Arithmetic

Section: Arithmetic Estimated study time: 45 minutes Content: GRE arithmetic covers the foundational number properties and operations tested throughout the Quantitative Reasoning sections. Unlike standardized tests for younger students, the GRE uses arithmetic in sophisticated multi-step problems and quantitative comparison questions. Mastery of arithmetic concepts is essential because they appear in questions testing algebra, data analysis, and geometry as well. Number properties are high-yield GRE content. Integers include all whole numbers and their negatives (…, −2, −1, 0, 1, 2, …). The GRE frequently tests whether zero is positive, negative, or neither (zero is neither positive nor negative), and whether fractions and decimals are integers (they are not). Odd and even rules: odd + odd = even; even + even = even; odd + even = odd; odd × odd = odd; even × anything = even. These rules extend to exponents and are frequently used in trap questions. Prime numbers are natural numbers greater than 1 with no positive divisors other than 1 and themselves. 2 is the only even prime. The first ten primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. GRE frequently asks about prime factorization. Every integer greater than 1 can be expressed as a unique product of prime factors (Fundamental Theorem of Arithmetic). Greatest Common Divisor (GCD) and Least Common Multiple (LCM): GCD is the largest integer dividing both numbers; LCM is the smallest positive integer divisible by both. For any two integers: GCD × LCM = Product of the two numbers. Fractions, decimals, and percents are all representations of rational numbers, and the GRE requires fluency in converting among them and performing operations. Percent change = (New − Old) /…