GRE Arithmetic Formulas Cheat Sheet: The Only List You Need for Quant

Use this GRE arithmetic formulas cheat sheet to answer typical Quant questions on percentages, ratios, LCM/GCD, averages, exponents/roots, absolute value, inequalities, rates/work/time, sets, and basic probability. Memorize the small list, then drill with realistic problems and the ETS on‑screen calculator. If you’re testing in 2026, this is sufficient coverage.

How to use this cheat sheet (and what’s on the GRE Quant now)

• What you need: a compact list of formulas, how to apply them under time, and when to skip the calculator.
• What’s on the test: foundations—arithmetic, number properties, fractions/percents/ratios, exponents and roots, averages and variability, rate/work, set counting, basic probability, and word problems (ETS, Sept 2023 outline for the shorter GRE).
• Structure: the shorter GRE has two Quant sections, 12 questions each, 21 minutes per section, with an on‑screen calculator. No external formula sheet is provided; you must know the basics cold.
• Tools that help: ETS PowerPrep Online, the Official Guide to the GRE General Test, Anki for spaced repetition, and a simple Google Sheet to log misses and formula gaps.
• How to drill: memorize a cluster (e.g., percents), do 10–15 mixed problems, then immediate error review. Re‑encode misses as Anki cards—include example numbers.

Refonte Learning teaches GRE by making you fluent in a minimal set of high‑yield moves, then pressure‑testing under section time. For more Quant structure and examples, start at our GRE Quant hub and the broader GRE hub.

Core number properties (the backbone of GRE arithmetic)

• Integer: whole number (…, −2, −1, 0, 1, 2, …).
• Even/odd: even = multiple of 2; odd = not a multiple of 2.
• Prime: integer > 1 with exactly two factors (1 and itself). First primes: 2, 3, 5, 7, 11, 13, 17, 19… (2 is the only even prime).
• Composite: integer > 1 that’s not prime.
• Positive/negative: sign matters in products and inequalities.
• Consecutive integers: n, n+1, n+2, … (or consecutive evens/odds: n, n+2, n+4, …).
• Absolute value: |x| is distance from 0; always nonnegative.

Quick facts you’ll actually use: - Even ± even = even; odd ± odd = even; even ± odd = odd. - Even × anything = even; odd × odd = odd. - If a and b are integers: a/b is an integer only if b divides a evenly. - Count of factors: if n = p₁^a × p₂^b × p₃^c, then number of positive factors = (a+1)(b+1)(c+1). - Consecutive integers are co‑prime in pairs (gcd of any two adjacent integers is 1).

Divisibility rules you should memorize

• 2: last digit even.
• 3: sum of digits divisible by 3.
• 4: last two digits form a number divisible by 4.
• 5: last digit 0 or 5.
• 6: divisible by 2 and 3.
• 8: last three digits form a number divisible by 8.
• 9: sum of digits divisible by 9.
• 10: last digit 0.

Why this matters: it speeds up factor/LCM/GCD questions and trailing zero counts (powers of 10).

Factors, multiples, GCD and LCM

• Factor (divisor): d is a factor of n if n = d×k for some integer k.
• Multiple: m is a multiple of n if m = n×k for some integer k.
• Greatest common divisor (gcd): largest integer dividing both numbers.
• Least common multiple (lcm): smallest positive integer that’s a multiple of both.

Prime factorization method: - Write each number as product of prime powers. - gcd: take the minimum exponent of common primes. - lcm: take the maximum exponent of all primes appearing.

Examples: - 60 = 2^2 × 3 × 5; 90 = 2 × 3^2 × 5. gcd(60,90) = 2^1 × 3^1 × 5^1 = 30. lcm(60,90) = 2^2 × 3^2 × 5 = 180. - Trailing zeros in n!: number of 5s in prime factorization of n! (since 2s are abundant). For 100!, floor(100/5)+floor(100/25)=20+4=24 trailing zeros.

LCM/GCD word‑problem templates: - Repeating cycles meet again after lcm(periods). - Splitting items evenly across groups uses gcd to find max group size.

Fractions and mixed numbers

• Simplify by dividing numerator and denominator by their gcd.
• Convert mixed to improper: a b/c = (ac + b)/c.
• Adding/subtracting: use a common denominator; with unlike denominators, use lcm.
• Multiplication: multiply tops and bottoms; cross‑cancel before multiplying to save time.
• Division: multiply by reciprocal.

