GRE DI: Frequently Asked Concepts

GRE Data Interpretation sets frequently draw from a well defined group of quantitative concepts. These include ratio, percentage, percentage change, absolute change, average, median, range, standard deviation, highest or lowest value, less than or greater than comparisons, subset or superset relationships, and finding missing data. The following video, a part of our comprehensive GRE prep online course, explains these frequently tested concepts with clarity and shows how they appear on real GRE Data Interpretation sets.

 

Summary: Frequently Tested Concepts on DI

Frequently tested concepts in Data Interpretation (DI) involve a variety of mathematical and statistical principles used to analyze information. Key topics include:

Ratios and Percentages

Comparing values and expressing parts of a whole or changes over time. 

Changes

Calculating both absolute changes (the direct difference between numbers) and percentage changes. 

Statistical Measures

Determining the Average (arithmetic mean), Median (the middle value in a set), and Range (the difference between the highest and lowest values).

Standard Deviation

Measuring the amount of variation or dispersion in a set of values. 

Extremes and Comparisons

Identifying the Highest and Lowest values in a dataset, as well as performing “Less than” or “Greater than” comparisons.

Sets

Understanding the relationship between Subsets and Supersets. 

Missing Data

Handling and solving for incomplete information within a dataset.

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GRE-style Practice Question 1

Correct Answer: B

 

For a detailed explanation, please refer to the video presented earlier on this page.

 

Following is a concise, step-wise written explanation…

 

Question

In 2020, if 40 percent of electricity generated from wind and 70 percent of electricity generated from hydropower were exported to neighboring countries, and no electricity from other sources was exported, approximately what percent of the total electricity generation was exported?

1. 11%
2. 13%
3. 17%
4. 22%
5. 28%

 

Step 1: Identify the Percentages from the Pie Chart

Look at the Year 2020 chart.

• Wind: 7.9% of total generation.
• Hydropower: 14.1% of total generation. 

Step 2: Calculate the Exported Portion of Each Source

The question asks for the export relative to the total generation.

• Export from Wind: 40% of 7.9% = 0.40 * 7.9 = 3.16% of total.
• Export from Hydropower: 70% of 14.1% = 0.70 * 14.1 = 9.87% of total. 

Step 3: Calculate the Total Export Percentage

Add the two export percentages together because no other sources were exported.

• Total Export = 3.16% + 9.87% = 13.03%. 

Step 4: Select the Closest Approximation

13.03% is approximately 13%.

 

Correct Answer: B

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GRE-style Practice Question 2

Correct Answer: B

 

For a detailed explanation, please refer to the video presented earlier on this page.

 

Following is a concise, step-wise written explanation…

 

Question

By approximately what percent did the median peach yield per tree increase from 2020 to 2021?

1. 4.0%
2. 5.3%
3. 12.8%
4. 20.4%
5. 25.7%

 

Step 1: Identify the values from the graph

Look at the line graph titled Average and Median Peach Yield Per Tree. Locate the dashed line representing the Median.

• In the year 2020, the median yield is 76 pounds.
• In the year 2021, the median yield is 80 pounds. 

Step 2: Calculate the absolute increase

Subtract the old value from the new value: 80 – 76= 4 pounds. 

Step 3: Calculate the percentage increase

Divide the increase by the original 2020 value and multiply by 100:

(4 / 76) * 100

= approximately 5.3%

 

Correct Answer: B

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GRE-style Practice Question 3

Correct Answer: B

 

For a detailed explanation, please refer to the video presented earlier on this page.

 

Following is a concise, step-wise written explanation…

 

Question

In 2016, the number of Vitamins and Supplements units sold was approximately how many times the number of Skincare units sold? 

1. 1.4
2. 2.4
3. 2.8
4. 3.6
5. 4.3

 

Step-by-Step Solution

Identify the values

Look at the table provided in the image for the year 2016.

• Vitamins and Supplements units sold: 823,921
• Skincare units sold: 348,690 

Simplify the numbers

Since the question asks for an approximate value, round the numbers to make the calculation easier.

• Vitamins and Supplements: approximately 824,000
• Skincare: approximately 349,000 

Set up the ratio

Divide the number of Vitamins and Supplements by the number of Skincare units. Ratio = 824,000 / 349,000 

Calculate the result

824 / 349 is roughly equal to 2.36. 

