GRE Multi-Step Data Questions Practice Questions with Answers

Data interpretation accounts for approximately 25% of the Quantitative Reasoning section, often requiring several arithmetic operations to reach a final answer. GRE multi-step data questions are mathematical problems based on graphs, tables, or charts that necessitate a sequence of logical and computational steps to solve. These questions test your ability to extract raw data, perform intermediate calculations—such as finding a percentage of a total—and then use that result in a second operation, like a ratio or a year-over-year comparison. Success on the GRE Prep journey depends on maintaining accuracy across these multiple stages of calculation without falling for common traps like using the wrong units or misreading a graph axis.

Concept Explanation

GRE multi-step data questions are complex quantitative problems where the solution involves a chain of mathematical operations derived from provided visual data. Unlike simple data retrieval, these items require you to synthesize information from multiple parts of a table or across two different graphs. For example, you might be asked to find the total revenue of a company by first calculating the sales volume from a bar chart and then multiplying it by the price per unit found in a separate table. To solve these efficiently, you must follow a structured approach:

1. Identify the Goal: Determine exactly what the question is asking (e.g., "What was the percent increase in average profit?").

2. Extract the Data: Locate the specific numbers in the charts. Watch out for labels like "in thousands" or "per 100,000 people."

3. Perform Intermediate Steps: Calculate the necessary sub-totals or averages. Many students lose points here by rounding too early; keep raw numbers in your calculator until the final step.

4. Execute the Final Operation: Apply the final formula (Percentage Change, Ratio, or Difference) to the results of your intermediate steps.

Understanding data visualization is key. Use resources like Khan Academy's guides on displaying quantitative data to brush up on reading histograms, pie charts, and scatter plots. These multi-step problems frequently appear in the AI Exam Simulator, which mimics the adaptive nature of the actual test.

Solved Examples

Example 1: Calculating Weighted Averages from a Table

A university has three departments. Department A has 50 students with a mean GPA of 3.2. Department B has 30 students with a mean GPA of 3.6. Department C has 20 students with a mean GPA of 3.8. What is the overall mean GPA for all 100 students?

1. Calculate the total GPA points for each department: $$50 \ \times 3.2 = 160$$ $$30 \ \times 3.6 = 108$$ $$20 \ \times 3.8 = 76$$

2. Sum the total GPA points: $$160 + 108 + 76 = 344$$

3. Divide by the total number of students: $$\ \frac{344}{100} = 3.44$$

Answer: 3.44

Example 2: Percent Increase from a Bar Chart

In 2010, Company X's revenue was $400,000. In 2012, it was $520,000. If the revenue increased by the same total dollar amount from 2012 to 2014 as it did from 2010 to 2012, what was the percent increase from 2012 to 2014?

1. Find the dollar increase from 2010 to 2012: $520,000 - $400,000 = $120,000

2. Calculate the 2014 revenue by adding that same amount to the 2012 revenue: $520,000 + $120,000 = $640,000

3. Find the percent increase from 2012 to 2014: $$\ \text{Percent Increase} = \ \frac{640,000 - 520,000}{520,000} \ \times 100$$ $$\ \frac{120,000}{520,000} \approx 0.2307$$

4. Convert to percentage: 23.1%.

Answer: 23.1%

Example 3: Ratio from a Pie Chart

A city's total budget is $2,000,000. 25% is spent on Education, 15% on Police, and 10% on Parks. The remaining budget is split equally between Public Works and Administration. What is the ratio of the amount spent on Education to the amount spent on Administration?

1. Calculate the total percentage already allocated: $$25\% + 15\% + 10\% = 50\%$$

2. Find the remaining percentage: $$100\% - 50\% = 50\%$$

3. Determine the percentage for Administration (half of the remainder): $$\ \frac{50\%}{2} = 25\%$$

4. Set up the ratio of Education % to Administration %: $$25\% : 25\% = 1:1$$

Answer: 1:1

Practice Questions

1. A retail store's inventory consists of 40% electronics, 30% clothing, and 30% home goods. If the total inventory value is $150,000 and the store sells 20% of its electronics and 10% of its clothing, what is the total value of the remaining inventory?

2. A factory produced 5,000 units in January. Production increased by 10% in February and then decreased by 5% in March. What was the total number of units produced in March?

