GMAT Focus Math Formulas Cheat Sheet 2026: Every Quant Formula You Need
Every GMAT Focus Quant formula in one place — arithmetic, percentages, number properties, algebra, word problems, statistics, counting and probability — with worked examples and the traps that catch test-takers. Geometry appendix included.
▶ Free College Predictor & study-abroad toolsWhat GMAT Focus Quant actually tests in 2026
The GMAT Focus Edition Quantitative Reasoning section is 21 questions in 45 minutes, and it is Problem Solving only — Data Sufficiency moved to the new Data Insights section. Importantly, geometry was removed from the Focus Quant section, so your formula memorisation should be weighted toward arithmetic, number properties, algebra and word problems. We still include a geometry appendix at the end because the concepts can appear inside Data Insights problems and on older test formats.
Arithmetic, fractions and percentages
Percentages are the single most tested arithmetic topic on the GMAT. Master percent change and successive percentages first.
| Concept | Formula |
|---|---|
| x percent of y | (x / 100) × y |
| What percent a is of b | (a / b) × 100 |
| Percent change | (New − Old) / Old × 100 |
| Successive % change (p then q) | Net = (1 + p/100)(1 + q/100) − 1 |
| Increase then decrease by same x% | Net change = −x² / 100 (always a net loss) |
| Fraction to percent | Multiply the fraction by 100 |
Ratios, proportions and averages
A ratio a : b splits a total into parts of size a/(a+b) and b/(a+b). Averages are just sum ÷ count — the trick is knowing when to use a weighted average.
| Concept | Formula |
|---|---|
| Average (arithmetic mean) | Sum ÷ Count |
| Sum from average | Average × Count |
| Weighted average | Σ(weight × value) ÷ Σ(weights) |
| Part of a total from a ratio a : b | Part = Total × a / (a + b) |
| Proportion (cross-multiply) | a/b = c/d ⟶ a·d = b·c |
Number properties (a GMAT favourite)
GMAT Focus leans heavily on number properties: even/odd, factors, divisibility and remainders. These rules save you from slow calculation.
- Even ± Even = Even, Odd ± Odd = Even, Even ± Odd = Odd
- Even × anything = Even; Odd × Odd = Odd
- Number of factors of N = p^a · q^b · r^c is (a+1)(b+1)(c+1)
- The product of any n consecutive integers is divisible by n!
- For two numbers: LCM × HCF = product of the two numbers
- Divisibility: by 3 or 9 if the digit sum is; by 4 if last two digits are; by 8 if last three are; by 6 if divisible by 2 and 3; by 11 if the alternating digit sum is divisible by 11
Algebra: identities, quadratics and exponents
Recognising algebraic identities instantly is how strong scorers avoid heavy expansion.
| Identity / rule | Formula |
|---|---|
| Square of a sum | (a + b)² = a² + 2ab + b² |
| Square of a difference | (a − b)² = a² − 2ab + b² |
| Difference of squares | a² − b² = (a + b)(a − b) |
| Sum / difference of cubes | a³ ± b³ = (a ± b)(a² ∓ ab + b²) |
| Quadratic roots | x = [ −b ± √(b² − 4ac) ] / (2a) |
| Sum & product of roots | Sum = −b/a , Product = c/a |
| Discriminant b² − 4ac | > 0: two real roots; = 0: one; < 0: none |
| Exponent rules | aᵐ·aⁿ = aᵐ⁺ⁿ ; aᵐ/aⁿ = aᵐ⁻ⁿ ; (aᵐ)ⁿ = aᵐⁿ ; a⁰ = 1 ; a⁻ⁿ = 1/aⁿ |
Word problems: speed, work, interest and mixtures
Most GMAT word problems reduce to one of these five engines. The two biggest traps are averaging speeds and confusing simple vs compound interest.
| Type | Formula |
|---|---|
| Distance | Distance = Speed × Time |
| Average speed | Total distance ÷ Total time (NOT the average of the speeds) |
| Equal distance at speeds x, y | Average speed = 2xy / (x + y) |
| Combined work rate | Time together = ab / (a + b) (when each alone takes a and b) |
| Simple interest | SI = P · R · T / 100 |
| Compound interest (amount) | A = P (1 + R/100)ᵀ ; CI = A − P |
| Profit / loss percent | (SP − CP) / CP × 100 |
| Mixtures (alligation) | Cheaper qty : Dearer qty = (Dearer − Mean) : (Mean − Cheaper) |
Statistics
The GMAT tests the meaning of these measures more than heavy computation — especially how mean, median and standard deviation shift when a set changes.
| Measure | Formula / rule |
|---|---|
| Mean | Sum of values ÷ Number of values |
| Median | Middle value (mean of the two middles if the count is even) |
| Mode | The most frequently occurring value |
| Range | Maximum − Minimum |
| Evenly spaced set | Mean = Median = (First + Last) / 2 |
| Standard deviation | Measures spread; SD = 0 only when every value is identical |
Counting and probability
Decide first whether order matters: order matters → permutations (P), order doesn't → combinations (C).
