GMAC-style assessment Executive MBA - Quantitative: Number Properties - Odds and Evens, Primes, Factors, Multiples, Remainders

What Is It?

Number Properties - Odds/Evens, Primes, Factors, Multiples, Remainders is a fundamental concept in mathematics that deals with the properties and relationships of numbers, particularly in the context of divisibility, primality, and remainder calculations.

In GMAC-style assessment, this topic is tested and applied in various ways, including data interpretation, pattern recognition, and problem-solving, which are essential skills for executive MBA students to master.

Why Does the Exam Ask This?

The exam asks this topic to measure the candidate's ability to apply mathematical concepts to real-world problems, think critically, and make sound judgments in a variety of situations. This topic assesses the candidate's understanding of number properties, which is crucial for data analysis, financial modeling, and decision-making in business.

What Do I Need to Know First?

To tackle this topic, you should be familiar with basic arithmetic operations, including addition, subtraction, multiplication, and division. You should also understand the concepts of even and odd numbers, prime numbers, factors, multiples, and remainders.

Topic Snapshot

Number Properties - Odds/Evens, Primes, Factors, Multiples, Remainders is a fundamental concept in mathematics that deals with the properties and relationships of numbers. It is a critical topic in GMAC-style assessment, as it is frequently used in data interpretation, pattern recognition, and problem-solving. Understanding this topic is essential for executive MBA students to develop their analytical and critical thinking skills.

Exam / Job / Audit Weighting

Frequency: High Difficulty Rating: Intermediate Question Type or Real-World Task Type: Multiple-choice questions, data interpretation, and problem-solving exercises

Difficulty Level

intermediate

Must-Know Rules, Formulas, Standards, or Principles

1. Even and Odd Numbers: An even number is any integer that can be exactly divided by 2, while an odd number is any integer that cannot be exactly divided by 2.
2. Prime Numbers: A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself.
3. Factors, Multiples, and Remainders: The product of two or more numbers is called a multiple of those numbers. The remainder of a division operation is the amount left over after the division.

Misconceptions

1. Even numbers are always divisible by 2: This is not true, as 0 is an even number but is not divisible by 2.
2. Prime numbers are always odd: This is not true, as 2 is a prime number but is even.
3. Factors are always positive integers: This is not true, as factors can also be negative integers.
4. Multiples are always positive integers: This is not true, as multiples can also be negative integers.
5. Remainders are always non-negative: This is not true, as remainders can also be negative.

Common Mistakes

1. Forgetting to check for even and odd numbers: Failing to identify whether a number is even or odd can lead to incorrect calculations.
2. Not considering prime numbers: Failing to recognize prime numbers can lead to incorrect factorization and multiple calculations.
3. Misunderstanding factors, multiples, and remainders: Failing to understand these concepts can lead to incorrect calculations and misunderstandings.
4. Not considering negative integers: Failing to consider negative integers can lead to incorrect calculations and misunderstandings.
5. Not checking for remainder calculations: Failing to check for remainder calculations can lead to incorrect results.

The Common Trap

The most common trap is to forget to check for even and odd numbers, leading to incorrect calculations and misunderstandings.

Terms to Remember

1. Even numbers: Numbers that can be exactly divided by 2.
2. Odd numbers: Numbers that cannot be exactly divided by 2.
3. Prime numbers: Positive integers greater than 1 that have no positive integer divisors other than 1 and themselves.
4. Factors: Numbers that can be multiplied together to get another number.
5. Multiples: Numbers that can be obtained by multiplying another number by an integer.
6. Remainders: The amount left over after a division operation.

Step-by-Step Process

1. Identify whether a number is even or odd: Check if the number can be exactly divided by 2.
2. Check for prime numbers: Check if the number has any positive integer divisors other than 1 and itself.
3. Calculate factors, multiples, and remainders: Use the correct formulas and rules to calculate these values.

Exam Answer Builder

1-mark Question

What is the remainder when 17 is divided by 5? - 0 - 1 - 2 - 3 - 4 Correct answer: 2 Key tip: Use the remainder formula to calculate the remainder.

2-mark Question

What is the product of 3 and 4? - 10 - 12 - 14 - 16 - 18 Correct answer: 12 Key tip: Multiply the numbers together to get the product.

3-mark Question

What is the greatest common divisor (GCD) of 12 and 15? - 3 - 5 - 6 - 9 - 10 Correct answer: 3 Key tip: Use the Euclidean algorithm to find the GCD.

5-mark Question

A company has 15 employees, and 3/5 of them are women. How many women are employed by the company? - 3 - 5 - 6 - 7 - 9 Correct answer: 9 Key tip: Calculate 3/5 of 15 to find the number of women employed.

Case Study or application-based Question

A retailer sells a total of 250 items, with 30% being sold at a discount. How many items were sold at a discount? - 75 - 80 - 85 - 90 - 95 Correct answer: 75 Key tip: Calculate 30% of 250 to find the number of items sold at a discount.

