TL;DR: The GMAT Focus Quant section gives you no calculator and no formula sheet. You need every formula memorized and fast enough to apply without computing aids. The formulas below cover arithmetic, algebra, geometry, statistics, and number properties. After reading this list, close it and write every formula from memory to find your real gaps.
You get 21 questions in 45 minutes on the GMAT Focus Quant section. No calculator. No formula reference. Every computation happens in your head or on scratch paper.
This is the single biggest difference between GMAT Quant and GRE Quant. The GRE gives you an on-screen calculator. The GMAT does not. Knowing a formula is not enough. You need to be able to execute the arithmetic behind it quickly and accurately, by hand. That means memorizing not just the formulas themselves but also building fluency with common computations: fraction-to-decimal conversions, squaring two-digit numbers, simplifying radicals.
This page organizes every formula the GMAT Quant section can test. Bookmark it, come back after every practice session, and use it as a self-test.
Mental Math Fundamentals
Before the formulas, get these computations automatic. Without a calculator, you will use them constantly.
Fraction-decimal equivalents you should know on sight:
- 1/2 = 0.5
- 1/3 = 0.333, 2/3 = 0.667
- 1/4 = 0.25, 3/4 = 0.75
- 1/5 = 0.2, 2/5 = 0.4, 3/5 = 0.6, 4/5 = 0.8
- 1/6 = 0.167, 5/6 = 0.833
- 1/8 = 0.125, 3/8 = 0.375, 5/8 = 0.625, 7/8 = 0.875
Perfect squares worth memorizing: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400.
Powers of 2: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024.
Powers of 3: 3, 9, 27, 81, 243.
These show up constantly in answer choices and in the intermediate steps of problems. Recognizing them saves you from long multiplication on scratch paper.
Arithmetic and Number Properties
Percent Change
$$\text{Percent change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100$$
A positive result is an increase. A negative result is a decrease. The denominator is always the original value.
Percent of a Number
$$\text{Part} = \text{Percent} \times \text{Whole}$$
Or equivalently: Part / Whole = Percent. On a no-calculator test, convert percentages to fractions when possible. 25% of 80 is easier as (1/4)(80) = 20 than as 0.25 x 80.
Simple Interest
$$I = P \times r \times t$$
Where P is principal, r is the annual rate (as a decimal), and t is time in years.
Compound Interest
$$A = P\left(1 + \frac{r}{n}\right)^{nt}$$
Where n is the number of compounding periods per year. The GMAT rarely gives you difficult compound interest numbers. When it does, the exponent is usually small (2 or 3), making manual computation feasible.
Divisibility Rules
These let you eliminate answer choices quickly without long division:
- Divisible by 2: last digit is even
- Divisible by 3: sum of digits is divisible by 3
- Divisible by 4: last two digits form a number divisible by 4
- Divisible by 5: last digit is 0 or 5
- Divisible by 6: divisible by both 2 and 3
- Divisible by 9: sum of digits is divisible by 9
Properties of Zero and One
- Zero is even, not positive, not negative
- One is not prime
- The smallest prime is 2
- Any number raised to the power of zero equals 1 (for nonzero bases)
Prime Factorization
Every positive integer greater than 1 can be expressed as a unique product of primes. To find the number of factors of a number, take its prime factorization, add 1 to each exponent, and multiply.
Example: 72 = 2^3 x 3^2. Number of factors = (3+1)(2+1) = 12.
LCM and GCF
- GCF (Greatest Common Factor): take the lowest power of each shared prime factor.
- LCM (Least Common Multiple): take the highest power of each prime factor present in either number.
- Useful relationship: GCF(a,b) x LCM(a,b) = a x b.
Algebra
Slope of a Line
$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\text{rise}}{\text{run}}$$
Slope-Intercept Form
$$y = mx + b$$
Where m is the slope and b is the y-intercept.
Point-Slope Form
$$y - y_1 = m(x - x_1)$$
Quadratic Formula
$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
Used when ax^2 + bx + c = 0. On the GMAT, try factoring first. Without a calculator, the quadratic formula involves more scratch work, so factoring saves time when it works.
