GMAT Focus Edition MOCK Test

This mock test is designed to give you a real feel for the GMAT Focus Edition. It includes questions from all three sections of the actual exam: Quantitative Reasoning, Verbal Reasoning, and Data Insights. The questions are similar in difficulty and style to what you’ll see on test day, so you can get a solid idea of what to expect.

Each section is timed for 45 minutes, just like the real exam. To get the most out of this practice, it’s best to take the test under timed conditions—this will help you get used to the pressure of the actual exam. Check out the table below for a quick breakdown of the GMAT Focus Edition’s structure!

Quantitative Reasoning 

(45 minutes)

Instructions: This section contains 21 Problem Solving questions. You have 45 minutes to complete this section. Calculators are not allowed.

1.  If x is 20% of y, and y is 30% of z, what percentage of z is x?                                                

(A) 5%  (B) 6%  (C) 10%  (D) 15% (E) 50%

2. A store sells apples at $0.80 each and bananas at $0.50 each. If a customer buys 6 apples and some bananas for a total of $10.30, how many bananas did the customer buy?                             

(A) 7  (B) 8  (C) 9  (D) 10  (E) 11

3. What is the largest prime factor of 91?                                   

(A) 7  (B) 11  (C) 13  (D) 17  (E) 19

4. If a + b = 10 and a^2 + b^2 = 52, what is the value of ab?                  

(A) 14  (B) 24  (C) 48  (D) 96  (E) 100

5. A car travels at an average speed of 60 miles per hour for 2 hours and then at an average speed of 75 miles per hour for the next hour. What is the average speed of the car for the entire 3-hour trip?             

(A) 65 mph  (B) 68 mph  (C) 70 mph  (D) 72 mph  (E) 78 mph

6. A mixture contains milk and water in the ratio 5:3. If 4 liters of water are added to the mixture, the ratio becomes 5:4. What is the total quantity of the original mixture?                       

(A) 20 liters (B)  24 liters  (C) 32 liters  (D) 40 liters  (E) 48 liters

7. If n is an integer, which of the following must be an even integer?                      

(A) n + 1  (B) 2n + 1  (C) n^2 + 1  (D) n(n + 1)  (E) n^3

8. A rectangular garden has a length that is twice its width. If the perimeter of the garden is 72 meters, what is the area of the garden in square meters?  

(A) 216  (B) 288  (C) 384  (D) 512  (E) 648

9. A train travels 360 kilometers in 4 hours. What is its speed in meters per second?             

(A) 10 m/s  (B) 25 m/s  (C) 90 m/s  (D) 144 m/s  (E) 360 m/s

10. If 3^x = 81, what is the value of x?                                

(A) 2  (B) 3  (C) 4  (D) 5  (E) 6

11. A company's profit increased by 20% in the first year and then decreased by 10% in the second year. What is the net percentage increase in profit over the two years?                  

(A) 8%  (B) 10%  (C) 12%  (D) 15%  (E) 30%

12. What is the value of 2/5 + 1/3 times 3/4? 

(A) 11/20 (B) 13/20 (C) 17/20 (D) 19/20 (E) 21/20

13. If the average of five consecutive integers is 12, what is the largest of these integers? 

(A) 10 (B) 12 (C) 14 (D) 16 (E) 18

14. A bag contains 5 red balls, 3 blue balls, and 2 green balls. If one ball is drawn at random from the bag, what is the probability that the ball is either red or blue? 

(A) 1/5 (B) 3/10 (C) 1/2 (D) 4/5 (E) 8/10

15. Simplify the expression: (2a^3b^2)^4 

(A) 8a^{12}b^8 (B) 16a^{7}b^{6} (C) 16a^{12}b^8 (D) 2a^{12}b^8 (E) 16a^{3}b^{2}

16. A person invests P dollars at an annual interest rate of r percent compounded annually. What will be the value of the investment after 3 years? 

17. If x^2 - 5x + 6 = 0, what are the possible values of x? 

(A) 1 and 6 (B) -1 and -6 (C) 2 and 3 (D) -2 and -3 (E) 5 and 1

18. A circular pizza has a diameter of 14 inches. What is the area of the pizza? (Use \pi = 22/7) 

(A) 44 sq inches (B) 88 sq inches (C) 154 sq inches (D) 308 sq inches (E) 616 sq inches

19. If the ratio of men to women in a company is 3:5, and there are 48 employees in total, how many men are there in the company? 

(A) 18 (B) 20 (C) 24 (D) 30 (E) 32

20. What is the remainder when 17^3 is divided by 8? 

(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

21. If a train travels at a speed of 80 km/h, how long will it take to cover a distance of 320 km? 

(A) 2 hours (B) 3 hours (C) 4 hours (D) 5 hours (E) 6 hours

Verbal Reasoning 

(45 minutes)

Instructions: This section contains 23 questions, including Reading Comprehension and Critical Reasoning questions. You have 45 minutes to complete this section.

Reading Comprehension

Passage 1 (approximately 120 words)

Although oft-maligned in modern culture, the pigeon once stood not only for speed and reliability but also for grace and beauty. Darwin himself became a pigeon fancier after beginning to work with the humble Columba livia, discovering them to be more fascinating than he had formerly believed. During the Victorian age, raising show pigeons was a popular hobby, with new breeds continuously arising as amateur (and not-so-amateur) ornithologists crossed animals in the hopes of creating ever more fantastic creatures. One of the most sought-after varieties was known as the Almond Tumbler, a name presumably derived from the color of the birds combined with the distinctive flight style. Throughout many generations, this bird was so manipulated as to have a beak so small as to prevent the adult birds from feeding their offspring. And yet, it was wildly popular, drawing high prices at auctions and winning competitions.

