GRE Quant: Lessons & Preparation Route
Short lessons, worked examples, and practice that connects.
Integer structure
Integer constraints often make a problem smaller. Divisibility, parity, factors, and remainders are related tools, but each describes a different property.
Fractions and magnitude
Fractions are numbers and ratios. Their size depends on both numerator and denominator; a larger numerator alone cannot settle a comparison.
Percent bases and changes
A percent describes a relationship to a specific base. Reverse changes and consecutive changes require equations, not informal subtraction of percentages.
Ratios, mixtures and work
A rate combines two quantities with units. Mixture concentrations are weighted by amount, while work rates describe fractions of one complete job per time unit.
Equations and restrictions
An equation encodes a constraint, while an inequality allows a set of values. Some algebraic operations introduce candidate solutions that need a final check.
Functions and quadratic structure
Functions attach an output to each permitted input. Algebraic form determines what is easy to read: a factored quadratic reveals zeros and a shifted-square form reveals its vertex: a minimum for a positive leading coefficient and a maximum for a negative one.
Powers, roots and cycles
Powers encode repeated multiplication. A last-digit question depends on a cycle, whereas a root question depends on the domain and the convention for the principal root.
Geometry with explicit conditions
Geometric conclusions require stated conditions. Length, area and volume scale differently, and a sketch cannot supply an unstated right angle or a missing equality.
Distribution summaries
A summary emphasizes part of a distribution. A mean uses every value; a median uses order; spread describes variation rather than location.
Counting and conditional probability
Probability uses the relevant sample space. A condition narrows that space, and a draw without replacement changes the available outcomes for the next draw.
Quantitative comparison strategy
Comparison asks which relationship must hold under all allowed conditions. Finding one convenient example is not enough when the variable can take many values.
Reading data as relationships
A table is a compact model with labels, units and a population. The arithmetic is usually straightforward after the correct row, denominator and comparison have been identified.
Prime exponents as constraints
Count choices of prime exponents and distinguish a perfect square from a multiple.
Precision, bounds and powers
Use an interval or an exact power before reaching for decimal approximations.
Sequences beyond one formula
Identify whether a recurrence, an alternating sign or a ratio controls the next term.
Domains, composition and piecewise rules
Treat a function as an instruction with a permitted input and a selected branch.
Solve inequalities by regions
Locate critical points, then test signs on the intervals they create.
Coordinates encode geometry
Recover geometric information through midpoint, distance, reflection and perpendicularity.
Right triangles and similarity
Connect side relationships to areas and angles without trusting the sketch.
Areas, surfaces and three dimensions
Separate a boundary length, a planar area and the surface or volume of a solid.
Frequency, percentile and spread
Read frequencies and describe position or dispersion using the stated definition.
Complement, independence and expectation
Choose an event model before combining probabilities.
Selections with constraints
Count unordered selections, repeated objects and forbidden arrangements separately.
Graphs as quantitative evidence
Use frequencies, coordinates and endpoints to recover relationships from a graph.
Selected quantitative foundations only; not full GRE coverage.