GMAC-style assessment Executive MBA - Quantitative: Word Problems - Rates, Ratios, Mixtures, Work, Overlapping Sets

What Is It?

This topic is about solving word problems related to rates, ratios, mixtures, work, and overlapping sets. It is tested in GMAC-style assessments, which are used for Executive MBA programs, to evaluate a candidate's ability to apply mathematical concepts to real-world business scenarios.

Why Does the Exam Ask This?

The exam asks this topic to measure the candidate's ability to apply mathematical concepts to solve practical business problems, which requires professional judgment, compliance logic, and operational risk management.

What Do I Need to Know First?

To tackle this topic, you should have a solid understanding of:
1. Basic algebra and equations
2. Ratios and proportions
3. Percentages and percentage changes
4. Basic statistics and data analysis
5. Basic mathematical operations (addition, subtraction, multiplication, division)

Topic Snapshot

This topic fits within the GMAC-style assessment's quantitative section and is crucial for evaluating a candidate's ability to apply mathematical concepts to solve business problems. It is a key area of focus for Executive MBA programs, as it helps candidates develop their problem-solving skills and ability to make informed business decisions.

Exam / Job / Audit Weighting

Frequency: 12-15% of total questions Difficulty Rating: Intermediate Question Type or Real-World Task Type: Word problems, case studies, and scenario-based questions

Difficulty Level

intermediate

Must-Know Rules, Formulas, Standards, or Principles

1. The rule of three: If a : b = c : d, then a * d = b * c
2. The concept of proportion: If a : b = c : d, then a / b = c / d
3. The formula for percentage change: (New Value - Old Value) / Old Value * 100

Misconceptions

1. Believing that ratios and proportions are the same thing
2. Assuming that percentage change is always positive
3. Failing to account for all variables in a word problem
4. Misinterpreting the meaning of "rate" and "ratio"
5. Ignoring the context of the problem when applying mathematical concepts

Common Mistakes

1. Failing to read the problem carefully and understand the context
2. Making assumptions about the data or variables
3. Failing to check units or dimensions
4. Ignoring the constraints or limitations of the problem
5. Failing to consider alternative solutions or perspectives

The Common Trap

The most common trap is failing to read the problem carefully and understand the context, which leads to misinterpreting the data or variables and applying the wrong mathematical concept.

Terms to Remember

1. Ratio: A comparison of two or more numbers
2. Proportion: A statement that two ratios are equal
3. Percentage change: The change in a value as a percentage of the original value
4. Rate: A measure of the speed or frequency of an event
5. Overlapping sets: Sets that have common elements

Step-by-Step Process

1. Read the problem carefully and understand the context
2. Identify the variables and data provided
3. Determine the mathematical concept required to solve the problem
4. Apply the mathematical concept to the data and variables
5. Check the units or dimensions and ensure the solution makes sense
6. Consider alternative solutions or perspectives and evaluate the results

Exam Answer Builder

1-mark Question

What is the formula for percentage change? - What it tests: Basic mathematical operations - Example Question: What is the formula for percentage change? - Key Tip: The formula is (New Value - Old Value) / Old Value * 100

2-mark or 3-mark Question

A company has two branches, one in New York and one in Los Angeles. The New York branch has 100 employees, and the Los Angeles branch has 150 employees. What is the ratio of employees in the New York branch to the Los Angeles branch? - What it tests: Ratios and proportions - Example Question: What is the ratio of employees in the New York branch to the Los Angeles branch? - Key Tip: The ratio is 100:150 or 2:3

5-mark or long-answer Question

A manufacturing company produces two types of products, A and B. Product A requires 2 hours of labor and 1 hour of machine time, while product B requires 1 hour of labor and 2 hours of machine time. If the company has 100 hours of labor available and 120 hours of machine time available, how many units of product A and product B can be produced? - What it tests: Linear programming and optimization - Example Question: How many units of product A and product B can be produced? - Key Tip: Set up a system of linear equations and solve for the variables

Case Study or application-based Question

A company is considering two different investment options, A and B. Option A has a 5% annual return and requires an initial investment of $10,000, while option B has a 7% annual return and requires an initial investment of $20,000. Which option is better, and why? - What it tests: Financial analysis and decision-making - Example Question: Which option is better, and why? - Key Tip: Calculate the net present value (NPV) of each option and compare the results

This vs That

This topic is often confused with the topic of "Statistics and Data Analysis." While both topics involve mathematical concepts, the key difference is that this topic focuses on applying mathematical concepts to solve business problems, whereas statistics and data analysis focuses on collecting and analyzing data to inform business decisions.

Time-Saver Hack

When faced with a word problem, try to identify the key variables and data provided, and then determine the mathematical concept required to solve the problem. This can help you to quickly focus on the relevant information and avoid getting bogged down in unnecessary details.

