GMAT Quantitative Reasoning: The Complete 2026 Guide

Why it matters: appears directly or indirectly in nearly every section

Core definition: percent change = (new − old) / old × 100. The reference point (“old”) is always the value you are changing from — mixing up the base is the single most common quant error.

• Successive changes multiply, never add: +10% then −10% equals ×1.10 ×0.90 = 0.99, a net −1%, not 0%.
• “A is 25% more than B” means B is 20% less than A — reciprocal percentages differ.
• Markup/discount chains: track the actual price at each step instead of memorizing shortcuts.

Why it matters: business-flavored word problems appear constantly

• Profit = selling price − cost price; profit margin is usually quoted on cost, but read carefully — some questions quote it on revenue.
• Discounts apply to list price, not cost. A store can sell “20% off” and still profit.
• Successive discounts of 20% and 10% equal a single 28% discount — not 30%.

Why it matters: the backbone of mixtures, sharing, and scaling problems

• To combine a:b and b:c into a:c, make the b terms match: a:b = 2:3 and b:c = 6:5 → a:b = 4:6, so a:c = 4:5... wait — a:b:c = 4:6:5.
• Ratio problems give you relative quantities; find the multiplier. If shares are 2:3:5 and the total is $500, one part is $50.
• Mixtures: track one ingredient (say salt) through combining and removing steps. Alligation — weighted averaging of concentrations — solves most of the rest.

Why it matters: weighted-average logic transfers to statistics, rates, and mixtures

• The plain average only works when every item counts equally. Whenever group sizes differ, you need the weighted average.
• A weighted average always sits between the smallest and largest group values — and sits closer to whichever group is bigger.
• Adding a new member above the current average pulls the average up; the size of the pull depends on how far above, not on percentages.

Why it matters: guaranteed appearances, and the most common source of blown pacing

• Distance = speed × time. Almost every variation reduces to building a small table of the three columns per moving object.
• Average speed is total distance ÷ total time — never the average of two speeds unless times are equal. Equal distances at a and b give harmonic averaging: 2ab/(a+b).
• Relative speed: objects moving opposite add speeds; same direction subtract.
• Work-rate: rates add. If A does a job in 6 days (rate 1/6) and B in 3 days (rate 1/3), together they take 1/(1/6+1/3) = 2 days.

Why it matters: small topic, reliable point, quick to master

• Simple interest grows linearly: SI = P·r·t/100 each year.
• Compound interest grows multiplicatively: balance = P(1+r)ⁿ. Two years at 10% is ×1.21, not ×1.20.
• The CI−SI gap widens over time; questions love asking for year-2 or year-3 balances where compounding visibly diverges.

Why it matters: computational fluency decides whether you finish the section

• Memorize benchmark conversions: 1/6 ≈ 16.7%, 1/8 = 12.5%, 1/9 ≈ 11.1%, 1/12 ≈ 8.3%. They turn ugly calculations into one-step ones.
• Compare fractions quickly by cross-multiplication or by benchmarking against 1/2.
• Estimate aggressively when answer choices are far apart — the GMAT deliberately spaces them for this reason.

Why it matters: the default model for word problems

• One equation, one unknown: isolate carefully, keep equations balanced.
• Two equations, two unknowns: substitution when one variable is already isolated; elimination when coefficients align.
• Special cases worth knowing: parallel lines (same slope) mean no solution; identical equations mean infinitely many.

Why it matters: factoring fluency saves 30–60 seconds per appearance

• Standard form ax² + bx + c = 0. Most GMAT quadratics factor cleanly over integers.
• Know these identities cold: (a+b)² = a² + 2ab + b², (a−b)² = a² − 2ab + b², and a² − b² = (a−b)(a+b). The difference-of-squares appears constantly in disguise.
• For roots r and s: sum = −b/a and product = c/a — often lets you answer without solving.
• Never divide both sides by a variable expression; you might delete a valid root.