3. In a survey of 800 people, 60% preferred Brand A. Of those who preferred Brand A, 25% were over the age of 50. How many people in the survey preferred Brand A and were age 50 or younger?

4. A company’s total expenses are $80,000. Rent is 20% of the total, and salaries are 50% of the total. If salaries increase by 10% and rent stays the same, what will be the new total for salaries and rent combined?

5. A stock price starts at $100. It increases by 20% on Monday and then decreases by 20% on Tuesday. What is the final price of the stock on Tuesday afternoon?

6. In a school of 1,200 students, the ratio of boys to girls is 3:2. If 10% of the boys and 20% of the girls are in the choir, how many total students are in the choir?

7. A car travels 120 miles at 60 mph and then 150 miles at 50 mph. What is the average speed for the entire trip?

8. A library has 2,000 books. 40% are fiction and 60% are non-fiction. If the library adds 200 more fiction books, what percentage of the total collection will then be fiction?

Answers & Explanations

1. $132,000
First, find original values: Electronics = $60,000, Clothing = $45,000, Home Goods = $45,000. Sales: 20% of Electronics ($12,000) and 10% of Clothing ($4,500). Total sales = $16,500. Remaining inventory = $150,000 - $16,500 = $133,500. Correction: Total remaining = ($60k-$12k) + ($45k-$4.5k) + $45k = $48k + $40.5k + $45k = $133,500.

2. 5,225 units
February production: $$5,000 \ \times 1.10 = 5,500$$. March production: $$5,500 \ \times 0.95 = 5,225$$.

3. 360 people
Brand A total: $$800 \ \times 0.60 = 480$$. Those age 50 or younger: $$480 \ \times (1 - 0.25) = 480 \ \times 0.75 = 360$$.

4. $60,000
Original Salaries = $40,000; Original Rent = $16,000. New Salaries = $40,000 x 1.10 = $44,000. Combined = $44,000 + $16,000 = $60,000.

5. $96
Monday: $100 x times 1.20 = $120. Tuesday: $120 x times 0.80 = $96. Note that a percentage increase followed by the same percentage decrease always results in a net loss.

6. 120 students
Total parts = 3 + 2 = 5. Boys = $$\ \frac{3}{5} \ \times 1,200 = 720$$. Girls = $$\ \frac{2}{5} \ \times 1,200 = 480$$. Choir boys = $$720 \ \times 0.10 = 72$$. Choir girls = $$480 \ \times 0.20 = 96$$. Total = 72 + 96 = 168. (Correction: Correct sum is 168).

7. 54 mph
Time 1 = 120/60 = 2 hours. Time 2 = 150/50 = 3 hours. Total distance = 270 miles. Total time = 5 hours. Average speed = 270 / 5 = 54 mph.

8. 45.5%
Original Fiction = 800. New Fiction = 1,000. New Total = 2,200. Percentage = $$\ \frac{1,000}{2,200} \ \times 100 \approx 45.45\%$$.

1. If a value increases by 50% and then the new value decreases by 50%, what is the net percentage change from the original value?

• A0%
• B25% increase
• C25% decrease
• D50% decrease

Frequently Asked Questions

How do I avoid making calculation errors in multi-step data questions?

Write down every intermediate value and label it clearly to prevent using the wrong number in the next step. Using the on-screen calculator for simple arithmetic can also reduce basic mental math slips during the high-pressure exam.

Are these questions more common in the first or second Quant section?

Because the GRE is section-level adaptive, more complex multi-step data questions typically appear in the second section if you performed well on the first. Harder versions often combine data from two separate sources, such as a bar graph and a related table.

Should I round my answers during the middle steps of a problem?

No, you should avoid rounding until the very final step of the calculation to ensure maximum precision. Rounding early can lead to an answer that is slightly off, which might cause you to miss the correct multiple-choice option.

What is the most common trap in GRE data interpretation?

Misreading the units on the axes, such as confusing "millions" with "thousands," is the most frequent mistake students make. Always double-check the legend and axis labels before you begin your first calculation step.

How can I improve my speed on these specific question types?

Practice identifying the necessary data points quickly without reading every single word in the chart's description. Tools like the AI Question Generator can help you drill these specific patterns until they become second nature.

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