GRE-Style: Quantitative Comparison — Algebraic Manipulation

GRE Quantitative · Axiom Academy

EXAMPLE GRE-Style: Quantitative Comparison — Algebraic Manipulation Manipulating an equation algebraically to compare two quantities without a calculator Given that 3x - 5 = 10 , compare the two quantities below. Nice work — you solved a QC problem by manipulating the given equation algebraically, the same way you'll handle most QC "solve first" questions on test day. Solve completely before comparing: a QC problem that gives you an equation is asking you to pin down the unknown's exact value first — don't guess the relationship from the equation's shape. Undo operations in reverse order: 3x - 5 = 10 was built by multiplying by 3, then subtracting 5 — so you undo the subtraction first, then the multiplication, to isolate x . Equivalent expressions are automatically equal: the same reasoning appears when a QC problem compares 2(x+3) with 2x + 6 — because the distributive property makes those expressions identical for every value of x , they're equal for the same reason: the algebra makes them the same quantity. Result: x = 5 exactly, so Quantity A equals Quantity B — the answer is (C). Whenever a QC problem gives you an equation, solve it fully — an exact value turns "which is greater?" into a simple, certain comparison.

This is the written version of the interactive lesson above. See the full GRE Quantitative course.