25%, 50%, and 100% as anchors. Almost any percentage problem on the ISEE is close enough to one of these to round and compare. 17% of 200 is close to 20% of 200, which is 40 — that's enough to settle a comparison without exact arithmetic, in most cases.
Worked Example
Setup: Column A: 0.49 + 0.51 + 0.49. Column B: 1.6. Compare the two quantities.
These are the patterns that major ISEE prep resources — including Kaplan and Princeton Review — flag again and again. The good news is each one has a clean fix once you know it's coming. Naming these ISEE QC questions traps in advance is half the battle.
Misreading shows up in two main forms: students mix up which column is which, or they miss a constraint stated above the columns (like "x > 0" or "a is an integer"). The fix is to underline the constraint as soon as you see it, then write A and B labels on your scratch paper if the format ever feels confusing.
The single most common QC trap. If your test values share the same sign and similar size, the relationship between the columns rarely changes — but that does not mean the relationship is fixed. Always include -1, 0, and a fraction in your cycle, especially when squaring or multiplication is involved.
Many students treat (D) as "I don't know," but on the ISEE it is a specific claim about the math. Use it only when test values prove the relationship is not fixed, or when you've shown the columns have multiple valid interpretations. If both columns are pure numbers, (D) is automatically wrong.
Five practice quantitative comparison questions covering the four strategies above. Try each one before clicking through to the explanation.
Two helpers for the QC section: a pacing estimator that turns "57 seconds per question" into a real-time number for your study target, and a decoder that translates the relationship you've established into an answer choice.
Enter how many of the 37 Quantitative Reasoning questions you want to attempt and how many minutes you plan to keep in reserve, and we'll show your average pace.
Pick the relationship you've established between Column A and Column B. We'll tell you the corresponding answer choice and a one-line check.