Why it matters: range reasoning separates strong scorers at the top of the adaptive ladder

• Solve like equations with one extra rule: multiplying or dividing by a negative flips the direction.
• Combine overlapping ranges on a number line rather than juggling symbols mentally.
• “At least/at most” phrasing defines inclusive endpoints (≤, ≥) — endpoint errors are graded wrong.

Why it matters: short questions, binary outcomes — cheap points when methodical

• |x| = distance from zero. |x| = 5 means x = 5 or x = −5.
• |expression| < k splits into −k < expression < k (a bounded range); |expression| > k splits into expression > k or expression < −k (two rays).
• Always solve both branches and check each against the original.

Why it matters: law-based manipulation questions reward precision, not speed-math

• Core laws: multiply powers → add exponents; divide → subtract; power of a power → multiply.
• Negative exponent means reciprocal; fractional exponent means root: x^(1/2) = √x, x^(1/3) = ∛x.
• (a+b)ⁿ ≠ aⁿ + bⁿ — expanding beats guessing.
• Simplify nested radicals by pulling out perfect squares first.

Why it matters: unfamiliar notation tests adaptability — the format itself is the difficulty

• f(x) notation: substitute whatever appears in parentheses everywhere x occurs.
• Composite functions work inside-out: f(g(x)) means evaluate g first.
• Symbol questions (e.g., x △ y = x² + y) are ordinary substitution wearing a costume. Translate once, then compute.
• Arithmetic sequences: nth term = first term + (n−1)d. Geometric: multiply by ratio r each step.

Why it matters: fast eliminations across many questions

• Addition/subtraction: odd ± odd = even; odd ± even = odd; even ± even = even.
• Multiplication: any even factor makes the product even; odd × odd = odd.
• Sign logic: negatives flip behavior under odd powers, preserve under even powers.

Why it matters: the master key — divisibility, factors, LCM/HCF all reduce to primes

• Every integer > 1 factors uniquely into primes. 360 = 2³ × 3² × 5.
• Factor counting from prime form: 2³ × 3² × 5¹ has (3+1)(2+1)(1+1) = 24 total factors.
• 1 is not prime. 2 is the only even prime — a favorite edge case.

Why it matters: direct question types plus shortcuts inside bigger problems

• GCD takes the lowest power of shared primes; LCM takes the highest power of all primes present.
• Handy checks: digit-sum divisible by 3 or 9; last two digits for 4; alternating digit-sum for 11.
• For any two positive integers: GCD × LCM = product of the numbers.

Why it matters: pattern-recognition questions that look impossible and take 40 seconds

• Remainders cycle with periodicity. Powers of 2 mod 7: 2, 4, 1, 2, 4, 1… — find the cycle length, then reduce the exponent.
• Units digits of large powers follow cycles of length ≤ 4 (e.g., 3: 3, 9, 7, 1, repeat). Reduce the exponent mod 4 and read off the answer.

Why it matters: transformation questions test understanding, not calculation

• Adding a constant to every value shifts the mean and median by exactly that constant; spread is unchanged.
• Multiplying every value scales the mean, median, and the spread by the same factor.
• The median resists outliers; the mean chases them. Questions exploit exactly this difference.

Why it matters: tested conceptually — know what changes spread and what doesn't

• Range = max − min. One extreme outlier can double it while leaving the mean nearly intact.
• Standard deviation measures spread around the mean. Adding a constant leaves SD unchanged; multiplying scales it.
• You will not need to compute SD by hand — compare spreads qualitatively.

Why it matters: counting discipline prevents double-counting errors under pressure

• Ask one question: does order matter? Yes → permutations (n!/(n−r)!). No → combinations (n!/(r!(n−r)!)).
• Slot method: arrange distinct items by filling positions one at a time — handles most “arrangement” questions without formulas.
• Restrictions first: seat the restricted people/items, then distribute the rest.

Why it matters: small question count but formula-light — reliable points

• P(event) = favorable outcomes ÷ total equally likely outcomes.
• Complement shortcut: P(at least one) = 1 − P(none). This reframe converts brutal counting into one multiplication.
• Independent events multiply probabilities; mutually exclusive events add them. Never confuse the two conditions.