Select the closest match

Looking at the options, 2.36 rounds to 2.4.

 

Correct Answer: B

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GRE-style Practice Question 4

Correct Answer: B

 

For a detailed explanation, please refer to the video presented earlier on this page.

 

Following is a concise, step-wise written explanation…

 

Question

Which of the following is closest to the mean peach yield per tree for the harvests in 2018 and 2019 combined?

1. 61.1
2. 71.8
3. 72.0
4. 72.2
5. 73.4

 

Given Data

2018:

Average yield per tree = 76 lb

Trees harvested = 756

2019:

Average yield per tree = 68 lb

Trees harvested = 848

Convert each year into total pounds harvested

2018 total = 76 × 756 = 57,456 lb
2019 total = 68 × 848 = 57,664 lb

Find weighted average: Add totals and divide by total trees

Combined mean yield per tree
= (57,456 + 57,664) ÷ (756 + 848)
≈ 71.8

 

Correct answer: B

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GRE-style Practice Question 5

Correct Answer: C

 

For a detailed explanation, please refer to the video presented earlier on this page.

 

Following is a concise, step-wise written explanation…

 

Question

The median of the 10 recorded particulate matter values in the air in the residential zone is approximately how many micrograms per cubic meter?

1. 62
2. 76
3. 81
4. 86
5. 93

 

Read the middle two values

There are 10 residential zone readings, so the median lies between the 5th and 6th values.

Identify them visually

From the chart, the two middle values are approximately 76 and 86.

Average the two middle values

Median ≈ (76 + 86) / 2 = 81

 

Correct Answer: C

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GRE-style Practice Question 6

Correct Answer: D

 

For a detailed explanation, please refer to the video presented earlier on this page.

 

Following is a concise, step-wise written explanation…

 

Question

For the years 2015 through 2022, what was the ratio of the range of the annual unemployment rate in Plyburn City to the range of the annual unemployment rate in the State of Bloomden?

1. 2 to 5
2. 3 to 5
3. 4 to 5
4. 5 to 4
5. 5 to 3

 

Identify the highest and lowest values for each series

From the chart, Piyburn City ranges approximately from 5.0% to 7.0%.
Bloomden ranges approximately from 6.0% to 7.6%.

Compute the ranges

Range for Piyburn City ≈ 7.0% − 5.0% = 2.0%
Range for Bloomden ≈ 7.6% − 6.0% = 1.6%

Form the ratio of the two ranges

Ratio = 2.0 : 1.6

Simplify the ratio

2.0 : 1.6 = 20 : 16

= 5 : 4

 

Correct Answer: D

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GRE-style Practice Question 7

Correct Answer: E

 

For a detailed explanation, please refer to the video presented earlier on this page.

 

Following is a concise, step-wise written explanation…

 

Question

For which of the following train lines was the standard deviation of the average daily commuters from 2013 to 2018 greatest?

1. Central line
2. Eastern line
3. Northern line
4. Southern line
5. Western line

 

Step-by-Step Explanation 

Concept

Standard deviation measures how spread out the numbers are from their average. To find the greatest standard deviation without complex math, look for the row with the largest difference between its highest and lowest values (the range). 

Analysis of the Data

• Central Line: Low is 62,057; High is 68,094. Difference is about 6,000.
• Eastern Line: Low is 21,957; High is 26,308. Difference is about 4,300.
• Northern Line: Low is 79,501; High is 85,748. Difference is about 6,200.
• Southern Line: Low is 49,202; High is 56,038. Difference is about 6,800.
• Western Line: Low is 34,859; High is 49,237. Difference is about 14,300. 

Conclusion

The Western Line shows the most significant fluctuations over the six year period. Because the data points for the Western Line are much more spread out than the others, it has the greatest standard deviation.

 

Correct Answer: E

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GRE-style Practice Question 8

Correct Answer: C

 

For a detailed explanation, please refer to the video presented earlier on this page.

 

Following is a concise, step-wise written explanation…

 

Question

For which of the following years was the ratio of the number of express deliveries to the number of packages delivered the greatest?

1. 2015
2. 2019
3. 2020
4. 2021
5. 2023

 

Step by Step Solution 

Identify the Data

For each year in the choices, find the value from the Express Deliveries chart and the Packages Delivered chart.

