Hard GRE Data Interpretation Questions Practice Questions

Concept Explanation

GRE Data Interpretation questions measure your ability to synthesize information from various graphical formats, such as bar graphs, line charts, pie charts, and complex tables, to solve multi-step mathematical problems. These questions are not merely about reading a value from a chart; they require you to apply concepts from arithmetic, algebra, and geometry to data sets that often contain extraneous information. Success on Hard GRE Data Interpretation Questions depends on your ability to identify relevant data quickly and perform accurate calculations under time pressure. For more comprehensive practice, you can explore Free GRE Practice Questions to build your foundation. To excel, you must become proficient in calculating percent changes, weighted averages, and ratios using data extracted from visual displays. According to the ETS Quantitative Reasoning overview, these questions make up a significant portion of the math section, often grouped in sets of three or more based on the same data source.

Solved Examples

1. Example 1: Percent Increase and Decrease. A table shows that Company X's revenue was $4.5 million in 2020 and grew by 12% in 2021, while Company Y's revenue was $6.0 million in 2020 and decreased by 8% in 2021. What is the difference in their revenues in 2021?
   1. Calculate Company X's 2021 revenue: $4.5 \times 1.12 = 5.04$ million.
   2. Calculate Company Y's 2021 revenue: $6.0 \times 0.92 = 5.52$ million.
   3. Find the difference: $5.52 - 5.04 = 0.48$ million, or $480,000.
2. Example 2: Weighted Averages. A pie chart shows that a library's collection consists of 40% Fiction, 35% Non-Fiction, and 25% Reference books. If the average age of Fiction books is 6 years, Non-Fiction is 10 years, and Reference is 4 years, what is the weighted average age of the entire collection?
   1. Set up the weighted average formula: $(0.40 \times 6) + (0.35 \times 10) + (0.25 \times 4)$.
   2. Calculate each part: $2.4 + 3.5 + 1.0$.
   3. Sum the parts: $6.9$ years.
3. Example 3: Ratio Analysis. A bar graph displays export values for two countries over five years. In Year 3, Country A exported $120 billion and Country B exported $150 billion. If Country A's exports increase by 20% in Year 4 and Country B's exports decrease by 10%, what is the ratio of Country A's exports to Country B's exports in Year 4?
   1. New value for Country A: $120 \times 1.20 = 144$.
   2. New value for Country B: $150 \times 0.90 = 135$.
   3. Establish the ratio: $\frac{144}{135}$.
   4. Simplify by dividing both by 9: $\frac{16}{15}$ or 16:15.

Practice Questions

1. In a certain city, the total budget for 2023 was $800 million. If 15% was spent on Education and the Education budget is set to increase by 25% in 2024 while the total budget remains the same, what percent of the 2024 total budget will Education represent?

2. A scatter plot shows the relationship between years of experience and salary for 20 employees. If the line of best fit is $y = 5000x + 35000$, what is the predicted salary for an employee with 12 years of experience?

3. A table lists the population of five districts. District A has 25,000 people with a density of 500 people per square mile. If District B has twice the area of District A but only 80% of its population, what is the population density of District B?

4. Referencing a double-bar graph: In 2010, the ratio of male to female students was 4:5. In 2020, the number of male students increased by 25% and female students increased by 10%. What is the new ratio of male to female students?

5. A pie chart shows energy sources for a state: Coal (30%), Gas (40%), Nuclear (20%), and Renewables (10%). If the total energy production is 2,500 Gigawatt-hours (GWh) and Renewables double while Coal decreases by 20%, what is the new total energy production?

6. Using a line graph showing stock prices over 6 months: If Stock A started at $50 and increased by 10% each month for 2 months, then decreased by 20% in the third month, what is its price at the end of month 3?

7. A table shows the number of cars sold by four dealers. Dealer 1 sold 150 cars at an average price of $20,000. Dealer 2 sold 100 cars at an average price of $30,000. What is the combined average price of the cars sold by these two dealers?

8. If the standard deviation of a set of data points in a frequency table is 0, what must be true about the data points? (Assume there is more than one data point).

Answers & Explanations

1. 18.75%. First, find the 2023 Education budget: $0.15 \times 800 = 120$ million. The 25% increase makes it $120 \times 1.25 = 150$ million. Since the total budget is still $800 million, the percentage is $\frac{150}{800} \times 100 = 18.75\%$.
2. $95,000. Substitute $x = 12$ into the equation: $y = 5000(12) + 35000$. $y = 60000 + 35000 = 95000$.
3. 200 people per sq mile. Area of A = $\frac{25000}{500} = 50$ sq miles. Area of B = $50 \times 2 = 100$ sq miles. Population of B = $25000 \times 0.80 = 20000$. Density of B = $\frac{20000}{100} = 200$.
4. 10:11. Let males = $4x$ and females = $5x$. New males = $4x \times 1.25 = 5x$. New females = $5x \times 1.10 = 5.5x$. Ratio = $\frac{5}{5.5} = \frac{50}{55} = \frac{10}{11}$.
5. 2,600 GWh. Original Renewables = $2500 \times 0.10 = 250$. Original Coal = $2500 \times 0.30 = 750$. Change in Renewables = +250. Change in Coal = $-0.20 \times 750 = -150$. Net change = $+250 - 150 = +100$. New total = $2500 + 100 = 2600$.
6. $48.40. Month 1: $50 \times 1.1 = 55$. Month 2: $55 \times 1.1 = 60.5$. Month 3: $60.5 \times 0.8 = 48.4$.
7. $24,000. Total revenue = $(150 \times 20000) + (100 \times 30000) = 3,000,000 + 3,000,000 = 6,000,000$. Total cars = 250. Average = $\frac{6,000,000}{250} = 24,000$. For more on averages, see GRE Practice Questions with Explanations.
8. All data points are identical. Standard deviation measures dispersion; if it is 0, there is no dispersion, meaning every value in the set is exactly the same.

1. If a pie chart representing a total of $5,000 has a sector for "Rent" at 72 degrees, what is the dollar amount allocated to Rent?

• A$500
• B$1,000
• C$1,200
• D$720

Frequently Asked Questions

How many Data Interpretation questions are on the GRE?

Data Interpretation questions typically appear as sets associated with a specific graphic, usually comprising about 3 to 6 questions per quantitative section. They are integrated into the Quantitative Reasoning measure rather than being a separate section.

What is the best strategy for multi-graph questions?

When faced with multiple graphs, first identify which graph contains the specific variables mentioned in the question and check for shared axes or units. Use Bevinzey's AI Exam Simulator to practice alternating between different data sources quickly.

Are calculators allowed for GRE Data Interpretation?

Yes, an on-screen calculator is provided during the GRE General Test, which is essential for the complex multiplication and division often required in hard data sets. However, you should still rely on estimation to verify that your calculated answers are logically sound.

What are the most common chart types on the GRE?

The most frequent formats include tables, bar graphs (including stacked and double bar), line graphs, and pie charts, with occasional scatter plots or box plots. Understanding how to read box plots and frequency distributions is vital for harder difficulty levels.

How can I avoid traps in Hard Data Interpretation questions?

Avoid traps by double-checking units (e.g., thousands vs. millions) and ensuring you are looking at the correct year or category specified in the prompt. Many wrong answers on the GRE are actually correct calculations for the wrong data point or time period.