How then did an animal once so well-loved come to be so loathed? As recently as World War II, the military used pigeons to carry messages, but today, many people would kick a pigeon before they would feed one. Perhaps it is just a problem of population density, a lack of esteem for that which is ubiquitous. Pigeons have become our constant urban companions and, as such, have been transformed from symbols of peace, plenty, and prosperity, to representatives of disease and decay. 

1. Which of the following assumptions is most necessary for the author's argument regarding why pigeons are now disliked?

A) People tend to associate animals with their historical roles rather than their current presence.
B) The more common an animal is, the less value it is likely to be given by society.
C) The Victorian age was a time of great interest in animal breeding and domestication.
D) Urban environments have made it harder for pigeons to maintain their natural behaviors.
E) The use of pigeons in warfare created negative associations with them.

2. Based on the passage, what can be inferred about the role of pigeons in Victorian society?

A) Pigeons were seen as purely decorative rather than functional animals.
B) The practice of breeding show pigeons was confined to the wealthy elite.
C) Pigeon breeding was both a scientific and aesthetic pursuit.
D) The high prices of pigeons at auctions led to economic disparity among breeders.
E) The Almond Tumbler was the most resilient breed developed during this period.

3. Which of the following versions of the underlined portion is the most grammatically and stylistically correct?

Original: "During the Victorian age, raising show pigeons was a popular hobby, with new breeds continuously arising as amateur (and not-so-amateur) ornithologists crossed animals in the hopes of creating ever more fantastic creatures."

A) with new breeds continuously arising as amateur (and not-so-amateur) ornithologists crossed animals in the hopes of creating ever more fantastic creatures.
B) with new breeds that arose continuously as amateur (and not-so-amateur) ornithologists crossed animals hoping to create ever more fantastic creatures.
C) with new breeds continuously arising as amateur (and not-so-amateur) ornithologists crossed them, hoping to create ever more fantastic creatures.
D) and new breeds continuously arose while amateur (and not-so-amateur) ornithologists crossed animals, hoping to create ever more fantastic creatures.
E) with amateur (and not-so-amateur) ornithologists crossing animals to create new breeds, continuously arising in the hope of creating ever more fantastic creatures.

Passage 2 (approximately 230 words)

The “Age of Imperialism,” a period from the late 1800s to the early 1900s, witnessed a significant expansion of European power across the globe. Driven by a complex interplay of economic, political, and social factors, European nations sought to establish colonies and exert influence over vast territories, particularly in Africa and Asia. Economically, the Industrial Revolution fueled a demand for raw materials and new markets, leading European powers to look overseas for resources and opportunities to sell their manufactured goods. Politically, imperial expansion was often seen as a measure of national strength and prestige, with nations competing to acquire the largest empires. This competition was intensified by strategic considerations, as control over key territories and trade routes was deemed essential for military and economic dominance.

Socially, a prevailing belief in European cultural and racial superiority, often termed the “civilizing mission,” provided a justification for imperial rule. Europeans believed they had a responsibility to bring their culture, technology, and governance to what they perceived as less developed societies. This ideology, while masking the exploitative nature of imperialism, played a significant role in shaping European attitudes and policies towards colonized peoples. The legacy of the Age of Imperialism continues to shape the political and economic landscape of many parts of the world, with former colonies grappling with the lasting impacts of European domination.

4. The main idea of the passage is that the Age of Imperialism was:  

(A) primarily driven by economic competition between European nations. 

(B) a period of unprecedented technological advancement in Europe. 

(C) a complex phenomenon resulting from economic needs, political ambitions, and social ideologies. 

(D) a time when European nations successfully spread their culture and values to other parts of the world. 

(E) a historical period that has had no lasting impact on the world today.

5. According to the passage, which of the following was a political motivation for European imperialism? 

(A) The need for raw materials to fuel industrial growth. 

(B) The desire to spread Christianity to new populations. 

(C) The belief in the superiority of European culture. 

(D) The competition for national strength and prestige through empire building.

(E) The search for new markets to sell European manufactured goods.

6. The term “civilizing mission” as used in the passage refers to the belief that: 

(A) European nations had a duty to protect indigenous populations from exploitation. 

(B) imperialism would ultimately lead to greater global peace and understanding. 

(C) European culture and governance were superior and should be brought to other societies. 

(D) colonized peoples were capable of self-governance and should be granted independence. 

(E) economic development in colonized territories was the primary goal of imperialism.

7. The passage suggests that the consequences of the Age of Imperialism: 

(A) have been entirely positive for former colonies. 

(B) are no longer relevant in the 21st century. 

(C) continue to influence the political and economic situations of many regions. 

(D) were limited to the economic exploitation of resources. 

(E) led to the immediate independence and prosperity of all colonized nations.

Passage 3 (approximately 340 words)

The development of artificial intelligence (AI) has sparked considerable debate about its potential impact on various aspects of society, including the labor market. While some fear widespread job displacement due to automation, others argue that AI will primarily augment human capabilities and create new types of jobs. Examining historical precedents of technological advancements can offer valuable insights into this ongoing discussion.

