Number properties
49 flashcards covering Number properties for the GMAT Quantitative section.
Number properties are the fundamental characteristics of numbers that help us understand how they behave in math problems. These include whether a number is even or odd, prime or composite, and concepts like factors, multiples, divisibility, and remainders. For example, knowing that even numbers are divisible by 2 or that primes have no divisors other than 1 and themselves allows you to simplify expressions and solve equations more effectively. Mastering these basics is essential for building a strong foundation in quantitative reasoning.
On the GMAT Quantitative section, number properties frequently appear in problem-solving and data sufficiency questions, often testing your ability to identify patterns or verify statements quickly. Common traps include assuming all numbers are positive, misapplying rules for divisibility, or overlooking parity in complex scenarios. Focus on practicing with integers, fractions, and modular arithmetic, as these skills can help you eliminate wrong answers and save time during the test.
A concrete tip: Always test edge cases, like zero or negative numbers, when evaluating properties.
Terms (49)
- 01
Integer
An integer is a whole number that can be positive, negative, or zero, with no fractional or decimal parts, and it is used in GMAT problems to discuss counting or properties like divisibility.
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Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself, such as 2, 3, or 5, and it appears in problems involving factors and multiples.
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Composite number
A composite number is a positive integer greater than 1 that is not prime, meaning it has divisors other than 1 and itself, like 4 or 6, and is relevant for factorization questions.
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Even number
An even number is an integer that is divisible by 2, such as 2, 4, or -6, and its properties affect outcomes in operations like addition or multiplication on the GMAT.
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Odd number
An odd number is an integer not divisible by 2, such as 1, 3, or -5, and understanding its behavior in arithmetic operations is key for parity problems.
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Divisibility by 2
A number is divisible by 2 if it is even, meaning its last digit is 0, 2, 4, 6, or 8, which helps quickly identify factors in GMAT math.
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Divisibility by 3
A number is divisible by 3 if the sum of its digits is divisible by 3, such as 12 (1+2=3), and this rule is used to check factors efficiently.
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Divisibility by 4
A number is divisible by 4 if the number formed by its last two digits is divisible by 4, like 124 (24÷4=6), aiding in factor analysis.
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Divisibility by 5
A number is divisible by 5 if it ends in 0 or 5, such as 15 or 20, and this simple rule is common in GMAT problems involving multiples.
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Divisibility by 6
A number is divisible by 6 if it is divisible by both 2 and 3, like 18, and combining these rules helps solve related questions.
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Divisibility by 9
A number is divisible by 9 if the sum of its digits is divisible by 9, such as 27 (2+7=9), which is useful for factoring exercises.
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Divisibility by 10
A number is divisible by 10 if it ends in 0, like 30, and this basic property often appears in problems with multiples or remainders.
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Divisibility by 11
A number is divisible by 11 if the difference between the sum of the digits in the odd positions and even positions is a multiple of 11, such as 121 (1-2+1=0).
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Factor
A factor of a number is an integer that divides it evenly without a remainder, like 2 and 3 for 6, and identifying factors is essential for GMAT number theory.
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Multiple
A multiple of a number is the product of that number and an integer, such as 10, 15, or 20 for 5, and it relates to sequences and divisibility.
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Greatest Common Divisor (GCD)
The greatest common divisor of two or more numbers is the largest number that divides all of them without a remainder, like 6 for 12 and 18, used in simplifying fractions.
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Least Common Multiple (LCM)
The least common multiple of two or more numbers is the smallest number that is a multiple of all of them, such as 12 for 4 and 6, and it helps with adding fractions.
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Prime factorization
Prime factorization is the process of breaking down a number into its prime number components, like 12 = 2 × 2 × 3, which is crucial for finding GCD and LCM.
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Consecutive integers
Consecutive integers are a sequence of integers that follow one another, like 3, 4, 5, and their sums or products often appear in algebraic word problems.
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Sum of consecutive integers
The sum of a set of consecutive integers can be calculated using the formula for the sum of an arithmetic series, such as the sum of 1 through 5 is 15, and this is tested in patterns.