| Concept | Formula |
|---|---|
| Permutations (order matters) | nPr = n! / (n − r)! |
| Combinations (order doesn't) | nCr = n! / [ r! (n − r)! ] , and nCr = nC(n−r) |
| Arrangements of n distinct items | n! |
| Arrangements with repeats | n! / (p! q! …) for repeated items |
| Circular arrangements of n | (n − 1)! |
| Probability of an event | Favourable outcomes ÷ Total outcomes |
| P(A or B) | P(A) + P(B) − P(A and B) |
| P(not A) | 1 − P(A) |
| Independent events | P(A and B) = P(A) × P(B) |
Sequences and series
Arithmetic (constant difference) and geometric (constant ratio) progressions, plus three sum shortcuts worth memorising.
| Concept | Formula |
|---|---|
| Arithmetic progression — nth term | aₙ = a + (n − 1)d |
| Arithmetic progression — sum | Sₙ = n/2 · (First + Last) = n/2 · [2a + (n−1)d] |
| Geometric progression — nth term | aₙ = a · r^(n−1) |
| Geometric progression — sum | Sₙ = a (rⁿ − 1) / (r − 1) , r ≠ 1 |
| Sum of first n integers | n(n + 1) / 2 |
| Sum of first n squares | n(n + 1)(2n + 1) / 6 |
| Sum of first n odd numbers | n² |
Geometry appendix (light on GMAT Focus, useful for Data Insights)
Geometry was removed from the standalone Focus Quant section, but these still help on Data Insights graphics and on older formats, so keep them on hand.
| Shape | Formula |
|---|---|
| Triangle area | ½ × base × height ; Heron's = √[s(s−a)(s−b)(s−c)], s = (a+b+c)/2 |
| Pythagoras | a² + b² = c² |
| Special right triangles | 45-45-90 sides 1 : 1 : √2 ; 30-60-90 sides 1 : √3 : 2 |
| Circle | Area = π r² ; Circumference = 2π r ; Sector area = (θ/360) π r² |
| Rectangle | Area = l × w ; Perimeter = 2(l + w) |
| Square | Area = s² ; Perimeter = 4s |
| Cylinder / sphere volume | Cylinder = π r² h ; Sphere = (4/3) π r³ |
| Interior angles of an n-gon | (n − 2) × 180° |
| Coordinate geometry | Distance = √[(x₂−x₁)² + (y₂−y₁)²] ; Slope = (y₂−y₁)/(x₂−x₁) ; Line: y = mx + b |
The five formula traps that cost the most points
Knowing the formula isn't enough — these are the misapplications GMAT question-writers deliberately bait.
- Averaging speeds. Average speed is total distance ÷ total time, never (x + y)/2 unless the times are equal.
- Successive percentages. A 20% rise then a 20% fall is a net 4% loss, not break-even.
- Simple vs compound interest. Read carefully — compound grows on the new balance each period.
- Permutation vs combination. 'How many ways to arrange' = permutation; 'how many ways to choose' = combination.
- Counting the endpoints. The number of integers from a to b inclusive is b − a + 1, not b − a.
How to lock these in — free GMAT practice
Formulas only stick when you apply them under timing. Take a free, full-length GMAT Focus mock test on LandingPrep — real 45-minute Quant timing and instant scoring — then come back to this sheet for anything you missed. No signup, no payment. Start your free GMAT mock test or open the free GMAT prep lessons.
Frequently asked questions
- Does GMAT Focus test geometry?
- Geometry was removed from the standalone Quantitative Reasoning section of the GMAT Focus Edition. The Quant section is Problem Solving only and emphasises arithmetic, number properties, algebra and word problems. Geometry concepts can still appear inside Data Insights questions, which is why we include a short geometry appendix.
- Is there a formula sheet provided during the GMAT?
- No. The GMAT does not provide a formula sheet or a physical calculator on the Quant section, so every formula on this cheat sheet must be memorised and automatic. An on-screen calculator is available only on the Data Insights section.
- How many formulas do I really need for the GMAT?
- Fewer than most students fear. Master percentages, number properties, the core algebra identities, the speed/work/interest engines, and the counting and probability rules on this page, and you cover the large majority of GMAT Focus Quant questions.
- What is the most important Quant area on GMAT Focus?
- Arithmetic and number properties — especially percentages, divisibility, factors and remainders — appear most often, followed by algebra and word problems. Weight your revision accordingly.
- How is GMAT Focus Quant scored?
- The Quantitative Reasoning section is scored from 60 to 90, and the three sections (Quant, Verbal, Data Insights) combine into a total score from 205 to 805. Strong Quant accuracy and pacing on the 21 questions in 45 minutes is the fastest route to a higher total.