Benchmarks to internalize: 1/2 = 0.5, 1/3 ≈ 0.333…, 2/3 ≈ 0.666…, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2, 2/5 = 0.4, 3/5 = 0.6, 4/5 = 0.8, 1/8 = 0.125, 3/8 = 0.375, 5/8 = 0.625, 7/8 = 0.875.

Decimals and place value

• Place values: tenths (10^−1), hundredths (10^−2), thousandths (10^−3), …
• Converting: fraction to decimal by long division (or recognize repeating patterns). Decimal to fraction: write over power of 10 and simplify.
• Rounding: to n decimal places, look at the next digit; 5 rounds up.
• Scientific notation: a×10^k with 1 ≤ a < 10; multiply/divide by adding/subtracting exponents.

Percent and percent change

• Percent to decimal: p% = p/100.
• Part–whole: part = percent × whole; percent = part/whole; whole = part/percent.
• Percent change: new = old × (1 ± r). Change% = (new − old)/old × 100%.
• Successive percentages multiply, they do not add: 20% off then 10% off → price × 0.8 × 0.9 = 0.72 → 28% total reduction.
• Markup/markdown: price_final = price_initial × (1 + markup) × (1 − discount).

Common traps: - Percent of what? Always anchor to the stated base. - Percent increase vs. decrease: not symmetric (increase 20% then decrease 20% ≠ original).

Ratios and proportions

• Ratio a:b can be scaled by any positive k → ka:kb.
• Part–part to part–whole: if a:b = 3:2, total parts = 5. If total = T, then A = 3T/5, B = 2T/5.
• Proportions: a/b = c/d ↔ ad = bc (cross‑multiply).
• Mixtures: use weighted average or alligation (see weighted averages).

Set up template: - If ratio A:B = r:s and A + B = T → A = r/(r+s) × T, B = s/(r+s) × T. - If A − B fixed: use ratio units to solve for scaling factor.

Averages and weighted averages

• Mean (average): mean = sum/n; sum = mean × n.
• Weighted average: mean_total = (w₁m₁ + w₂m₂ + …)/(w₁ + w₂ + …).
• Combined groups: total sum is additive; total count is additive.
• Median: middle value when ordered; for even n, average of middle two.
• Mode: most frequent value.
• Range: max − min.

Quick levers: - Moving average trick: If you add k numbers each equal to M, the mean stays the same. - If a new data point is x, new mean = old_mean + (x − old_mean)/new_n.

Variability (standard deviation: what you need and nothing more)

GRE rarely asks you to compute full standard deviation. Know: - If you add the same constant to every element, standard deviation doesn’t change. - If you multiply every element by k, standard deviation is multiplied by |k|. - A set closer to its mean has smaller standard deviation.

Exponents and roots

Exponent rules (for real numbers a,b and integers m,n, with a,b ≠ 0 as needed): - a^m × a^n = a^(m+n). - a^m / a^n = a^(m−n). - (a^m)^n = a^(mn). - (ab)^n = a^n b^n. - (a/b)^n = a^n / b^n. - a^(−n) = 1/a^n. - a^(1/n) = nth root of a (if defined); a^(m/n) = nth root of (a^m).

Specials and patterns: - Squares end digits: 0→0, 1→1, 2→4, 3→9, 4→6, 5→5, 6→6, 7→9, 8→4, 9→1 (helpful for unit‑digit questions). - Powers of 10: 10^k shifts decimal k places. - Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100…; perfect cubes: 1, 8, 27, 64, 125, 216…

Radicals: - √(ab) = √a × √b if a,b ≥ 0. - Rationalizing: multiply by conjugate or by √b/√b to clear radicals from denominators.

Absolute value and inequalities

• |x| definition: |x| = x if x ≥ 0; |x| = −x if x < 0.
• |x − a| < r means x is within r units of a: a − r < x < a + r.
• |x − a| > r means x is more than r units from a: x < a − r or x > a + r.
• Multiplying or dividing an inequality by a negative flips the sign.

Compound inequalities: - a < bx + c < d → solve by isolating x in the middle, respecting inequality direction when multiplying/dividing by negatives.