• 2015: 302 / 964
• 2019: 523 / 1356
• 2020: 461 / 952
• 2021: 422 / 1016
• 2023: 480 / 1329 

Simplify and Estimate

Look for the year where the top number is the largest part of the bottom number.

• 2015: 302 / 964 is roughly 300 / 960 or about 0.31
• 2019: 523 / 1356 is roughly 520 / 1350 or about 0.38
• 2020: 461 / 952 is nearly 461 / 950, which is almost 0.50 or 50 percent
• 2021: 422 / 1016 is roughly 420 / 1000 or 0.42
• 2023: 480 / 1329 is roughly 480 / 1330 or about 0.36 

Compare Results

The year 2020 has a numerator that is nearly half of its denominator.

In all other years, the express deliveries are much less than half of the total packages.

Therefore, the ratio for 2020 is the highest.

 

Correct Answer: C

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GRE-style Practice Question 9

Correct Answer: E

 

For a detailed explanation, please refer to the video presented earlier on this page.

 

Following is a concise, step-wise written explanation…

 

Question

For how many of the months at which readings were taken was the difference in particulate matter in the air between the two zones greater than 10 micrograms per cubic meter?

1. 3
2. 4
3. 5
4. 6
5. 7

 

Step by Step Solution

Understand the Goal

The question asks to count the number of months where the gap between the Industrial Zone line and the Residential Zone line is more than 10 units on the vertical axis.

Analyze the Grid

Each horizontal line on the vertical axis represents an increment of 10 micrograms. Therefore, a difference greater than 10 means the two points must be separated by more than one full grid square vertically. 

Check Each Month

• Jan 2022: Industrial is 95, Residential is 70. Difference is 25. (Count = 1)
• Mar 2022: Industrial is 105, Residential is 90. Difference is 15. (Count = 2)
• May 2022: Industrial is 100, Residential is 95. Difference is 5.
• Jul 2022: Industrial is 90, Residential is 65. Difference is 25. (Count = 3)
• Sep 2022: Industrial is 88, Residential is 58. Difference is 30. (Count = 4)
• Nov 2022: Industrial is 100, Residential is 65. Difference is 35. (Count = 5)
• Jan 2023: Industrial is 93, Residential is 88. Difference is 5.
• Mar 2023: Industrial is 93, Residential is 100. Difference is 7.
• May 2023: Industrial is 95, Residential is 108. Difference is 13. (Count = 6)
• Jul 2023: Industrial is 90, Residential is 75. Difference is 15. (Count = 7) 

Final Count

There are 7 months where the difference is greater than 10.

 

Correct Answer: E

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GRE-style Practice Question 10

Correct Answer: A

 

For a detailed explanation, please refer to the video presented earlier on this page.

 

Following is a concise, step-wise written explanation…

 

Question

Total waste generated by households in Rockwin City in August 2023: 120,000 tons.

If 40 percent of the glass waste generated by households came from beverage bottles, approximately how many tons of beverage bottle waste were generated by households?

1. 5,760
2. 8,640
3. 14,400
4. 48,000
5. 62,400

 

Step 1: Find total glass waste

The table shows that Glass is 12 percent of the total waste.

Total Glass = 12 percent of 120,000

Total Glass = 0.12 * 120,000 = 14,400 tons.

Step 2: Find beverage bottle waste

The question states that beverage bottles make up 40 percent of the glass waste.

Bottle Waste = 40 percent of 14,400

Bottle Waste = 0.40 * 14,400 = 5,760 tons.

 

Correct Answer: A

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GRE-style Practice Question 11

Correct Answer: B

 

For a detailed explanation, please refer to the video presented earlier on this page.

 

Following is a concise, step-wise written explanation…

 

Question

In 2022, the total crop production in Hartland Region was 140,000 tons. Which of the following is closest to the total crop production, in tons, from crops not listed in the table?

1. 19,000
2. 26,600
3. 32,800
4. 81,000
5. 113,400

 

Step 1: Find the percentage of listed crops

Add all the percentages given in the table: 24 percent + 18 percent + 15 percent + 11 percent + 8 percent + 5 percent = 81 percent. 

Step 2: Find the percentage of crops not listed

Subtract the total listed percentage from 100 percent: 100 percent – 81 percent = 19 percent.

Step 3: Calculate the total tons for unlisted crops

Multiply the total production by the unlisted percentage: 140,000 * 0.19 = 26,600.

 

Correct Answer: B

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