Difference of Squares
$$a^2 - b^2 = (a+b)(a-b)$$
This identity is one of the most frequently tested algebra concepts on the GMAT. Recognize it in both directions.
Perfect Square Trinomials
$$(a+b)^2 = a^2 + 2ab + b^2$$ $$(a-b)^2 = a^2 - 2ab + b^2$$
Exponent Rules
- $a^m \times a^n = a^{m+n}$
- $\frac{a^m}{a^n} = a^{m-n}$
- $(a^m)^n = a^{mn}$
- $a^0 = 1$ (for any nonzero a)
- $a^{-n} = \frac{1}{a^n}$
- $a^{1/n} = \sqrt[n]{a}$
On the GMAT, exponent problems frequently require simplifying expressions with the same base. Convert roots to fractional exponents when the problem mixes radicals and exponents.
Absolute Value
$$|x| = x \text{ if } x \geq 0, \quad |x| = -x \text{ if } x < 0$$
For equations: |x| = a means x = a or x = -a. For inequalities: |x| < a means -a < x < a. |x| > a means x > a or x < -a.
Inequalities
When you multiply or divide both sides of an inequality by a negative number, flip the inequality sign. This is one of the most common traps on the GMAT.
Geometry
Triangles
Area of a triangle: $$A = \frac{1}{2} \times base \times height$$
The height is always perpendicular to the base, not the slant side.
Pythagorean theorem (right triangles only): $$a^2 + b^2 = c^2$$
Where c is the hypotenuse. Common Pythagorean triples you should recognize on sight: 3-4-5, 5-12-13, 8-15-17. Multiples also apply: 6-8-10, 9-12-15, 10-24-26. Recognizing these triples is especially valuable on the GMAT because you cannot use a calculator to verify your computation.
30-60-90 triangle side ratios: $$1 : \sqrt{3} : 2$$
The side opposite 30 degrees is the shortest. The hypotenuse is always twice the shortest side.
45-45-90 triangle side ratios: $$1 : 1 : \sqrt{2}$$
Both legs are equal. The hypotenuse is either leg times the square root of 2.
Sum of interior angles of any triangle: 180 degrees.
Sum of interior angles of any polygon: $$(n - 2) \times 180°$$
Where n is the number of sides.
Circles
Area of a circle: $$A = \pi r^2$$
Circumference of a circle: $$C = 2\pi r = \pi d$$
Arc length (a portion of the circumference): $$\text{Arc length} = \frac{\theta}{360} \times 2\pi r$$
Where the angle is the central angle in degrees.
Area of a sector: $$\text{Sector area} = \frac{\theta}{360} \times \pi r^2$$
Rectangles and Quadrilaterals
Area of a rectangle: A = length x width.
Perimeter of a rectangle: P = 2(length) + 2(width).
Area of a square: A = side squared.
Diagonal of a square: d = side times the square root of 2.
Area of a parallelogram: A = base x height. The height is perpendicular to the base.
Area of a trapezoid: $$A = \frac{1}{2}(b_1 + b_2) \times h$$
Where b1 and b2 are the parallel sides.
3D Shapes
Volume of a rectangular solid (box): V = length x width x height.
Volume of a cylinder: V = pi times r squared times height.
Surface area of a rectangular solid: SA = 2(lw + lh + wh).
Statistics and Probability
Mean (Arithmetic Average)
$$\bar{x} = \frac{\text{sum of all values}}{n}$$
A useful rearrangement: sum = mean x count. This lets you work backward from an average to find a missing value.
Median
The middle value when all values are ordered. For an even number of values, the median is the average of the two middle values.
Mode
The value that appears most frequently.
Range
$$\text{Range} = \text{maximum} - \text{minimum}$$
Standard Deviation
The GMAT does not ask you to calculate standard deviation from scratch. You need to understand what it measures (spread around the mean) and how to compare two data sets. A set with values clustered near the mean has a lower standard deviation than one with values spread far from the mean. Adding or subtracting a constant to every value does not change the standard deviation. Multiplying every value by a constant multiplies the standard deviation by that constant.