Sequences (arithmetic sequences on the GRE)

• Arithmetic sequence: terms differ by constant d. nth term: a_n = a_1 + (n − 1)d.
• Sum of first n terms: S_n = n/2 × (first + last) = n/2 × (2a_1 + (n − 1)d).
• Average of consecutive integers from m to n is (m + n)/2; count is n − m + 1; sum is average × count.

Rates, time, distance (and work)

Distance–rate–time: - d = r × t; r = d/t; t = d/r. - Average speed over whole trip: total distance / total time (not the average of speeds unless distances are equal).

Work: - Work rate r = jobs per unit time. If Worker A: r_A and Worker B: r_B, together rate = r_A + r_B. - If time to finish alone is t_A and t_B, then r_A = 1/t_A, r_B = 1/t_B, together time t = 1/(1/t_A + 1/t_B) = (t_A t_B)/(t_A + t_B). - For variable rates or partial work, use the additive rates framework on each interval.

Mixtures (by amount or concentration): - Amount of solute = volume × concentration. - Final concentration = total solute / total volume. - Replacement problems: if you remove x liters from V and replace with pure water, solute multiplier after one operation is (1 − x/V); after k operations: (1 − x/V)^k.

Interest: - Simple interest: A = P(1 + rt), r in years. - Compound interest (n times per year): A = P(1 + r/n)^(nt). - Continuous compounding: A = Pe^(rt).

Proportionality and scale

• Direct variation: y = kx; ratio y/x is constant.
• Inverse variation: y = k/x; product xy is constant.
• Rule of three: set up proportional relationships to solve scaling problems quickly.

Counting and probability (the arithmetic you actually need)

Counting basics: - Multiplication principle: if task A has m ways and task B has n ways, total m×n ways (if independent stages). - Addition principle: if disjoint choices A or B, total m + n ways. - Permutations without repetition: P(n, k) = n!/(n − k)!. - Combinations: C(n, k) = n!/[k!(n − k)!]. - With restrictions, build first, then subtract forbidden (complement strategy).

Probability basics: - P(event) = favorable outcomes / total outcomes. - Complement: P(not A) = 1 − P(A). - Independent events: P(A and B) = P(A)P(B). - Mutually exclusive: P(A or B) = P(A) + P(B) (if exclusive). In general, P(A ∪ B) = P(A) + P(B) − P(A ∩ B).

Sets and Venn diagrams

Two sets A and B (finite counts): - |A ∪ B| = |A| + |B| − |A ∩ B|. - Only in A = |A| − |A ∩ B|; only in B = |B| − |A ∩ B|.

Three sets A, B, C: - |A ∪ B ∪ C| = |A| + |B| + |C| − |A ∩ B| − |A ∩ C| − |B ∩ C| + |A ∩ B ∩ C|.

Use totals to back‑solve missing regions; watch the wording: “at least one,” “only,” and “none.”

Estimation, bounds, and the calculator

• Front‑end estimation: round numbers to 1–2 significant digits to sanity‑check.
• Upper/lower bounds: if you over‑ or under‑approximate, keep track of direction to avoid crossing the correct answer.
• GRE on‑screen calculator: good for division with remainders, square roots, and long decimal/percent conversions; avoid it for simple integer arithmetic to save time.
• Memory and Ans features help chain computations—practice on PowerPrep first so you don’t learn them on test day.

Mini‑library of must‑know arithmetic identities and moves

• Difference of squares: a^2 − b^2 = (a − b)(a + b).
• Sum/product of consecutive integers: n(n + 1)/2 for 1 through n.
• Sum of arithmetic series: S_n = n/2(2a_1 + (n − 1)d).
• Sum of first n odd numbers = n^2; sum of first n even numbers = n(n + 1).
• Average × count = sum (re‑arrange to find missing element quickly).
• For remainders: if a ≡ r (mod m), then a + km has same remainder r when divided by m.

High‑yield examples (by topic)

Percent change with successive discounts: - A jacket listed at $100 is discounted 25%, then an additional 10%. Final price = 100 × 0.75 × 0.90 = $67.50. Overall discount = 32.5% (not 35%).

