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Quantitative Reasoning

21 questions. 45 minutes. No calculator.

Pure problem-solving. No geometry. No data sufficiency. Just math reasoning at its core.

Arithmetic

Arithmetic Fundamentals

The bedrock of Quant. ~30% of questions test these directly. Master them or nothing else matters.

Arithmetic

Fractions & Decimals

Proper, improper, mixed numbers
Add/subtract with common denominators
Multiply & divide fractions
Complex fractions (fractions within fractions)
Converting between fractions, decimals, percentages
Terminating vs repeating decimals
Arithmetic

Percentages

Trap: 20% increase then 20% decrease ≠ original. It's 96%.

"X percent of Y" calculations
Percent increase and decrease
Successive percentage changes
Percent greater/less than
Converting fractions ↔ decimals ↔ percentages
Arithmetic

Number Properties

The #1 most tested topic in Data Sufficiency. Know these cold.

Even/odd rules under +, −, ×
Positive/negative sign rules
Prime numbers (know all 25 primes under 100)
Factors, multiples, divisibility rules
GCF and LCM
Prime factorization
Remainder theory
Units digit patterns
Arithmetic

Powers, Roots & Exponents

Exponent rules (multiply, divide, power-of-power)
Negative and zero exponents
Fractional exponents = roots
Simplifying radical expressions
Rationalizing denominators
Arithmetic

Ratios & Proportions

The ratio multiplier: if ratio is 3:5, values are 3k and 5k. Find k.

Two-part and three-part ratios
Ratio multiplier technique
Direct and inverse proportion
Cross-multiplication for proportions
Algebra

Algebra & Equations

The largest Quant topic. Equations appear in nearly every question. This is non-negotiable.

Algebra

Linear Equations

Key insight: n equations with n unknowns = solvable (usually).

Single-variable equations
Systems of 2 equations (substitution)
Systems of 2 equations (elimination)
Solving for one variable in terms of another
Algebra

Quadratic Equations

FOIL (expanding binomials)
Factoring quadratics
Special identities: a²−b² = (a+b)(a−b)
Perfect square trinomials
Zero-product property
Algebra

Inequalities & Absolute Value

Most common trap: forgetting to flip the inequality sign.

Solving linear inequalities
FLIP the sign when multiplying/dividing by negative
Compound inequalities (AND / OR)
Absolute value equations: |x| = a means x = a or x = −a
Absolute value inequalities
Algebra

Functions & Sequences

Function notation f(x)
Domain and range
Composite functions f(g(x))
Custom/symbolic operations
Arithmetic sequences (common difference)
Geometric sequences (common ratio)
Algebra

Coordinate Geometry

The ONLY geometry on the GMAT Focus Edition. No triangles, no circles.

Slope formula and y = mx + b
Parallel lines (equal slopes)
Perpendicular lines (negative reciprocal slopes)
Distance and midpoint formulas
Graphing inequalities in the coordinate plane
Word Problems

Word Problems

Translation is the skill. Read the English, write the equation, solve. ~25% of Quant.

Word Problems

Rate, Speed & Distance

D = R × T (the master formula)
Average speed = total distance / total time
Converging: speeds add up
Same direction: speeds subtract
Round trip problems
Catch-up rate problems
Word Problems

Work & Time Problems

If A takes 6 hrs and B takes 3 hrs, together: 1/6 + 1/3 = 1/2 → 2 hours.

Work = Rate × Time
Combined rates: 1/A + 1/B = 1/Total
Opposing work (filling vs draining)
Pipes and cisterns
Word Problems

Mixtures & Interest

Combining solutions of different concentrations
Weighted average approach
Simple interest: SI = PRT
Compound interest: A = P(1 + r/n)^(nt)
Profit, loss, and markup calculations
Statistics

Statistics & Counting

High-value topics. Counting + probability + sets = 15-20% of Quant.

Statistics

Descriptive Statistics

Mean (arithmetic average)
Weighted average
Median (middle value)
Mode (most frequent)
Range (max − min)
Standard deviation (concept only, no complex calc)
Statistics

Counting & Probability

Fundamental counting principle
Permutations: n!/(n-r)!
Combinations: n!/(r!(n-r)!)
Restricted arrangements
Basic probability = favorable/total
Complementary probability: P(at least 1) = 1 − P(none)
Independent events: multiply
Mutually exclusive: add
Statistics

Sets & Venn Diagrams

Union and intersection
Two-set overlapping problems
Three-set overlapping problems
Set matrix method (two-way table)
Overlapping set formula
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