Quick Answer
An integer is a whole number that can be positive, negative, or zero. On the Digital SAT, integers appear frequently across both Math modules, particularly in student-produced response questions where answers must often be non-decimal. Mastering integers is essential for solving approximately 15-20% of algebraic and data analysis problems.
An integer is any member of the set {..., -3, -2, -1, 0, 1, 2, 3, ...}, representing a number without a fractional or decimal component. In mathematical notation, the set of all integers is often denoted by the symbol Z.
Question: If 4x + 9 < 22 and x is a positive integer, what is the greatest possible value of x? Solution: Subtract 9 from both sides: 4x < 13. Divide by 4: x < 3.25. Since x must be an integer, the greatest value is 3.
Mistake 1: Forgetting that zero is an integer and is neither positive nor negative.
Mistake 2: Assuming 'integer' only refers to positive numbers, thereby ignoring negative whole numbers in algebraic solutions.
Mistake 3: Rounding to the nearest integer incorrectly in word problems when the context (like 'minimum' or 'maximum') requires a specific floor or ceiling value.
Students targeting 750+ should know that the SAT frequently uses the 'integer' constraint in quadratic equations and systems of equations to limit potential solutions, often requiring the use of the discriminant or factorability rules to ensure the roots are integers.
Composite Number
A composite number is a positive integer greater than 1 that has more than two distinct factors. On the Digital SAT, these appear typically in Math Module 1 or 2 within number theory or factoring questions. Understanding them is crucial for identifying prime versus non-prime options in multiple-choice questions about integer properties.
Multiple
A multiple is the product of any integer and another integer. On the Digital SAT, multiples appear frequently in Math Modules 1 and 2, often within word problems involving cycles or sequences. Typically, students must calculate the Least Common Multiple (LCM) to solve problems concerning synchronized events or common denominators.
Practice on Lumist
7,000+ questions with AI-powered feedback
Prime Number
A prime number is a positive integer greater than 1 with exactly two distinct factors: 1 and itself. On the Digital SAT, prime numbers frequently appear in Math Module 1 and 2 within Number Properties or Algebra questions. Students typically encounter at least one question involving prime factorization or integer constraints per test.