Ratio to counts: - The ratio of cats to dogs is 3:5 and there are 56 animals total. Total parts = 8 → each part = 56/8 = 7. Cats = 3×7 = 21; dogs = 5×7 = 35.

Weighted average: - Class A average 80 (20 students); Class B average 90 (30 students). Combined average = (80×20 + 90×30)/(20 + 30) = (1600 + 2700)/50 = 86.

Work together: - A finishes in 6 hours; B in 4 hours. Together time t = (6×4)/(6 + 4) = 24/10 = 2.4 hours.

LCM for repeats: - One beacon flashes every 12 seconds, another every 18. They flash together every lcm(12,18) = 36 seconds.

Simple remainder: - What is remainder when 5^23 is divided by 4? Powers of 5 mod 4 → 5 ≡ 1 mod 4 → 5^23 ≡ 1^23 ≡ 1 → remainder 1.

Absolute value inequality: - Solve |x − 5| < 2 → 3 < x < 7.

Mixture concentration: - Mix 3 L of 20% solution with 2 L of 50% solution. Solute = 0.6 + 1.0 = 1.6 L; volume = 5 L; final concentration = 1.6/5 = 32%.

The compact arithmetic formula list (one‑screen refresher)

• Divisibility: 2,3,4,5,6,8,9,10 tests.
• LCM/GCD by prime powers: gcd = min exponents; lcm = max exponents.
• Fractions: add via lcm; multiply tops; divide by reciprocal.
• Percents: part = p×whole; change = new − old; successive changes multiply.
• Ratios: A = r/(r+s) × total; scale by any k.
• Means: mean = sum/n; weighted mean = sum of weighted means / total weight.
• Median: middle; range = max − min; SD scales by |k|.
• Exponents: add exponents in multiply; subtract in divide; power of a power multiplies.
• Absolute value: |x − a| < r → a − r < x < a + r.
• Sequences: a_n = a_1 + (n − 1)d; S_n = n/2(first + last).
• Rate: d = rt; work together t = (t_A t_B)/(t_A + t_B).
• Interest: simple A = P(1 + rt); compound A = P(1 + r/n)^(nt).
• Probability: complement = 1 − p; independent multiply; exclusive add.
• Sets: |A ∪ B| = |A| + |B| − |A ∩ B|; 3‑set inclusion–exclusion.

Calculator strategy and time management for the shorter GRE

• Use the calculator only when it beats mental math: multi‑step decimal division, square roots, awkward percents.
• Keep entries clean: parenthesis around numerators/denominators when keying fractions.
• Estimate first; if choices are far apart, you may not need exact arithmetic.
• Pacing: 12 questions in 21 minutes = ~1:45 per question. Quick binning—if not sure of a path in 25–30 seconds, mark/flag and move.

Common traps and how to dodge them

• Mis‑anchored percent: “20% of the original” vs. “20% of the new.” Write a one‑line equation before computing.
• Weighted average mis‑weighting: the weights are counts, not percentages unless totals match.
• Order of operations: PEMDAS (but multiplication and division share precedence; left to right). Parentheses save points.
• Remainder confusion: remainders are strictly between 0 and divisor − 1.
• Negative signs in inequalities: flip when multiplying or dividing by a negative.

Drill framework (with PowerPrep and realistic mocks)

• Memorize one cluster per day (e.g., divisibility + LCM/GCD).
• Create 10–15 targeted drills in a Google Sheet: one column for problem, one for the formula you used, one for the error type if you miss.
• Take official‑style timed sets. ETS PowerPrep’s section interface is your gold standard.
• Review by formula, not by question. Re‑encode misses into Anki cards with: prompt, minimal formula, one numeric example, and a short explanation.

Practice next with our mock tests and PowerPrep-style practice and slot the sessions into one of our study plans by score target.

Q&A: fast answers to common follow‑ups

What are the most important GRE arithmetic formulas?

Know percent/percent change, ratio to counts, weighted mean, LCM/GCD via prime powers, exponent laws, absolute value inequalities, d = rt and work‑together time, simple/compound interest, basic probability, and two‑ and three‑set inclusion–exclusion. These cover the majority of Quant cases where a single formula unlocks the solution path.

Does the GRE provide a formula sheet?