The Industrial Revolution, for instance, led to significant shifts in employment patterns, with many traditional craft-based jobs being replaced by factory work. However, it also spurred the growth of new industries and created demand for skilled workers to operate and maintain the new machinery. Similarly, the advent of computers and the internet transformed the nature of work, automating many routine tasks but also giving rise to entirely new fields such as software development, data analysis, and digital marketing.

Proponents of AI argue that it will follow a similar trajectory. They contend that while AI may automate certain tasks currently performed by humans, it will also free up human workers to focus on more creative, strategic, and complex endeavors. Furthermore, the development, implementation, and maintenance of AI systems will itself generate a plethora of new job opportunities. For example, AI ethicists, AI trainers, and AI-powered service providers are roles that are already emerging in response to the growing prevalence of AI.

Conversely, concerns about job displacement are valid, particularly for jobs that involve repetitive or rule-based tasks. As AI algorithms become more sophisticated, they may be able to perform these tasks more efficiently and cost-effectively than human workers. This could lead to significant unemployment in certain sectors if proactive measures are not taken to reskill and upskill the workforce.

Ultimately, the impact of AI on the labor market will likely be multifaceted. It is improbable that AI will lead to complete automation and mass unemployment across all sectors. Instead, a more plausible scenario is one where AI and humans collaborate, with AI handling routine tasks and providing insights, while humans contribute their unique skills in areas such as creativity, critical thinking, emotional intelligence, and complex problem-solving. The key to navigating this transition successfully lies in investing in education and training programs that equip individuals with the skills needed to thrive in an AI-driven economy.

8. The primary purpose of the passage is to: 

(A) argue that AI will inevitably lead to mass unemployment. 

(B) discuss the ethical implications of artificial intelligence. 

(C) analyze the potential effects of AI on the future of work. 

(D) provide a historical overview of technological advancements. 

(E) promote the adoption of AI in various industries.

9. The author uses the examples of the Industrial Revolution and the advent of computers and the internet to illustrate: 

(A) the dangers of rapid technological change. 

(B) how technological advancements have historically transformed the labor market. 

(C) the superiority of human skills over automated processes. 

(D) the failure of past predictions about technological unemployment. 

(E) the importance of government regulation in managing technological change.

10. According to the passage, proponents of AI believe that it will: 

(A) eliminate the need for human workers in most industries. 

(B) primarily automate creative and strategic tasks. 

(C) augment human capabilities and create new job categories. 

(D) lead to a decline in overall productivity and economic growth. 

(E) have a minimal impact on the existing labor market.

11. The passage suggests that concerns about job displacement due to AI are: 

(A) entirely unfounded and based on fear-mongering. 

(B) only relevant for highly skilled and specialized professions. 

(C) valid, especially for jobs involving repetitive tasks. 

(D) exaggerated by those who oppose technological progress. 

(E) already being effectively addressed by current economic policies.

12. The author concludes that the most likely impact of AI on the labor market will be: 

(A) a complete takeover of all jobs by intelligent machines. 

(B) a scenario where humans and AI work together collaboratively. 

(C) a significant decrease in the demand for skilled workers. 

(D) a return to traditional craft-based economies. 

(E) an unpredictable and chaotic transformation with no clear outcome.

Passage 4 (approximately 180 words)

The concept of “nudge” has gained prominence in behavioral economics and public policy. A nudge is a subtle intervention that steers people towards making better choices without restricting their freedom of choice. Unlike traditional regulations or mandates, nudges work by influencing people’s behavior in a predictable way based on an understanding of cognitive biases.

One common example of a nudge is the default option. People tend to stick with the default option, even if it’s not necessarily the best choice for them. For instance, automatically enrolling employees in a retirement savings plan, with the option to opt out, significantly increases participation rates compared to a system where employees have to actively sign up.

Another type of nudge involves framing information in a particular way. For example, highlighting the benefits of energy conservation in terms of money saved rather than environmental impact can be more effective in encouraging people to reduce their energy consumption. By understanding how psychological factors influence decision-making, policymakers can design nudges to promote desirable behaviors in areas such as health, finance, and environmental sustainability.

13. The primary focus of the passage is on: 

(A) the limitations of traditional economic models. 

(B) the ethical considerations of behavioral economics. 

(C) the definition and application of nudges in influencing behavior. 

(D) the role of government in regulating individual choices. 

(E) the importance of financial incentives in promoting desired outcomes.

14. According to the passage, a key characteristic of a nudge is that it: 

(A) forces people to make specific choices. 

(B) relies on strict regulations and penalties. 

(C) subtly guides behavior without limiting options. 

(D) primarily targets individuals with low levels of education. 

(E) always involves providing direct financial rewards.

15. The example of automatically enrolling employees in a retirement savings plan illustrates the effectiveness of which type of nudge? 

(A) Framing information 

(B) Social norms 

(C) Default option 

(D) Loss aversion 

(E) Anchoring bias

16. The passage suggests that nudges can be used to:

(A) manipulate people into making choices that benefit corporations. 

(B) replace the need for traditional laws and regulations entirely. 

(C) encourage positive behaviors in various domains like health and finance. 

(D) identify and correct fundamental flaws in individual decision-making processes. 

