Last updated July 07, 2026 · Reviewed by the AnvayaPrep team
Introduction
The Arithmetic unit is the quantitative backbone of the GMAT. It covers the numerical concepts that underlie virtually every other topic on the exam: how numbers are structured and related, how fractions and decimals represent parts of wholes, how ratios and proportions scale relationships, how percents measure change, and how exponents model multiplicative growth. Topics in this unit include integers, divisibility, multiples, factors, prime numbers, remainders, number properties, fractions, decimals, percents, ratios, proportions, exponents, roots, scientific notation, order of operations, absolute value, estimation, rates, distance-rate-time, interest, profit and loss, mixtures, weighted averages, work problems, and arithmetic word problems.
Because these concepts are not isolated skills but an interconnected system, weakness in one area compounds across others. A student who does not control fraction operations will also struggle with probability, rates, and algebraic expressions. A student who misapplies percent change rules will err on successive-percent and interest problems. The Arithmetic unit rewards cumulative mastery: every hour invested here multiplies across the rest of the Quantitative Reasoning section.
The GMAT does not test arithmetic through rote calculation. It tests conceptual understanding, pattern recognition, and strategic decision-making. Questions are designed so that students who understand why a rule works are faster and more accurate than those who merely memorize it. This unit develops both layers simultaneously.
Learning Objectives
- Perform operations on fractions, decimals, and integers accurately and efficiently, including conversion among all three forms
- Apply the fundamental percent formula to find parts, wholes, and percent change, including successive and reverse percent problems
- Use ratio and proportion reasoning to find actual values from ratio relationships and to solve scaling problems
- Evaluate expressions with exponents and roots using the product, quotient, power, and distribution rules, including negative and fractional exponents
- Solve rate, distance-rate-time, work, mixture, interest, and profit-and-loss problems by identifying the correct formula and unknown
- Apply divisibility rules, prime factorization, and number property reasoning to problems involving integers, factors, multiples, and remainders
- Recognize the structure of arithmetic word problems, translate verbal relationships into equations, and verify solutions against the question asked
- Use estimation and benchmark values strategically to eliminate answer choices without full calculation
High-Yield Concepts
The following topics carry the highest frequency and difficulty weight in GMAT Arithmetic questions.
| Topic | Core Rule or Formula | Common GMAT Trap | ||||||
|---|---|---|---|---|---|---|---|---|
| Fractions | To add/subtract, find common denominator; multiply straight across; divide by flipping the second fraction | Adding numerators AND denominators when adding fractions | ||||||
| Percents | Percent change = (New - Old) / Old x 100; original is always the base | Using the wrong base; adding successive percent changes | ||||||
| Ratios | x:y means x = mk, y = nk; ratio alone never gives actual values | Treating ratio numbers as actual values | ||||||
| Exponents | Same base: multiply adds exponents, divide subtracts; power-to-power multiplies | Adding exponents when adding terms (2^3 + 2^4 does not equal 2^7) | ||||||
| Divisibility | A number is divisible by n if the remainder is 0; use prime factorization for LCM/GCF | Confusing divisibility with being a multiple | ||||||
| Rates | Distance = Rate x Time; combined work rate = sum of individual rates | Averaging rates directly instead of using harmonic mean logic | ||||||
| Successive Percents | Net multiplier = (1 + r1/100)(1 + r2/100); changes do not simply add | Assuming 20% up then 20% down returns to start | ||||||
| Weighted Average | Total = sum of (value x weight) / sum of weights | Averaging group averages when group sizes differ | ||||||
| Interest | Simple: I = Prt; Compound: A = P(1+r)^t | Applying simple interest formula to compound questions | ||||||
| Absolute Value | x | = x if x >= 0; | x | = -x if x < 0; produces two cases in equations | Treating | x | = a as having only one solution |
On every percent problem, before calculating, identify which value is the base (the "whole" that comes after "of"). Using the wrong base is the single most common source of wrong answers in percent questions.