Weighted Average
$$\text{Weighted average} = \frac{w_1x_1 + w_2x_2 + ... + w_nx_n}{w_1 + w_2 + ... + w_n}$$
This comes up frequently on the GMAT in mixture, ratio, and combined-group problems.
Basic Probability
$$P(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}$$
Probability of A and B (independent events): $$P(A \text{ and } B) = P(A) \times P(B)$$
Probability of A or B: $$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$$
Combinations and Permutations
Combinations (order does not matter): $$nCr = \frac{n!}{r!(n-r)!}$$
Permutations (order matters): $$nPr = \frac{n!}{(n-r)!}$$
The distinction: choosing 3 people for a committee from 10 is a combination. Arranging 3 books on a shelf from 10 is a permutation.
Rate, Work, and Distance
Distance Formula
$$D = r \times t$$
Where D is distance, r is rate (speed), and t is time. Know the rearrangements: r = D/t and t = D/r.
Average Speed
When the same distance is covered at two different speeds: $$\text{Average speed} = \frac{2 r_1 r_2}{r_1 + r_2}$$
Average speed is not the simple average of the two speeds unless equal time (not equal distance) is spent at each speed.
Combined Work Rate
Two workers completing one job together: $$\text{Time together} = \frac{xy}{x + y}$$
Where x is the time for worker A alone and y is the time for worker B alone. For three workers: find the combined rate (1/x + 1/y + 1/z = 1/T) and solve for T.
Estimation Strategies for No-Calculator Problems
Because every calculation on the GMAT is done by hand, estimation is not a shortcut. It is a core skill.
When answer choices are spread apart (for example: 12, 45, 98, 150, 210), rough estimation is often enough to identify the correct answer without completing the full computation.
When multiplying, round one factor up and the other down to keep your estimate close. For instance, 48 x 52 is close to 50 x 50 = 2,500 (actual: 2,496).
When dividing, convert to friendly fractions. 247/51 is close to 250/50 = 5.
For percent problems, use benchmarks: 10% is easy to compute, so 15% = 10% + 5% (half of 10%). 12.5% = 1/8.
On a question-level adaptive test like the GMAT Focus, every question matters. Estimation lets you move through easier problems faster, saving time for harder ones.
How to Use This Page
Reading formulas is not the same as knowing them. After you go through this list, close it and write out every formula from memory. Anything you cannot reproduce from memory is a gap.
Then practice applying them without a calculator. Pull up official GMAT practice problems and work through them on paper. The formula is only useful if you can pair it with clean, efficient scratch work.
The formulas that show up most often on GMAT Focus Quant, roughly ordered: percent change, Pythagorean theorem, D=rt, combined work rate, weighted averages, probability, area of a circle, exponent rules, and the special right triangles. If your study time is limited, build fluency in those first.
What to Do Next
- Close this page and write out every formula from memory on a blank sheet of paper. Mark anything you missed or hesitated on.
- Work through 10 official GMAT practice problems using only scratch paper. No calculator, no looking back at this page. Note which formulas tripped you up.
- For percent change and combined work rate problems specifically, write the formula at the top of your scratch paper before starting any problem involving those concepts. This prevents careless errors while the formula becomes automatic.
- Build a mental math drill routine: practice squaring two-digit numbers, converting fractions to decimals, and simplifying radicals for 5 minutes before each study session.
- Read our GMAT Focus time management guide to pair formula knowledge with pacing strategy across all 21 questions.
The GMAT Quant section rewards preparation that goes deeper than memorization. You need the formulas in your head and the arithmetic skills to execute them under time pressure, without a calculator. The GRE course is $25 per month with a free diagnostic if the GRE is an option for your profile. For a structured approach to building test readiness alongside the rest of your deferred MBA application, coaching can help you build a study plan that fits your timeline and target score.