(E) create a society where all individuals make perfectly rational choices.

Critical Reasoning

17. A recent study found that people who regularly eat fish have a lower risk of heart disease. Therefore, to reduce your risk of heart disease, you should include fish in your diet.

Which of the following, if true, would most weaken the conclusion? 

(A) The study did not control for other lifestyle factors that might affect heart disease risk. 

(B) Fish is a good source of omega-3 fatty acids, which are known to be beneficial for heart health. 

(C) People who eat fish regularly also tend to exercise more often. 

(D) The type of fish consumed in the study varied greatly among participants. 

(E) Some types of fish contain high levels of mercury, which can be harmful to health.

18. Company X has seen a decline in sales of its flagship product over the past year. To boost sales, the company plans to launch a new advertising campaign featuring celebrities endorsing the product. The company believes that celebrity endorsements will attract more customers and increase sales.

Which of the following, if true, would most strengthen the company's belief? 

(A) The company's competitors have successfully used celebrity endorsements to increase their sales. 

(B) The flagship product has received consistently positive reviews from consumers. 

(C) The company's advertising budget for the new campaign is significantly larger than previous campaigns. 

(D) Consumer surveys indicate that the target demographic for the product is highly influenced by celebrity endorsements. 

(E) The celebrities chosen for the campaign are known to be heavy users of the company's product.

19. A local government is considering implementing a new public transportation system to reduce traffic congestion. Opponents argue that the system will be too expensive and will not significantly alleviate traffic problems. Proponents claim that it will provide an affordable and efficient alternative to driving, thereby reducing congestion and improving air quality.

Which of the following would be most important to evaluate in order to determine the likely success of the new public transportation system? 

(A) The current level of traffic congestion in the area. 

(B) The cost of implementing and maintaining the new transportation system. 

(C) The availability of existing public transportation options. 

(D) The willingness of commuters to use the new public transportation system. 

(E) The potential impact of the new system on local businesses.

20. All birds have feathers. Penguins are birds. Therefore, penguins have feathers.

The reasoning in the argument above is: 

(A) circular 

(B) flawed because it makes an unwarranted assumption 

(C) valid 

(D) invalid because it relies on anecdotal evidence 

(E) flawed because it confuses correlation with causation

21. A study found a strong positive correlation between ice cream sales and the number of drownings at beaches. Therefore, increased ice cream sales cause more drownings.

Which of the following, if true, most seriously weakens the conclusion? 

(A) There is no plausible mechanism by which eating ice cream could cause someone to drown. 

(B) Both ice cream sales and the number of drownings tend to increase during the summer months. 

(C) The study was conducted only at beaches with a high volume of tourists. 

(D) People who buy ice cream at the beach are more likely to go swimming. 

(E) The correlation between ice cream sales and drownings is stronger in some regions than in others.

22. If the price of gasoline increases, then the demand for smaller, more fuel-efficient cars will increase. The price of gasoline has increased. Therefore, the demand for smaller, more fuel-efficient cars will increase.

The structure of the argument above is: 

(A) Affirming the consequent 

(B) Denying the antecedent 

(C) Hypothetical syllogism 

(D) Modus ponens 

(E) Modus tollens

23. A company implemented a new policy allowing employees to work from home two days a week. After six months, a survey of employees showed increased job satisfaction and no decrease in productivity. Therefore, the work-from-home policy has been successful.

Which of the following, if true, would most weaken the conclusion? 

(A) The survey was conducted anonymously, ensuring honest responses. 

(B) Employees who chose to work from home were already among the most productive. 

(C) The company saved money on office utilities during the six-month period. 

(D) Some employees reported feeling isolated while working from home. 

(E) The company's overall profitability increased during the six-month period.

Data Insights 

(45 minutes)

Instructions: This section contains 20 questions of various types. You have 45 minutes to complete this section. An on-screen calculator is available for use.

1. Data Sufficiency: What is the value of integer "a"? 

(1) a - b = 1 (2) ab = 20 

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. 

(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. 

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. 

(D) EACH statement ALONE is sufficient. (E) Statements (1) and (2) TOGETHER are NOT sufficient.

2. Data Sufficiency: Is the positive integer m divisible by 12? 

(1) m is divisible by 6. (2) m is divisible by 8. 

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. 

(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. 

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. 

(D) EACH statement ALONE is sufficient. 

(E) Statements (1) and (2) TOGETHER are NOT sufficient.

Multi-Source Reasoning

Set 1:

Tab 1: Email from Project Manager

Subject: Update on Marketing Campaign Performance

Hi Team,

Here's a summary of the performance of our recent marketing campaign over the last quarter. We focused on three main channels: social media, email marketing, and search engine advertising. Our total marketing spend for the quarter was $50,000. Social media accounted for 40% of the budget, email marketing for 35%, and search engine advertising for the remaining 25%.

Tab 2: Sales Report

3. Multi-Source Reasoning: What was the cost per lead generated by the social media channel? 

(A) $16.67 (B) $20.83 (C) $25.00 (D) $33.33 (E) $41.674. 

4. Multi-Source Reasoning: Which marketing channel had the highest return on investment (ROI) based on the revenue generated and the budget allocated to that channel? 

(A) Social Media (B) Email Marketing (C) Search Engine Advertising (D) All channels had the same ROI. (E) It cannot be determined from the information provided.