Successive percent changes cannot be added. A 10% increase followed by a 10% decrease results in a net change of -1%, not 0%. Always multiply the change multipliers: 1.10 x 0.90 = 0.99.
Study Strategy
Begin with fractions, decimals, and percents because these three concepts are structurally identical (parts of a whole expressed differently) and because fluency in converting among them is assumed throughout the test. Once those are solid, move to ratios and proportions, which extend fraction thinking to multi-variable relationships. Then tackle exponents and roots, which introduce multiplicative structure. Rates, distance-time, work, and mixture problems build on all prior arithmetic and represent the most complex word-problem formats in this unit.
For each topic, study in this sequence: understand the core concept, learn the formula or rule and why it works, work through the standard question types, then drill the variations the GMAT favors (successive changes, reverse problems, data sufficiency framing). Do not skip the "why it works" step. The GMAT exploits students who know a rule but do not understand it.
Prioritize active recall over passive review. After studying a concept, close the notes and solve three to five problems from memory. This is more efficient than re-reading the same content.
Common Mistakes
Fractions: Adding the numerators and denominators directly (1/2 + 1/3 = 2/5 is wrong; the correct answer is 5/6). Canceling terms across addition or subtraction, such as simplifying (x + 3)/(x + 5) to 3/5. Multiplying mixed numbers without first converting to improper fractions.
Decimals: Assuming more decimal places means a larger number (0.9 is greater than 0.875). Placing the decimal point by counting from the left instead of the right when multiplying.
Percents: Computing "reverse percent" problems by subtracting the percent from the final value instead of dividing by the multiplier. Misreading "200% more than X" as "200% of X" (the former means 3X; the latter means 2X).
Ratios: Treating the ratio 3:4 as meaning the quantities are exactly 3 and 4 rather than 3k and 4k. Calculating the fraction of one part as a fraction over the ratio number rather than the total (if boys:girls = 3:5, the fraction of boys is 3/8, not 3/5).
Exponents: Applying the power rule to sums: (x + y)^2 does not equal x^2 + y^2. Forgetting that even exponents always produce non-negative results regardless of the sign of the base. Assuming (-3)^2 = -9 when in fact it equals 9.
Rates and Work: Averaging two rates directly when working with combined rates. Forgetting to align units (hours versus minutes, miles versus kilometers).
Number Properties: Treating any integer divisible by 2 as a prime candidate for divisibility rules. Confusing a number's factors with its multiples.
Exam Tips
Estimation first. Before calculating, look at the answer choices. If they are spread far apart, estimation will eliminate all but one option in under 30 seconds. Reserve full calculation for problems where choices are close together.
Memorize key conversions. The fraction-decimal-percent equivalents that save the most time: 1/2 = 0.5 = 50%; 1/4 = 0.25 = 25%; 1/3 = 0.333 = 33.3%; 1/8 = 0.125 = 12.5%; 2/3 = 0.667 = 66.7%; 1/5 = 0.2 = 20%. Instant recall of these eliminates conversion steps in many problems.
Know common powers. Powers of 2 through 2^10, powers of 3 through 3^5, and perfect squares through 15^2 appear constantly. Recognizing that 32 = 2^5 and 27 = 3^3 allows immediate manipulation of exponential equations.
For Data Sufficiency arithmetic questions, ask what minimum information is required. For percent problems, both the percent AND an actual value (or the total) are typically needed. Knowing only that sales increased 20% is insufficient without knowing the original sales figure.
Work backward from answer choices when algebraic setup is slow. Substitute answer choices directly into the problem, starting with the middle value if choices are ordered numerically. This strategy is fastest when the calculation is straightforward once you have the candidate value.
In word problems, identify and underline the question before solving. The GMAT includes trap answer choices that represent intermediate calculations. Solving for the right quantity but stopping one step early is one of the most common errors under time pressure.
For division of fractions, use "Keep, Change, Flip": keep the first fraction, change the operation from division to multiplication, and flip the second fraction. For percent change, use "NOON": New minus Old, Over Not-new (the original).
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