Arithmetic and Number Properties
GRE Quantitative Reasoning covers arithmetic, algebra, geometry, and data analysis at roughly the level of high school mathematics. The arithmetic portion tests number properties and operations frequently. Key number property categories include: integers and divisibility (prime numbers, factors, multiples, divisibility rules); fractions, decimals, and percentages (conversion between forms, percent change calculations, ratio and proportion); powers and roots (rules of exponents, square roots, cube roots, simplification); and absolute value (definition, equations and inequalities with absolute value). A common GRE arithmetic focus is percent change: percent change = [(new - old) / old] × 100. Note that a 50% increase followed by a 50% decrease does not return to the original value — it results in a 25% net decrease. This is because the 50% decrease applies to the larger post-increase value. Divisibility shortcuts frequently appear: a number is divisible by 3 if its digits sum to a multiple of 3; divisible by 9 if digits sum to a multiple of 9; divisible by 6 if divisible by both 2 and 3. Prime numbers below 20: 2, 3, 5, 7, 11, 13, 17, 19. Note that 1 is not prime by definition. Two is the only even prime number.