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GRE Quant: Line Diagrams for Overlapping Sets

Line diagrams provide a clear and structured way to represent overlapping sets by placing values along a single line. This format helps you sequence information smoothly, track shared elements accurately, and maintain correct totals throughout the setup. The approach supports layered GRE Quant questions that involve overlaps and combined counts.

The following video, part of our GRE preparation course, explains line diagrams for overlapping sets in a simple and structured manner. It shows how to build the diagram step by step, place values correctly, and update counts as information unfolds. The video then applies the method on GRE-style problems so you experience the application first-hand. Use this learning steadily across your GRE practice exercises and GRE sectional mocks, and GRE mocks.

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Overview: Line Diagram…

Overview of line

Summary of Line Diagram Application

A line diagram is a tool used to analyze data presented as ranges. This method is particularly useful when data points are classified into specific numerical intervals.

 

Answer to the question on the slide is 40%

 

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

 

For visual illustration, here is a snapshot from the video…

Line diagram - example

Following is a concise, step-wise written explanation…

 

Question

On average, 80% members of a group consume greater than 2000 calories a day and 60% members consume less than 2500 calories a day. What percent of members consume between 2000 and 2500 calories a day?

 

Explanation

Identify the Ranges

  • Total group percentage is 100%.
  • Members consuming 2000 calories or less: 100% minus 80% equals 20%.
  • Members consuming 2500 calories or more: 100% minus 60% equals 40%.

Calculate the Middle Range

  • The total group is made of three parts: those 2000 or less, those between 2000 and 2500, and those 2500 or more.
  • Add the known outside ranges: 20% plus 40% equals 60%.
  • Subtract this sum from the total: 100% minus 60% equals 40%.

 

Correct Answer: 40%

Conceptual Example…

Conceptual example

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

 

For visual illustration, here is a snapshot from the video…

Conceptual example - 2

Following is a concise, step-wise written explanation…

 

Questions

On average, 40 percent members of a group consume 2000 or fewer calories a day, 70 percent members consume 2500 or fewer calories a day, and 20 percent members consume 3000 or more calories a day.

What percent of members consume…

  1. Between 2500 and 3000 calories a day?
  2. Between 2000 and 2500 calories a day?
  3. Between 2000 and 3000 calories a day?
  4. More than 2000 calories a day?
  5. Less than 3000 calories a day?

 

Step By Step Solution

First, identify the percentage of people in each calorie range provided:

  • 0 to 2000 calories: 40 percent
  • 0 to 2500 calories: 70 percent
  • 3000 or more calories: 20 percent

Question 1: Between 2500 and 3000

  • Total group is 100 percent.
  • Subtract those who consume 2500 or fewer (70 percent) and those who consume 3000 or more (20 percent).
  • Calculation: 100 – 70 – 20 = 10 percent.

Correct Answer: 10 percent

Question 2: Between 2000 and 2500

  • Subtract those who consume 2000 or fewer (40 percent) from those who consume 2500 or fewer (70 percent).
  • Calculation: 70 – 40 = 30 percent.

Correct Answer: 30 percent

Question 3: Between 2000 and 3000

  • Add the group from 2000 to 2500 (30 percent) and the group from 2500 to 3000 (10 percent).
  • Calculation: 30 + 10 = 40 percent.

Correct Answer: 40 percent

Question 4: More than 2000

  • Subtract those who consume 2000 or fewer (40 percent) from the total (100 percent).
  • Calculation: 100 – 40 = 60 percent.

Correct Answer: 60 percent

Question 5: Less than 3000

  • Subtract those who consume 3000 or more (20 percent) from the total (100 percent).
  • Calculation: 100 – 20 = 80 percent.

Correct Answer: 80 percent

When to Use Venn Diagram and When to Use Line Diagram…

When to use Venn diagram and when to use line diagram

When deciding how to represent overlapping sets of information, the choice between a Venn Diagram and a Line Diagram depends on whether the data is classified by categories or by numerical ranges.

 

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

 

For visual illustration, here is a snapshot from the video…

venn diagram and line diagram

Following is a written explanation…

 

Venn Diagram

Venn diagrams are the go-to tool when data is classified into distinct types or categories. This format is most effective when subjects can belong to one, both, or none of the specified groups.

  • Application: Identifying commonalities and differences between qualitative groups.
  • Example: In a survey, 70 percent drink tea, 50 percent drink coffee, and 25 percent drink neither.

Line Diagram

Line diagrams are used when data is classified into ranges along a continuous scale. This is particularly useful for visualizing overlaps in numerical data, such as scores, ages, or timeframes.

  • Application: Mapping out boundaries and intersections on a numerical spectrum.
  • Example: In a test, 70 percent scored 80 percent or less, and 50 percent scored 40 percent or more.

GRE-style Practice Question 1

GRE-style practice question 1

Correct Answer: 30

 

Following is a concise, step-wise written explanation…

 

Question

Of 150 students who appeared for a test, 105 scored below 80% and 75 scored above 60%. How many students scored more than 60% but less than 80%?

 

Step 1

Find the number of students who scored 80% or more.

Total students = 150

Students below 80% = 105

Students who scored 80% or more = 150 – 105 = 45

Step 2

Find the number of students who scored between 60% and 80%.

Total students who scored above 60% = 75

This group of 75 includes students between 60% and 80%, plus the 45 students who scored 80% or more.

Students between 60% and 80% = 75 – 45 = 30

 

Correct Answer: 30

GRE-style Practice Question 2

GRE-style practice question 2

Correct Answer: 46

 

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

 

For visual illustration, here is a snapshot from the video…

practice question 2 - solution

Following is a concise, step-wise written explanation…

 

Question

In a survey, 82 percent of adult men reported getting more than 50 hours of sleep per week, and 64 percent reported getting less than 65 hours. What percent of adult males surveyed reported getting more than 50 hours of sleep per week but less than 65?

 

Solution

To solve this, we need to find the overlap between two groups of men. Let us look at the total population as 100 percent.

Step 1: Identify the groups

  • Group A: Men getting more than 50 hours = 82 percent.
  • Group B: Men getting less than 65 hours = 64 percent.

Step 2: Understand the combined total

If we add these two percentages together: 82 + 64 = 146 percent.

Step 3: Calculate the overlap

Since the total number of people cannot exceed 100 percent, the amount over 100 percent represents the men who belong to both groups. These are the men who get more than 50 hours AND less than 65 hours.

146 – 100 = 46 percent.

Logic Check

If 82 percent are above 50 hours, then 18 percent must be at or below 50 hours.

If 64 percent are below 65 hours, then 36 percent must be at or above 65 hours.

To find the middle section (between 50 and 65), we subtract these two outside groups from the total: 100 – 18 – 36 = 46 percent.

 

Correct Answer: 46

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