No. The GRE General Test offers an on‑screen calculator in Quant but no formula sheet. You’re expected to know foundational arithmetic and number properties. That’s why a focused checklist—like this one—paired with official‑style practice is the most efficient preparation route for speed and accuracy.

How should I memorize GRE formulas without cramming?

Use spaced repetition with Anki: one card per formula, cloze deletions for key parts, and a tiny worked example. Review daily in short sessions and force recall from context. Then apply each card in 2–3 real problems. Memory solidifies when retrieval is followed by immediate use under mild time pressure.

What percent formulas appear most often on GRE Quant?

Expect part–whole calculations, percent change with successive changes, and “what percent of” comparisons. Quickly convert percentages to decimals, anchor the base correctly, and multiply successive changes. Many data interpretation questions hide percent traps; estimating before calculating often exposes the correct choice faster.

What’s the fastest way to handle ratio and mixture questions?

Translate ratios into parts of a whole: if r:s and total T, then r/(r+s)×T and s/(r+s)×T. For mixtures, use weighted averages or the alligation rule to skip algebra. Draw a quick number line between concentrations, and weight inversely by the distances to the target concentration.

When should I use the GRE calculator vs. mental math?

Use the calculator for messy long division, square roots, and multi‑step decimals; avoid it for clean integers, fraction simplification, and ratio part calculations. Estimate first, decide if exactness matters, and only then key values. Practicing in PowerPrep builds the reflexes you’ll need on test day.

Worked problems (from simple to exam‑ready)

1) Percent increase followed by decrease - A value increases by 30% then decreases by 20%. Net multiplier = 1.30 × 0.80 = 1.04 → 4% overall increase. This shows why successive percents multiply.

2) GCD/LCM to split groups - You have 72 pencils and 90 pens and want identical sets with no leftovers and the greatest number of sets. Number of sets = gcd(72, 90) = 18. Each set has 72/18 = 4 pencils and 90/18 = 5 pens.

3) Average with a missing score - Five scores average 84. Four known scores total 320. Total sum = 84 × 5 = 420. Missing = 420 − 320 = 100.

4) Work together with partial time - Machine A completes a job in 12 hours; Machine B in 8. They work together for 3 hours; what fraction remains? Combined rate = 1/12 + 1/8 = 5/24 job/hour. In 3 hours they finish 15/24 = 5/8. Remaining = 3/8.

5) Absolute value inequality with parameters - Solve |2x − 3| ≤ 7 → −7 ≤ 2x − 3 ≤ 7 → add 3: −4 ≤ 2x ≤ 10 → divide by 2: −2 ≤ x ≤ 5.

6) Remainders with big exponents - Find remainder of 7^202 when divided by 5. 7 ≡ 2 (mod 5). 2^1 ≡ 2; 2^2 ≡ 4; 2^3 ≡ 3; 2^4 ≡ 1; cycle length 4. 202 mod 4 = 2 → remainder = 2^2 = 4.

7) Simple vs. compound interest - $1,000 at 6% for 3 years: simple A = 1000(1 + .06×3) = 1180. Compound annually: A = 1000(1.06)^3 ≈ 1191.02. Difference grows with time and rate.

8) Sets with “at least one” - 200 students: 120 take math, 90 take science, 50 take both. At least one = 120 + 90 − 50 = 160. Neither = 200 − 160 = 40.

9) Mixture replacement - A 20‑L tank has 30% saline. Remove 5 L and replace with water. New concentration multiplier: (1 − 5/20) = 0.75. New concentration = 0.30 × 0.75 = 22.5%.

10) Weighted mean by counts - Three sections: 18 students avg 72, 22 students avg 85, 10 students avg 90. Combined average = (18×72 + 22×85 + 10×90)/50 = (1296 + 1870 + 900)/50 = 4066/50 = 81.32.

Data Interpretation arithmetic (speed patterns)

• Convert chart/graph quantities to clean ratios before percent comparisons.
• For bar and line combinations, compute differences first; then percent change if asked.
• Round both numerator and denominator in the same direction when estimating a ratio to preserve relative size.
• Keep a scratch ledger: labels → raw numbers → simplified fraction → decimal/percent. One line per question avoids copy errors.