5. Multi-Source Reasoning: If the company aims to increase the overall conversion rate by at least 2 percentage points in the next quarter, and the number of leads generated by each channel remains the same, what is the minimum number of additional conversions needed across all channels? 

(A) 35 (B) 70 (C) 105 (D) 140 (E) 280

Set 2:

Tab 1: Article Excerpt

A recent study compared the effectiveness of two different teaching methods for mathematics: Method A, which emphasizes rote memorization, and Method B, which focuses on conceptual understanding. The study involved 100 students who were randomly assigned to one of the two methods. After a six-month period, all students took the same standardized mathematics test.

Tab 2: Study Results

6. Multi-Source Reasoning: Based on the data, students taught with Method B had a higher average test score than students taught with Method A. Select Yes if this statement is supported by the data, and No if it is not.

(A) Yes (B) No

1. 7. Multi-Source Reasoning: Which teaching method resulted in a greater dispersion of test scores among the students? Select Method A if the data suggests this, Method B if it suggests that, or Cannot be determined if the data does not provide enough information.

(A) Method A (B) Method B (C) Cannot be determined. 

8. Multi-Source Reasoning: If a student from Method B scored one standard deviation below the mean for their group, their score would be higher than the average score of students in Method A. Select True if this statement is true based on the data, and False if it is false.

(A) True (B) False

Table Analysis

Table: Global Sales of Electric Vehicles by Region (in thousands)

9. Table Analysis: In which year did the "Rest of World" region experience the largest percentage increase in electric vehicle sales compared to the previous year? 

(A) 2021 (B) 2022 (C) 2023 (D) 2024 (E) The percentage increase was the same across all years.

10. Table Analysis: What was the approximate average annual growth rate of total global electric vehicle sales between 2020 and 2024? 

(A) 15% (B) 20% (C) 25% (D) 30% (E) 35%

11. Table Analysis: If the trend in Asia Pacific sales continues at the same absolute increase from 2024 to 2025, what would be the projected sales in thousands for that region in 2025? 

(A) 2100 (B) 2200 (C) 2300 (D) 2400 (E) 2500

Graphics Interpretation

Graph: Quarterly Profits of Company Z (in millions of dollars)

[Imagine a line graph here with the following data points: Q1 2023: 5 Q2 2023: 7 Q3 2023: 6 Q4 2023: 8 Q1 2024: 9 Q2 2024: 11 Q3 2024: 10 Q4 2024: 12]

12. Graphics Interpretation: What was the highest quarterly profit achieved by Company Z during the period shown? 

(A) $8 million (B) $9 million (C) $10 million (D) $11 million (E) $12 million

13. Graphics Interpretation: By approximately what percentage did the profit increase from Q3 2023 to Q3 2024? 

(A) 17% (B) 33% (C) 50% (D) 67% (E) 83%

14. Graphics Interpretation: Which of the following statements is best supported by the trend shown in the graph? 

(A) Company Z's profits are consistently increasing each quarter. (B) Company Z experiences a seasonal dip in profits during the third quarter. (C) Company Z's profits in 2024 were generally higher than in 2023. (D) Company Z's profits peaked in the first quarter of each year. (E) Company Z's profits are directly correlated with the time of year.

Two-Part Analysis

15. Two-Part Analysis: A bakery sells two types of cakes: chocolate and vanilla. A chocolate cake requires 2 cups of flour and 3 eggs, while a vanilla cake requires 3 cups of flour and 2 eggs. The bakery has 24 cups of flour and 25 eggs available. What is the maximum number of cakes the bakery can make, and how many of them will be chocolate cakes?

16. Two-Part Analysis: A company is considering two investment options. Option A offers a guaranteed return of 8% per year. Option B offers a 10% return in the first year, but the return in the second year is uncertain. For the total return over two years to be the same for both options, what would the return in the second year for Option B need to be, and what would be the average annual return for Option B over the two years?

17. Two-Part Analysis: A store sells notebooks for $2 each and pens for $1 each. A customer buys a total of 10 items and spends $16. How many notebooks did the customer buy, and how many pens did the customer buy?

18. Two-Part Analysis: A train travels from City X to City Y at a speed of 60 mph and returns from City Y to City X at a speed of 40 mph. What is the average speed of the train for the entire round trip, and what was the total distance traveled if the total time taken was 5 hours?

19. Two-Part Analysis: A company has 100 employees, of whom 60 are female. 40% of the male employees have a graduate degree, and 30% of the female employees have a graduate degree. How many male employees have a graduate degree, and what is the total number of employees with a graduate degree?

20. Two-Part Analysis: A rectangular room has a length that is 5 feet longer than its width. If the area of the room is 150 square feet, what is the width of the room, and what is the perimeter of the room?

