Algebra

Section: Algebra Estimated study time: 45 minutes Content: Algebra is the language of GRE Quantitative Reasoning. Questions often present word problems requiring translation into algebraic equations, and algebraic reasoning underpins quantitative comparison and data interpretation questions as well. GRE algebra covers: linear equations, systems of equations, inequalities, absolute value equations, quadratic equations, exponents and radicals, and functions. Linear equations and systems are the most frequently tested algebraic topics. A linear equation in one variable has exactly one solution. Systems of two linear equations in two unknowns: if the equations are consistent and independent (not parallel, not identical), there is exactly one solution — solve by substitution or elimination. If the system is inconsistent (parallel lines), no solution exists. If the equations are dependent (same line), infinite solutions exist. Inequalities follow most of the same rules as equations with one critical exception: multiplying or dividing both sides by a negative number reverses the inequality sign. Compound inequalities (a < x < b) are solved by performing the same operation on all three parts simultaneously. Absolute value inequalities: |x| < k means −k < x < k (between), while |x| > k means x < −k or x > k (outside). A common GRE trap is forgetting to consider the negative case when solving |expression| = constant. Exponent rules are heavily tested: x^a × x^b = x^(a+b); x^a / x^b = x^(a−b); (x^a)^b = x^(ab); x^0 = 1 (for x ≠ 0); x^(−n) = 1/x^n; x^(1/n) = nth root of x. Fractional exponents combine roots and powers: x^(m/n) = (x^(1/n))^m = nth root of x^m. Radicals: √(ab) = √a × √b; √(a/b) = √a / √b; but √(a+b) ≠ √a +…