Mini Scenarios

Basic Scenario

A company has two branches, one in New York and one in Los Angeles. The New York branch has 100 employees, and the Los Angeles branch has 150 employees. What is the ratio of employees in the New York branch to the Los Angeles branch? - What to notice: The ratio of employees in the two branches

Applied Scenario

A manufacturing company produces two types of products, A and B. Product A requires 2 hours of labor and 1 hour of machine time, while product B requires 1 hour of labor and 2 hours of machine time. If the company has 100 hours of labor available and 120 hours of machine time available, how many units of product A and product B can be produced? - What to notice: The constraints and limitations of the problem

Tricky Scenario

A company is considering two different investment options, A and B. Option A has a 5% annual return and requires an initial investment of $10,000, while option B has a 7% annual return and requires an initial investment of $20,000. Which option is better, and why? - What to notice: The time value of money and the risk associated with each option

Diagnostic MCQ Bank

Question 1

What is the formula for percentage change? - Options: (New Value - Old Value) / Old Value * 100, (New Value - Old Value) / New Value * 100, (Old Value - New Value) / Old Value * 100 - Correct Answer: (New Value - Old Value) / Old Value * 100 - Explanation: The formula for percentage change is (New Value - Old Value) / Old Value * 100 - Why the correct answer is right: This formula accurately calculates the percentage change between two values - Why the trap option is tempting: The other options may seem plausible, but they do not accurately calculate the percentage change

Question 2

A company has two branches, one in New York and one in Los Angeles. The New York branch has 100 employees, and the Los Angeles branch has 150 employees. What is the ratio of employees in the New York branch to the Los Angeles branch? - Options: 100:150, 150:100, 2:3 - Correct Answer: 100:150 - Explanation: The ratio of employees in the New York branch to the Los Angeles branch is 100:150 - Why the correct answer is right: This ratio accurately reflects the number of employees in each branch - Why the trap option is tempting: The other options may seem plausible, but they do not accurately reflect the ratio of employees

Question 3

A manufacturing company produces two types of products, A and B. Product A requires 2 hours of labor and 1 hour of machine time, while product B requires 1 hour of labor and 2 hours of machine time. If the company has 100 hours of labor available and 120 hours of machine time available, how many units of product A and product B can be produced? - Options: 20 units of product A and 30 units of product B, 30 units of product A and 20 units of product B, 40 units of product A and 60 units of product B - Correct Answer: 30 units of product A and 20 units of product B - Explanation: The company can produce 30 units of product A and 20 units of product B - Why the correct answer is right: This solution accurately maximizes the production of both products given the available resources - Why the trap option is tempting: The other options may seem plausible, but they do not accurately maximize the production of both products

Question 4

A company is considering two different investment options, A and B. Option A has a 5% annual return and requires an initial investment of $10,000, while option B has a 7% annual return and requires an initial investment of $20,000. Which option is better, and why? - Options: Option A is better because it has a higher return, Option B is better because it has a higher return, Both options are equally good because they have the same return - Correct Answer: Option B is better because it has a higher return - Explanation: Option B is better because it has a higher annual return of 7% - Why the correct answer is right: This option accurately reflects the higher return of option B - Why the trap option is tempting: The other options may seem plausible, but they do not accurately reflect the higher return of option B

Question 5

A company has two branches, one in New York and one in Los Angeles. The New York branch has 100 employees, and the Los Angeles branch has 150 employees. What is the ratio of employees in the New York branch to the Los Angeles branch? - Options: 100:150, 150:100, 2:3 - Correct Answer: 100:150 - Explanation: The ratio of employees in the New York branch to the Los Angeles branch is 100:150 - Why the correct answer is right: This ratio accurately reflects the number of employees in each branch - Why the trap option is tempting: The other options may seem plausible, but they do not accurately reflect the ratio of employees

Real-World Patterns

This topic shows up in real work in the following ways:
1. Financial analysis and decision-making: Companies must analyze financial data and make decisions about investments, budgeting, and resource allocation.
2. Operations management: Companies must manage resources, inventory, and production to meet customer demand and maximize efficiency.
3. Human resources management: Companies must manage employee data, talent acquisition, and employee development to meet business objectives.
4. Marketing and sales: Companies must analyze customer data and develop marketing strategies to meet customer needs and maximize sales.
5. Supply chain management: Companies must manage inventory, logistics, and transportation to meet customer demand and minimize costs.

30-Second Cheat Sheet

1. The rule of three: If a : b = c : d, then a * d = b * c
2. The concept of proportion: If a : b = c : d, then a / b = c / d
3. The formula for percentage change: (New Value - Old Value) / Old Value * 100
4. The ratio of employees in the New York branch to the Los Angeles branch is 100:150
5. The company can produce 30 units of product A and 20 units of product B

Related Concepts

1. Statistics and data analysis
2. Financial analysis and decision-making
3. Operations management

Verified Source List

1. GMAC (Graduate Management Admission Council)
2. CFA Institute (Chartered Financial Analyst)
3. IFRS (International Financial Reporting Standards)
4. ISO (International Organization for Standardization)
5. OpenStax (free online textbooks and educational resources)
6. Khan Academy (free online education and learning resources)
7. Harvard Business Review (business publications and research)
8. McKinsey & Company (management consulting firm)
9. The Economist (business publications and research)
10. Business Insider (business publications and research)