Answer Key and Explanations

Quantitative Reasoning

1. B Explanation: x = 0.20y and y = 0.30z. Substituting the second equation into the first, we get x = 0.20(0.30z) = 0.06z. This means x is 6% of z.
2. A Explanation: The cost of 6 apples is 6 \times \$0.80 = \$4.80. The remaining amount spent on bananas is \$10.30 - \$4.80 = \$5.50. Since each banana costs \$0.50, the number of bananas is \$5.50 / \$0.50 = 11.
3. C Explanation: The factors of 91 are 1, 7, 13, and 91. The prime factors are 7 and 13. The largest prime factor is 13.
4. B Explanation: We know that (a + b)^2 = a^2 + b^2 + 2ab. Substituting the given values, we have 10^2 = 52 + 2ab, so 100 = 52 + 2ab. This gives 2ab = 48, and ab = 24.
5. B Explanation: Total distance traveled is (60 \times 2) + (75 \times 1) = 120 + 75 = 195 miles. Total time is 2 + 1 = 3 hours. Average speed is 195 / 3 = 65 mph.
6. C Explanation: Let the original quantities of milk and water be 5x and 3x liters respectively. After adding 4 liters of water, the ratio becomes 5x : (3x + 4) = 5 : 4. Cross-multiplying gives 20x = 15x + 20, so 5x = 20, and x = 4. The total quantity of the original mixture is 5x + 3x = 8x = 8 \times 4 = 32 liters.
7. D Explanation: If n is even, n = 2k, then n(n + 1) = 2k(2k + 1), which is even. If n is odd, n = 2k + 1, then n(n + 1) = (2k + 1)(2k + 2) = (2k + 1)2(k + 1), which is also even. Therefore, n(n + 1) must be an even integer.
8. B Explanation: Let the width be w meters and the length be 2w meters. The perimeter is 2(w + 2w) = 2(3w) = 6w = 72, so w = 12 meters. The length is 2w = 24 meters. The area is length \times width = 24 \times 12 = 288 square meters.
9. B Explanation: The speed of the train is 360 km / 4 hours = 90 km/h. To convert to meters per second, we multiply by 1000/3600: 90 \times \frac{1000}{3600} = 90 \times \frac{5}{18} = \frac{450}{18} = 25 m/s.
10. C Explanation: We need to find x such that 3^x = 81. Since 3^1 = 3, 3^2 = 9, 3^3 = 27, and 3^4 = 81, the value of x is 4.
11. A Explanation: Let the initial profit be P. After the first year, the profit is P(1 + 0.20) = 1.20P. In the second year, the profit decreases by 10%, so the profit becomes 1.20P(1 - 0.10) = 1.20P(0.90) = 1.08P. The net increase is 1.08P - P = 0.08P, which is an 8% increase.
12. B Explanation: \frac{2}{5} + \frac{1}{3} \times \frac{3}{4} = \frac{2}{5} + \frac{3}{12} = \frac{2}{5} + \frac{1}{4} = \frac{8}{20} + \frac{5}{20} = \frac{13}{20}.
13. C Explanation: Let the five consecutive integers be n, n+1, n+2, n+3, n+4. Their average is \frac{n + (n+1) + (n+2) + (n+3) + (n+4)}{5} = \frac{5n + 10}{5} = n + 2 = 12. So, n = 10. The integers are 10, 11, 12, 13, 14. The largest is 14.
14. D Explanation: Total number of balls is 5 + 3 + 2 = 10. Number of red or blue balls is 5 + 3 = 8. The probability of drawing a red or blue ball is \frac{8}{10} = \frac{4}{5}.
15. C Explanation: (2a^3b^2)^4 = 2^4 \times (a^3)^4 \times (b^2)^4 = 16a^{3 \times 4}b^{2 \times 4} = 16a^{12}b^8.
16. A Explanation: After 1 year, the value is P(1 + \frac{r}{100}). After 2 years, it is P(1 + \frac{r}{100})^2. After 3 years, it is P(1 + \frac{r}{100})^3.
17. C Explanation: We need to solve the quadratic equation x^2 - 5x + 6 = 0. Factoring the quadratic, we get (x - 2)(x - 3) = 0. The possible values of x are 2 and 3.
18. C Explanation: The radius of the pizza is half the diameter, so r = 14 / 2 = 7 inches. The area of a circle is given by A = \pi r^2. Using \pi = 22/7, the area is A = (22/7) \times 7^2 = (22/7) \times 49 = 22 \times 7 = 154 square inches.
19. A Explanation: The ratio of men to women is 3:5, so the total ratio parts are 3 + 5 = 8. The fraction of men in the company is 3/8. The number of men is (3/8) \times 48 = 3 \times 6 = 18.
20. A Explanation: 17^3 = 17 \times 17 \times 17 = 289 \times 17 = 4913. When 4913 is divided by 8, 4913 = 8 \times 614 + 1. The remainder is 1. Alternatively, 17 \equiv 1 \pmod{8}, so 17^3 \equiv 1^3 \equiv 1 \pmod{8}.
21. C Explanation: Time = Distance / Speed = 320 km / 80 km/h = 4 hours.