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Product of consecutive integers
The product of consecutive integers, like 4 × 5 × 6, is always even if the set includes at least one even number, which is a common trap in GMAT questions.
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Remainder
A remainder is the amount left over after division, such as 5 when 17 is divided by 6, and it is central to modular arithmetic problems on the test.
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Modular arithmetic
Modular arithmetic deals with remainders when numbers are divided by a modulus, like 7 mod 3 = 1, and it helps solve problems involving cycles or patterns.
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Absolute value
The absolute value of a number is its distance from zero on the number line, so | -3 | = 3, and it is used in inequalities and distance problems.
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Properties of exponents
Properties of exponents include rules like a^m × a^n = a^(m+n) and (a^m)^n = a^(m×n), which are applied in simplifying expressions and solving equations.
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Positive numbers
Positive numbers are greater than zero, like 2 or 5, and their properties contrast with negatives in operations, affecting results in GMAT math.
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Negative numbers
Negative numbers are less than zero, like -2 or -5, and understanding their behavior in addition, multiplication, and division is key for accuracy.
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Zero
Zero is a neutral number that is neither positive nor negative, and it acts as an identity for addition but changes multiplication outcomes, as in GMAT traps.
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Rational numbers
Rational numbers are numbers that can be expressed as a fraction of two integers, like 1/2 or 3, and they are distinguished from irrationals in basic classification.
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Irrational numbers
Irrational numbers cannot be expressed as a simple fraction, like √2 or π, and recognizing them helps in problems involving roots or approximations.
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Parity
Parity refers to whether a number is even or odd, and mixing parities in operations, like even + odd = odd, is a frequent topic in GMAT logic.
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Distributive property
The distributive property states that a(b + c) = ab + ac, such as 2(3 + 4) = 6 + 8, and it is used to simplify expressions in various problems.
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Associative property
The associative property allows regrouping in addition or multiplication, like (a + b) + c = a + (b + c), and it applies to integers in equation manipulation.
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Commutative property
The commutative property means that the order of addition or multiplication does not matter, such as a + b = b + a, and it is relevant for rearranging terms.
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Identity elements
Identity elements are numbers that do not change the value when added or multiplied, like 0 for addition and 1 for multiplication, used in basic operations.
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Inverse operations
Inverse operations, such as addition and subtraction, undo each other, and understanding them helps solve equations involving integers.
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Even plus odd
The sum of an even number and an odd number is always odd, like 2 + 3 = 5, and this is a common trap in parity questions.
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Odd times even
The product of an odd number and an even number is always even, such as 3 × 4 = 12, which is tested in multiplication properties.
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Factors of a number
The factors of a number are all integers that divide it evenly, and for 12, they are 1, 2, 3, 4, 6, and 12, often required in counting problems.
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GCD of two numbers
To find the GCD of two numbers, list their factors and select the greatest common one, like GCD of 8 and 12 is 4, using methods like Euclidean algorithm.
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Strategy for remainder problems
In remainder problems, divide and note the leftover, or use modular equations, such as finding the remainder of 25 divided by 7, which is 4.
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Properties of squares
Squares of integers are always non-negative, and the square of an even number is even while an odd number's square is odd, appearing in patterns.
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Perfect squares
Perfect squares are integers that are the square of another integer, like 9 (3²), and identifying them helps in factoring or root problems.
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Difference of squares
The difference of squares formula is a² - b² = (a - b)(a + b), such as 25 - 16 = (5 - 4)(5 + 4), used for factoring quadratics.
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Base 10 system
The base 10 system uses powers of 10 for place values, like units, tens, and hundreds, which is foundational for understanding numbers in calculations.
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Place value
Place value indicates the value of a digit based on its position, such as the 2 in 234 representing 200, and it aids in addition and multiplication.
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Rounding numbers
Rounding a number means approximating it to a nearby value based on rules, like rounding 3.7 to 4, which is useful in estimation problems.
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Consecutive even integers
Consecutive even integers are even numbers that follow each other, like 2, 4, 6, and their sums or averages are common in sequences.
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Consecutive odd integers
Consecutive odd integers are odd numbers that follow each other, like 1, 3, 5, and properties like their sum being odd for an odd count are tested.