10‑minute daily formula workout (repeatable)

• Minute 0–2: run a one‑screen review (the compact list above); say each item aloud.
• Minute 3–7: do four mixed questions (one each: percent, ratio, LCM/GCD, rate/work). Timebox to ~1 minute each.
• Minute 8–10: write two error flashcards: formula, a clean example, trap to avoid, and a one‑sentence solution path.

How to build an Anki deck that sticks

• One formula per card; front has a cloze deletion (“Mean = {{c1::sum}}/{{c2::n}}”).
• Back includes: minimal explanation, a 10‑second numeric example, and a variant trap.
• Tag by topic: percent, ratio, LCM/GCD, averages, exponents, sets, rate/work.
• Review 5–10 minutes per day; suspend cards once you’re accurate at speed.

What to expect on test day (and how arithmetic shows up)

• GRE Quant asks multiple choice (single/best answer), numeric entry, and select‑in‑all‑that‑apply formats.
• Arithmetic appears in word problems, data interpretation tables/graphs, and clean abstraction (e.g., divisibility or remainder logic).
• The ETS on‑screen calculator has memory, basic arithmetic, percent, and square root; learn its key layout before test day.
• The shorter GRE timing (from Sept 2023: 2×12 Quant questions, 21 minutes each) rewards concise arithmetic. Over‑calculating is the most common time sink.

From formulas to a score jump: your next 7 days

Day 1: Divisibility, primes, LCM/GCD. - Memorize rules and the prime‑power method. Drill with 10 factorization problems and 5 LCM/GCD word problems.

Day 2: Fractions and ratios. - Simplify aggressively; practice ratio → counts flow. Mix in proportion cross‑multiplication traps.

Day 3: Percent and percent change. - Set up “multiplier” thinking; do 10 data‑interpretation percent questions.

Day 4: Averages and weighted averages. - Alternate between algebra and mental models; include a combined‑group set.

Day 5: Exponents/roots and absolute value/inequalities. - Focus on exponent laws and |x − a| bands; add two remainder‑with‑powers questions.

Day 6: Rates/work/mixtures and simple/compound interest. - Run 10 d=rt problems and 5 work‑together; cap with two mixture replacements.

Day 7: Full timed set + review. - Do a 12‑question, 21‑minute Quant set. Immediate error review and flashcard updates.

Slot these into our structured study plans by score target and, when ready, simulate full sections using our mock tests and PowerPrep-style practice.

Why study GRE arithmetic with Refonte (and not just memorize)

Refonte Learning is a UK‑registered EdTech in Dover, England. Our differentiator: GRE prep bundled with a real internship‑placement pathway, not just test tricks. In Quant, we teach the minimum viable formula set, then drill decision‑making at speed using official‑style timing and feedback loops that working engineers and analysts rely on.

• Practitioners teaching practitioners: we use the same quantitative thinking in data, cloud, and software roles.
• Cohort‑based accountability: timed sets, feedback, and office hours.
• Results you can verify: Trustpilot 4.7 stars across 76 reviews (claimed profile).

Explore the GRE + internship career pathway, or if you want topical refreshers first, start at the GRE Quant hub and the general GRE hub. When you’re ready to map your plan, book a call.

Extended examples by topic (exam‑style)

A) Percent and data interpretation - A company’s Q1 revenue is $2.4M and Q2 is $2.76M. Percent change = (2.76 − 2.4)/2.4 = 0.36/2.4 = 0.15 = 15%. If costs rise from $1.5M to $1.725M (15%), profit margins remain constant at 0.45M to 0.495M (both 18.75% of revenue). Recognize proportional growth.

B) Ratio with additive constraint - The ratio of red to blue marbles is 4:3. When 14 blue marbles are added, the ratio becomes 8:9 (red:blue). Let red = 4k, blue = 3k initially. After adding, 4k : (3k + 14) = 8 : 9 → 36k = 32k + 112 → 4k = 112 → k = 28. Red = 112, blue initially 84.

C) Weighted mean and missing weight - A portfolio has assets with returns 5%, 8%, and 12%. The 8% asset is twice the weight of the 5% asset, and the 12% asset equals the 5% asset’s weight. If total return is 8.5%, find weights. Let 5% weight = x → 8% weight = 2x, 12% weight = x; total = 4x. Weighted return = (0.05x + 0.08·2x + 0.12x)/(4x) = (0.05 + 0.16 + 0.12)/4 = 0.33/4 = 8.25%. To reach 8.5%, adjust 12% weight slightly above x and reduce 5% slightly below x; solve linearly if asked.