Verbal Reasoning

1. B Explanation: The passage suggests that pigeons have become disliked because they are now too common. This assumption supports the idea that ubiquity reduces esteem.
2. C Explanation: The passage notes that both amateur and professional ornithologists bred pigeons, indicating both scientific and aesthetic interest.
3. C Explanation: This version maintains clarity and grammatical correctness while keeping the meaning intact.
4. C Explanation: The passage explicitly mentions the interplay of economic (demand for resources and markets), political (national strength and prestige), and social (belief in European superiority) factors as drivers of the Age of Imperialism.
5. D Explanation: The passage states that "politically, imperial expansion was often seen as a measure of national strength and prestige, with nations competing to acquire the largest empires."
6. C Explanation: The passage defines the "civilizing mission" as the European belief that they had a responsibility to bring their culture, technology, and governance to other societies they deemed less developed.
7. C Explanation: The final sentence of the passage states, "The legacy of the Age of Imperialism continues to shape the political and economic landscape of many parts of the world..."
8. C Explanation: The passage explores both the potential benefits (augmentation of human capabilities, creation of new jobs) and risks (job displacement) of AI on the labor market, thus analyzing its potential effects.
9. B Explanation: The author uses the Industrial Revolution and the advent of computers/internet as historical examples of how technological advancements have led to significant changes in employment patterns.
10. C Explanation: The passage states that proponents of AI argue it will "augment human capabilities and create new types of jobs."
11. C Explanation: The passage acknowledges that "concerns about job displacement are valid, particularly for jobs that involve repetitive or rule-based tasks."
12. B Explanation: The author concludes that a "more plausible scenario is one where AI and humans collaborate, with AI handling routine tasks...while humans contribute their unique skills..."
13. C Explanation: The passage defines "nudge" and provides examples of how it can be used in public policy to influence behavior.
14. C Explanation: The passage explicitly states that a nudge "steers people towards making better choices without restricting their freedom of choice."
15. C Explanation: The example of automatic enrollment leverages the tendency of people to stick with the "default option."
16. C Explanation: The passage concludes by stating that policymakers can use nudges "to promote desirable behaviors in areas such as health, finance, and environmental sustainability."
17. A Explanation: If the study did not control for other factors, then the lower risk of heart disease could be due to those other factors, not necessarily the consumption of fish.
18. D Explanation: If the target demographic is highly influenced by celebrity endorsements, then the company's belief that this strategy will boost sales is strengthened.
19. D Explanation: The willingness of commuters to use the new system is crucial to determining whether it will be successful in reducing traffic congestion.
20. C Explanation: The argument follows a classic deductive structure: All A are B, C is A, therefore C is B. This is a valid syllogism.
21. B Explanation: The fact that both ice cream sales and drownings increase in the summer suggests that a third factor (the season or warmer weather) might be causing both, rather than one causing the other.
22. D Explanation: The argument follows the form: If P, then Q. P. Therefore, Q. This is the structure of Modus Ponens, a valid form of deductive reasoning.
23. B Explanation: If the employees who chose to work from home were already highly productive, then the lack of decrease in productivity might be due to their inherent productivity, not solely the work-from-home policy.

