Hard GRE Multi-Step Data Questions Practice Questions

Concept Explanation

Hard GRE multi-step data questions are quantitative reasoning problems that require the integration of multiple data points from tables, charts, or graphs to perform a sequence of calculations. Unlike simpler data interpretation tasks that ask for a single value, these advanced problems demand that you extract information, convert units, calculate percentages, and often compare results across different categories. Success on these items depends on your ability to synthesize information found in complex data sets and maintain accuracy through several logical stages.

To navigate these challenges, you must first identify exactly what the question is asking. Often, the final answer depends on a value that isn't explicitly listed in the data. For instance, you might need to find the total revenue of a company by first calculating the individual sales volumes from a bar chart and then multiplying them by prices found in a separate table. These questions are a core component of the GRE Prep curriculum because they test both mathematical precision and logical reasoning. Utilizing tools like an AI Exam Simulator can help you simulate the pressure of these multi-layered problems under timed conditions.

Solved Examples

Below are three examples of how to approach multi-step data interpretation problems systematically.

1. Example 1: Percentage of a Sub-group
   A table shows that Company X has 500 employees. 60% of employees are in the Production department. Of the Production employees, 20% have advanced degrees. How many Production employees do not have advanced degrees?
   Solution:

   1. Calculate the total number of Production employees: $500 \times 0.60 = 300$.

   2. Identify the percentage of Production employees without advanced degrees: $100\% - 20\% = 80\%$.

   3. Calculate the final number: $300 \times 0.80 = 240$.

   4. The answer is 240.

2. Example 2: Weighted Averages from Charts
   A pie chart shows a portfolio's distribution: 40% Stocks, 50% Bonds, and 10% Cash. The total value is $200,000. If Stocks grow by 10%, Bonds grow by 5%, and Cash remains the same, what is the new total value of the portfolio?
   Solution:

   1. Find the initial value of each asset: Stocks = $0.40 \times 200,000 = \$80,000$; Bonds = $0.50 \times 200,000 = \$100,000$; Cash = $0.10 \times 200,000 = \$20,000$.

   2. Calculate growth for each: New Stocks = $80,000 \times 1.10 = \$88,000$; New Bonds = $100,000 \times 1.05 = \$105,000$.

   3. Sum the new values: $88,000 + 105,000 + 20,000 = \$213,000$.

   4. The answer is $213,000.

3. Example 3: Rate and Ratio Integration
   A factory produces 1,200 units in 8 hours. The ratio of defective units to non-defective units is 1:24. If the cost to repair each defective unit is $15, what is the total repair cost for one 8-hour shift?
   Solution:

   1. Determine the total parts in the ratio: $1 + 24 = 25$.

   2. Find the number of defective units: $\frac{1}{25} \times 1,200 = 48$.

   3. Calculate the total cost: $48 \times 15 = \$720$.

   4. The answer is $720.

Practice Questions

1. A retail store's total revenue in 2022 was $800,000. In 2023, the revenue from electronics (which accounted for 30% of 2022 revenue) increased by 20%, while all other revenue remained the same. What was the total revenue in 2023?

2. A survey of 1,500 people found that 40% prefer Brand A. Of those who prefer Brand A, 25% are over the age of 60. How many people who prefer Brand A are age 60 or younger?

3. In a specific region, the population is 2.4 million. 15% of the population are students. If 20% of the students attend private schools and the rest attend public schools, how many students attend public schools?

4. A data set consists of five numbers with a mean of 20. If a sixth number, $x$, is added, the new mean becomes 22. What is the value of $x$?

5. A company spends 25% of its $1.2 million budget on marketing. If the marketing budget is then split between digital and print in a 3:2 ratio, how much more money is spent on digital marketing than print marketing?

6. On a map, 0.5 inches represents 20 miles. If a rectangular plot of land on the map is 1.5 inches by 2 inches, what is the actual area of the plot in square miles?