This vs That

This topic is similar to the concept of divisibility, but it also deals with prime numbers, factors, multiples, and remainders.

Time-Saver Hack

To quickly identify whether a number is even or odd, simply check if the last digit is 0, 2, 4, 6, or 8 (even) or 1, 3, 5, 7, or 9 (odd).

Mini Scenarios

Basic Scenario

A company has 15 employees, and 3/5 of them are women. How many women are employed by the company? - 3 - 5 - 6 - 7 - 9 Correct answer: 9 What to notice: This scenario requires the application of fractions and division to find the number of women employed.

Applied Scenario

A retailer sells a total of 250 items, with 30% being sold at a discount. How many items were sold at a discount? - 75 - 80 - 85 - 90 - 95 Correct answer: 75 What to notice: This scenario requires the application of percentages and division to find the number of items sold at a discount.

Tricky Scenario

A company has 24 employees, and 1/4 of them are managers. How many managers are employed by the company? - 4 - 5 - 6 - 7 - 8 Correct answer: 6 What to notice: This scenario requires the application of fractions and division to find the number of managers employed, but also requires the consideration of the fact that the number of employees is not a multiple of 4.

Diagnostic MCQ Bank

Question 1

What is the remainder when 17 is divided by 5? - 0 - 1 - 2 - 3 - 4 Correct answer: 2 Explanation: Use the remainder formula to calculate the remainder. Why the correct answer is right: The remainder formula is used to find the remainder of a division operation. Why the trap option is tempting: The trap option is tempting because it is close to the correct answer, but it is not the correct answer.

Question 2

What is the product of 3 and 4? - 10 - 12 - 14 - 16 - 18 Correct answer: 12 Explanation: Multiply the numbers together to get the product. Why the correct answer is right: Multiplying the numbers together gives the correct product. Why the trap option is tempting: The trap option is tempting because it is close to the correct answer, but it is not the correct answer.

Question 3

What is the greatest common divisor (GCD) of 12 and 15? - 3 - 5 - 6 - 9 - 10 Correct answer: 3 Explanation: Use the Euclidean algorithm to find the GCD. Why the correct answer is right: The Euclidean algorithm is used to find the GCD of two numbers. Why the trap option is tempting: The trap option is tempting because it is close to the correct answer, but it is not the correct answer.

Question 4

A company has 15 employees, and 3/5 of them are women. How many women are employed by the company? - 3 - 5 - 6 - 7 - 9 Correct answer: 9 Explanation: Calculate 3/5 of 15 to find the number of women employed. Why the correct answer is right: Calculating 3/5 of 15 gives the correct number of women employed. Why the trap option is tempting: The trap option is tempting because it is close to the correct answer, but it is not the correct answer.

Question 5

A retailer sells a total of 250 items, with 30% being sold at a discount. How many items were sold at a discount? - 75 - 80 - 85 - 90 - 95 Correct answer: 75 Explanation: Calculate 30% of 250 to find the number of items sold at a discount. Why the correct answer is right: Calculating 30% of 250 gives the correct number of items sold at a discount. Why the trap option is tempting: The trap option is tempting because it is close to the correct answer, but it is not the correct answer.

Real-World Patterns

1. Financial calculations: Number properties are used in financial calculations, such as calculating interest rates, investment returns, and loan payments.
2. Data analysis: Number properties are used in data analysis, such as identifying patterns, trends, and correlations in data.
3. Problem-solving: Number properties are used in problem-solving, such as solving equations, inequalities, and systems of equations.

30-Second Cheat Sheet

1. Even and odd numbers: Even numbers can be exactly divided by 2, while odd numbers cannot.
2. Prime numbers: Prime numbers are positive integers greater than 1 that have no positive integer divisors other than 1 and themselves.
3. Factors, multiples, and remainders: Factors are numbers that can be multiplied together to get another number, multiples are numbers that can be obtained by multiplying another number by an integer, and remainders are the amount left over after a division operation.
4. Greatest common divisor (GCD): The GCD of two numbers is the largest number that divides both numbers without leaving a remainder.
5. Remainder formula: The remainder formula is used to find the remainder of a division operation.

Related Concepts

1. Divisibility: Divisibility is the concept of determining whether a number can be divided by another number without leaving a remainder.
2. Fractions: Fractions are used to represent part of a whole or a ratio of two numbers.
3. Percentages: Percentages are used to represent a proportion of a whole or a ratio of two numbers.

Verified Source List

1. GMAC: Graduate Management Admission Council (GMAC) is a non-profit organization that administers the Graduate Management Admission Test (GMAT).
2. Mathematical Association of America (MAA): MAA is a professional organization that promotes mathematics education and research.
3. National Council of Teachers of Mathematics (NCTM): NCTM is a professional organization that promotes mathematics education and research.
4. Khan Academy: Khan Academy is a non-profit organization that provides free online education resources, including mathematics.
5. OpenStax: OpenStax is a non-profit organization that provides free online textbooks, including mathematics.