Data Insights

1. E Explanation: (1) a - b = 1 \implies a = b + 1. Substituting into (2): (b + 1)b = 20 \implies b^2 + b - 20 = 0 \implies (b + 5)(b - 4) = 0. So, b = -5 or b = 4. If b = -5, a = -4. If b = 4, a = 5. Two possible values for a. (2) ab = 20. Many integer pairs satisfy this equation (e.g., 1 and 20, 2 and 10, 4 and 5, -1 and -20, etc.). Not sufficient. Together: We found two possible values for a (-4 and 5). Not sufficient.
2. C Explanation: (1) m is divisible by 6 means m = 6k for some integer k. m could be 6 (not divisible by 12) or 12 (divisible by 12). Not sufficient. (2) m is divisible by 8 means m = 8j for some integer j. m could be 8 (not divisible by 12) or 24 (divisible by 12). Not sufficient. Together: m is divisible by both 6 and 8. The least common multiple of 6 and 8 is 24. So, m must be a multiple of 24 (24, 48, 72, ...), all of which are divisible by 12. Sufficient.
3. A Explanation: Social media budget = 40% of $50,000 = 0.40 \times 50,000 = 20,000. Cost per lead = Total cost / Number of leads = $20,000 / 1200 = $16.67 (approximately).
4. B Explanation: Social Media ROI: Revenue ($60,000) / Cost ($20,000) = 3 Email Marketing ROI: Revenue ($120,000) / Cost (35% of $50,000 = $17,500) = 120,000 / 17,500 = 6.86 (approximately) Search Engine Advertising ROI: Revenue ($80,000) / Cost (25% of $50,000 = $12,500) = 80,000 / 12,500 = 6.4 Email Marketing had the highest ROI.
5. B Explanation: Current total conversions = (1200 \times 0.05) + (1500 \times 0.08) + (800 \times 0.10) = 60 + 120 + 80 = 260. Total leads = 1200 + 1500 + 800 = 3500. Current overall conversion rate = 260 / 3500 = 0.0743 (7.43%). Target conversion rate = 7.43\% + 2\% = 9.43\%. Target number of conversions = 3500 \times 0.0943 = 330.05. Additional conversions needed = 330.05 - 260 = 70.05. Minimum additional conversions needed is 70.
6. A Explanation: Yes, the average test score for Method B (82) is higher than that for Method A (75).
7. A Explanation: Standard deviation measures the dispersion of scores. Method A has a standard deviation of 10, while Method B has a standard deviation of 8. A higher standard deviation indicates greater dispersion.
8. A Explanation: One standard deviation below the mean for Method B is 82 - 8 = 74. The average score for Method A is 75. So, a student from Method B scoring one standard deviation below the mean (74) would have a score lower than the average score of students in Method A (75). The statement is False.
9. A Explanation: Percentage increase for Rest of World: 2021: ((75 - 50) / 50) \times 100\% = 50\% 2022: ((100 - 75) / 75) \times 100\% = 33.33\% 2023: ((125 - 100) / 100) \times 100\% = 25\% 2024: ((150 - 125) / 125) \times 100\% = 20\% The largest percentage increase was in 2021.
10. C Explanation: Total sales in 2020 = 1550. Total sales in 2024 = 4050. Total increase = 4050 - 1550 = 2500. Number of years = 4. Average annual increase = 2500 / 4 = 625. Approximate average annual growth rate = (625 / 1550) \times 100\% = 40.32\%. This calculation is for absolute increase. For compound annual growth rate, we use the formula: (Final Value / Initial Value)^(1/n) - 1 = (4050 / 1550)^(1/4) - 1 = (2.6129)^(0.25) - 1 = 1.273 - 1 = 0.273 or 27.3%. Closest option is 25%.
11. B Explanation: The absolute increase in Asia Pacific sales from 2020 to 2021 was 1000 - 700 = 300. From 2021 to 2022, it was 1300 - 1000 = 300. From 2022 to 2023, it was 1600 - 1300 = 300. From 2023 to 2024, it was 1900 - 1600 = 300. The consistent absolute increase is 300. Projected sales in 2025 = 1900 + 300 = 2200 thousands.
12. E Explanation: By observing the line graph data, the highest quarterly profit is 12 million in Q4 2024.
13. D Explanation: Profit in Q3 2023 = $6 million. Profit in Q3 2024 = $10 million. Percentage increase = ((10 - 6) / 6) \times 100\% = (4 / 6) \times 100\% = 0.6667 \times 100\% = 66.67\%. Approximately 67%.
14. C Explanation: Comparing the profits in 2023 (Q1: 5, Q2: 7, Q3: 6, Q4: 8) with those in 2024 (Q1: 9, Q2: 11, Q3: 10, Q4: 12), the profits in each quarter of 2024 were higher than the corresponding quarter in 2023.
15. C, G Explanation: Let c be the number of chocolate cakes and v be the number of vanilla cakes. Flour constraint: 2c + 3v \leq 24 Egg constraint: 3c + 2v \leq 25 We want to maximize c + v. Try option C (9 cakes): If c=5, v=4 \implies 2(5) + 3(4) = 10 + 12 = 22 \leq 24 and 3(5) + 2(4) = 15 + 8 = 23 \leq 25. This works. Try option B (8 cakes): If c=4, v=4 \implies 2(4) + 3(4) = 8 + 12 = 20 \leq 24 and 3(4) + 2(4) = 12 + 8 = 20 \leq 25. If c=6, v=3 \implies 2(6) + 3(3) = 12 + 9 = 21 \leq 24 and 3(6) + 2(3) = 18 + 6 = 24 \leq 25. If c=3, v=6 \implies 2(3) + 3(6) = 6 + 18 = 24 \leq 24 and 3(3) + 2(6) = 9 + 12 = 21 \leq 25. Maximum number of cakes is 9, with 5 chocolate cakes.
16. A, F Explanation: Option A: Return over 2 years = P(1 + 0.08)^2 = P(1.0816). Option B: Return over 2 years = P(1 + 0.10)(1 + x) = P(1.1)(1 + x), where x is the return in the second year. For total return to be the same: 1.0816 = 1.1(1 + x) \implies 1.0816 / 1.1 = 1 + x \implies 0.98327 = 1 + x \implies x = -0.0167 or -1.67%. This doesn't match the options. Let's consider simple interest for two years. Option A: Total return = P + 2(0.08P) = 1.16P. Option B: Total return = P(1 + 0.10 + x) = P(1.10 + x). 1.16 = 1.10 + x \implies x = 0.06 or 6%. Average annual return for Option B = (0.10 + 0.06) / 2 = 0.16 / 2 = 0.08 or 8%.
17. C, G Explanation: Let n be the number of notebooks and p be the number of pens. n + p = 10 2n + 1p = 16 Subtracting the first equation from the second: (2n + p) - (n + p) = 16 - 10 \implies n = 6. Substituting n = 6 into the first equation: 6 + p = 10 \implies p = 4. Number of notebooks = 6, Number of pens = 4.
18. B, F Explanation: Let the distance between City X and City Y be d. Time taken to travel from X to Y = d / 60. Time taken to travel from Y to X = d / 40. Total time = d/60 + d/40 = (2d + 3d) / 120 = 5d / 120 = d / 24 = 5 hours. So, d = 5 \times 24 = 120 miles. Total distance traveled = 2d = 2 \times 120 = 240 miles. Average speed = Total distance / Total time = 240 / 5 = 48 mph.
19. A, E Explanation: Number of male employees = 100 - 60 = 40. Number of male employees with graduate degree = 40\% of 40 = 0.40 \times 40 = 16. Number of female employees with graduate degree = 30\% of 60 = 0.30 \times 60 = 18. Total number of employees with a graduate degree = 16 + 18 = 34.
20. B, F Explanation: Let the width of the room be w feet. Then the length is w + 5 feet. Area = w(w + 5) = 150 \implies w^2 + 5w - 150 = 0. Factoring the quadratic: (w + 15)(w - 10) = 0. Since width must be positive, w = 10 feet. Length = w + 5 = 10 + 5 = 15 feet. Perimeter = 2(length + width) = 2(15 + 10) = 2(25) = 50 feet.