GRE Quantitative Comparison Guide for Nepali Students

GRE Quantitative Comparison Guide for Nepali Students explains the four fixed answer outcomes, simplification, case testing, variable restrictions, estimation, geometry diagrams and review strategy. The method below focuses on the response format as well as the mathematics, because a correct calculation can still produce a wrong selection when the question is misread.

Information checked on 24 July 2026 against the current ETS Quantitative Reasoning overview, official test-taking strategies, Math Review and POWERPREP information.

Key facts at a glance

Know the four fixed outcomes

Every Quantitative Comparison question presents Quantity A and Quantity B. You decide whether A is greater, B is greater, the quantities are equal, or the relationship cannot be determined from the information given.

Memorise the order and wording of these outcomes so test-day attention stays on the comparison. When you prove one quantity is greater, pause before selecting to avoid reversing the first two choices.

Understand what must be proved

A fixed outcome must hold for every value or configuration allowed by the prompt. One example where A is greater does not prove A is always greater. It only demonstrates one permitted case.

In contrast, two valid cases with different relationships are enough to establish that the relationship cannot be determined. For example, if one case gives A > B and another gives A < B or A = B, no single fixed comparison follows.

Read restrictions before comparing

Record whether variables are real numbers, integers, positive, nonnegative, distinct or ordered. Do not import a restriction that is not stated. Under standard ETS conventions, numbers used are real unless indicated otherwise.

A relationship that holds for positive x may fail for negative x, zero or a fraction. Restrictions define the universe over which your conclusion must remain true.

Simplify the comparison directly

Place a mental question mark between A and B and apply reversible simplifications to both sides. Cancel common positive factors, combine terms, factor expressions or compare a difference with zero.

Avoid solving for each quantity separately when a shared structure can be removed. If A – B factors neatly, the sign of that factorisation may decide the relationship.

Track signs during transformations

Multiplying or dividing an inequality by a known negative reverses its direction. If the sign of a variable expression is unknown, do not cancel or divide by it without cases.

Squaring can remove sign information, and taking square roots can introduce restrictions. Note whether a transformation is reversible for every allowed value before treating the simplified comparison as equivalent.

Plug in numbers strategically

ETS recommends considering appropriate zero, positive, negative, small, large, fractional and decimal values. Select cases that probe a vulnerability in the relationship rather than random convenient numbers.

Start with boundary values and sign changes when allowed. If an expression contains x – 1, test values below, equal to and above 1. If a denominator contains x, include negative and fractional values but exclude zero.

Use counterexamples correctly

A counterexample disproves a universal relationship. If you suspect equality, one valid case with unequal quantities defeats it. If you suspect A is always greater, one valid equal or smaller case defeats that claim.

Two examples that happen to agree do not prove the result. After testing, look for an algebraic reason or ask whether another permitted region remains unexplored.

Build a critical-point case matrix

List values where the expression changes behaviour: zeros of factors, denominator exclusions, endpoints, absolute-value centres and points where two formulas become equal. Divide the permitted domain around those points and test one representative from each interval.

A tiny matrix with columns for the case, Quantity A, Quantity B and relationship prevents repeated random substitution. It also shows whether your examples cover every meaningful region or only one comfortable range.

Do not overuse cannot be determined

ETS warns against choosing the final outcome when both quantities can be computed from the information given. If variables cancel or the diagram supplies enough constraints, a definite result may exist.

Use cannot determine because you found logically valid variation, not because the calculation feels difficult. Demonstrate the changing relationship on scratch paper.

Compare fractions without risky decimals

For positive denominators, cross-products can compare fractions exactly. If denominator signs are unknown, first establish their signs or test cases. Common benchmarks such as 0, one-half and 1 can speed estimation.

Decimal conversion can hide exact equality or introduce rounding. Keep fractions symbolic when the structure is simple.

Compare exponents and roots

A larger base or exponent does not automatically create a larger value when bases can be negative or between 0 and 1. Examine sign, parity and range.

For nonnegative quantities, squaring both sides can simplify a root comparison, but confirm the nonnegative condition first. Preserve domain restrictions when simplifying radicals.

Handle absolute value

Interpret |x – c| as distance between x and c. Compare distances on a number line or split around critical points. Absolute value is nonnegative, but its size depends on how far the value lies from the centre.

Do not assume |x| = x unless x is known nonnegative. Test positive and negative cases when restrictions allow both.

Approach mean and median comparisons

A summary statistic may not determine the entire dataset. Construct small valid lists that satisfy the given mean, median, range or count, then see whether the target changes.

Use sum = mean × count for exact constraints. Keep values ordered when the median matters, and confirm every constructed list meets all conditions.

Use geometry conventions

Ordinary GRE geometry figures are not necessarily drawn to scale. Base conclusions on stated lengths, angles, parallel marks and geometric properties rather than appearance.

If a figure is underdetermined, redraw it while preserving stated facts and vary the free parts. Different valid shapes may produce different comparisons.

Use coordinate and graph scale carefully

ETS treats coordinate systems and graphical data presentations as drawn to scale, so visual estimation can support comparison. Exact coordinates, labels and scales remain the strongest evidence when available.

Watch for broken axes and nonzero baselines in data graphs. A visible height difference may not represent the ratio your eye first suggests.

Estimate before calculating

Many Quantitative Comparison questions require only order, not exact values. Bound a square root, compare percent multipliers or use scale relationships before opening the calculator.

If an estimate clearly separates the quantities, stop. If values are close, switch to exact simplification.

Compare units and scale

Quantities must describe comparable dimensions before a greater-than relationship is meaningful. Convert units consistently and notice whether one expression represents length, area, volume, rate or a pure ratio.

Scaling can decide the comparison without exact calculation. If every length grows by k, perimeter grows by k, area by k squared and volume by k cubed. For rates, keep numerator and denominator labels visible so an inverted unit does not create a false comparison.

Use the calculator selectively

The GRE provides a basic on-screen calculator, but ETS notes that it supplements rather than replaces reasoning. Most questions do not require difficult computation.

Estimate first, use the calculator for genuinely tedious operations and check the result against sign and magnitude. Calculator output cannot resolve an unrestricted-variable case by itself.

Manage time and review

If a comparison remains unclear after a structured attempt, mark it and move on. ETS allows review and answer changes within the section while time remains, and no points are subtracted for incorrect Quant answers.

On review, revisit the exact uncertainty: missing sign case, untested boundary, diagram flexibility or algebra step. Avoid restarting a complete solution without a reason.

Keep a comparison error log

Classify misses as reversed answer choice, added restriction, missed sign, invalid cancellation, insufficient cases, false visual assumption, unnecessary computation or calculator error. Record the earliest flawed decision.

Re-solve later and produce either a general proof or two explicit counterexamples. That evidence is more useful than remembering the official outcome.

Practise with official resources

Use the ETS Quantitative Reasoning overview for the four outcomes and official strategies. Use the Math Review for content gaps and POWERPREP for current interface and timing.

Practise comparisons across arithmetic, algebra, geometry and data rather than treating the format as one content chapter. The same proof-versus-counterexample logic should transfer.

Follow a seven-step routine

Read restrictions; identify the target relationship; simplify shared structure; estimate; test vulnerable cases; seek proof or counterexample; then select the matching fixed outcome carefully.

Before submitting, ask whether your evidence covers every allowed case. If not, continue analysis or demonstrate variation.

Connect test work with applications

For programme research, documents and overseas-study planning, visit MKS Education. For structured GRE practice support, explore MKS Prep. Verify each university’s current testing policy.

Set score goals from programme evidence and coordinate preparation with score-reporting and application deadlines.

Frequently asked questions