7. A tank is being filled with water at a rate of 5 gallons per minute. After 40 minutes, the tank is 25% full. What is the total capacity of the tank in gallons?

8. A group of 200 students took a test. The average score for the first 120 students was 80, and the average score for the remaining students was 90. What was the average score for the entire group?

9. A machine produces 400 widgets per hour. For every 100 widgets produced, 3 are rejected. In a 10-hour workday, how many widgets are not rejected?

10. The price of a stock decreased by 20% in January and then increased by 30% of its new price in February. If the stock started at $100, what was the price at the end of February?

Answers & Explanations

1. $848,000: Electronics revenue in 2022 was $0.30 \times 800,000 = 240,000$. The increase is $0.20 \times 240,000 = 48,000$. Total 2023 revenue = $800,000 + 48,000 = 848,000$.

2. 450: Brand A preference = $0.40 \times 1,500 = 600$. Those 60 or younger = $75\%$ of 600. $0.75 \times 600 = 450$.

3. 288,000: Total students = $0.15 \times 2,400,000 = 360,000$. Public school students = $80\%$ of 360,000. $0.80 \times 360,000 = 288,000$.

4. 32: Sum of 5 numbers = $5 \times 20 = 100$. Sum of 6 numbers = $6 \times 22 = 132$. $x = 132 - 100 = 32$.

5. $60,000: Marketing budget = $0.25 \times 1,200,000 = 300,000$. Ratio parts = $3+2=5$. Digital = $\frac{3}{5} \times 300,000 = 180,000$. Print = $\frac{2}{5} \times 300,000 = 120,000$. Difference = $180,000 - 120,000 = 60,000$.

6. 4,800 square miles: Scale is 1 inch = 40 miles. Dimensions are $1.5 \times 40 = 60$ miles and $2 \times 40 = 80$ miles. Area = $60 \times 80 = 4,800$.

7. 800 gallons: Water in tank = $5 \times 40 = 200$ gallons. Since 200 is 25% of the total, Total = $200 \div 0.25 = 800$.

8. 84: Total points = $(120 \times 80) + (80 \times 90) = 9,600 + 7,200 = 16,800$. Average = $16,800 \div 200 = 84$.

9. 3,880: Total produced = $400 \times 10 = 4,000$. Rejection rate is 3%. Non-rejected = $97\%$. $0.97 \times 4,000 = 3,880$.

10. $104: After Jan = $100 \times 0.80 = 80$. After Feb = $80 \times 1.30 = 104$.

1. A company's revenue increased from $500,000 to $600,000. If 40% of the $600,000 revenue came from a single client, how much did that client contribute?

• A$200,000
• B$240,000
• C$100,000
• D$400,000

Frequently Asked Questions

What makes a data question "multi-step" on the GRE?

A multi-step question requires you to perform sequential operations, such as finding a value from a graph and then using that value in a percentage or ratio calculation. These questions often link different data sets together, requiring more than one logical jump to reach the final answer.

How can I avoid simple calculation errors in these problems?

The best way to avoid errors is to write down each intermediate value and label it clearly. Since these problems involve several stages, losing track of what a specific number represents (e.g., "total sales" vs "profit") is the most common cause of incorrect answers.

Are the charts in GRE data questions drawn to scale?

According to ETS, charts and graphs are generally drawn to scale unless otherwise noted. However, you should always rely on the numerical data provided rather than trying to estimate values visually from the bars or lines.

Should I use the on-screen calculator for every step?

While the calculator is helpful, using it for very simple arithmetic can actually slow you down and lead to input errors. Reserve the calculator for complex divisions or large multi-digit multiplications while performing basic additions or percentage conversions mentally or on scratch paper.

Why is unit conversion important in multi-step data questions?

Many hard GRE questions provide data in one unit (like minutes or grams) but ask for the answer in another (like hours or kilograms). Failing to convert units between steps is a frequent trap that leads to one of the incorrect multiple-choice options.

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