D) LCM/GCD application in scheduling - Buses leave a station every 18 and 24 minutes starting together at 8:00. They meet every lcm(18, 24) = 72 minutes → 9:12, 10:24, etc. If a third bus every 30 minutes is added, next triple meet after lcm(18, 24, 30) = 360 minutes → 2:00 PM.

E) Exponents and unit digit - Unit digit of 7^123? Pattern of 7’s units: 7, 9, 3, 1 (cycle 4). 123 mod 4 = 3 → units digit 3.

F) Remainders with divisibility - Find the smallest positive integer n such that 35n is a multiple of 72. Factor: 35 = 5 × 7; 72 = 2^3 × 3^2. We need n to supply 2^3 and 3^2 and clear any overlap: n must contain 2^3 × 3^2 = 8 × 9 = 72. But 35n divisible by 72 → n must be 72/gcd(35,72) = 72/1 = 72 (since gcd(35,72)=1). Smallest n = 72.

G) Rate and average speed trap - Drive 60 miles at 30 mph, then 60 miles at 60 mph. Average speed = total distance / total time = 120 / (2 + 1) = 40 mph (not 45). Distances equal, so harmonic mean of speeds applies: 2ab/(a + b) = 2×30×60/90 = 40.

H) Mixture and alligation - Make 30% solution from 20% and 50%. Target 30% lies 10 points from 20% and 20 points from 50%. Inverse weighting: parts of 50% : parts of 20% = 10 : 20 = 1 : 2. For 900 mL final, 300 mL of 50% and 600 mL of 20%.

I) Sets with exactly conditions - In a survey, 40 like tea, 50 like coffee, 20 like both. Exactly one = (40 − 20) + (50 − 20) = 50. At least one = 40 + 50 − 20 = 70. Neither if total 100 → 30.

J) Inequality with sign flip - Solve −3(2x − 5) ≥ 9 → −6x + 15 ≥ 9 → −6x ≥ −6 → divide by −6 and flip: x ≤ 1.

What the official test makers say (so you calibrate correctly)

• ETS specifies that Quant emphasizes arithmetic, algebra, geometry, and data analysis, with an on‑screen calculator available; no formula sheet is supplied. The shorter test (effective September 2023) runs about 1 hour 58 minutes total, with two Quant sections of 12 questions each and 21 minutes per section.
• Translation: arithmetic fluency is a real edge. If you can translate words to numbers and apply one of a dozen moves here, you’ll beat the clock.

Build your plan with Refonte

• Start with the formula clusters above; print or copy the compact list.
• Drill with official‑style items: use ETS PowerPrep and our mock tests and PowerPrep-style practice.
• Slot into a target‑score roadmap with our study plans by score target.
• When you want structure and accountability, join our cohort and add the GRE + internship career pathway.
• If you’re deciding pathways, book a call to see how the internship track pairs with your grad‑school timeline.

We deliver GRE prep bundled with a real industry pathway, not just a test score. That’s the difference at Refonte Learning—and it shows when you translate arithmetic into results on exam day and into workflows at work.

Quick reference: formula‑to‑question mapping

• Divisibility/LCM/GCD → split/packaging, schedules, trailing zeros, least repeats.
• Fractions/ratios → recipes, class counts, map scales, mixture buckets.
• Percent/percent change → discounts/markups, growth rates, DI charts.
• Averages/weighted mean → class merges, portfolio returns, score additions.
• Exponents/roots → unit digits, scientific notation, remainder cycles.
• Absolute value/inequalities → ranges, tolerances, distance from target.
• Rates/work/mixtures/interest → travel, productivity, concentration, finance.
• Sets/probability → survey overlaps, at least/at most, simple picks.

Final checklist before your next timed set

• Warm‑up: recite percent, ratio, LCM/GCD, d=rt, and weighted mean formulas.
• Decide on calculator usage per question before touching it.
• Estimate first; if two choices die immediately, you’ve bought time.
• Show one line of algebra per step to avoid arithmetic slips.
• Finish with a scan for sign errors, unit conversions, and base of percent.

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