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We will be solving interesting sets as a part of this series LRDI of the Day. I will be posting a video solution by the end of the day. You can keep a track of all the sets by clicking here:

LRDI of the Day#LRDIoftheDay #16

Venn Diagrams (CAT Original Set)

The set has been put up here for better visibility:

Help Distress (HD) is an NGO involved in providing assistance to people suffering from natural disasters. Currently, it has 37 volunteers. They are involved in three projects: Tsunami Relief (TR) in Tamil Nadu, Flood Relief (FR in Maharashtra, and Earthquake Relief (ER) in Gujarat. Each volunteer working with Help Distress has to be involved in at least one relief work project.

• A maximum number of volunteers are involved in the FR project. Among them, the number of volunteers involved in FR project alone is equal to the volunteers having additional involvement in the ER project.

• The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects.

• 17 volunteers are involved in the TR project.

• The number of volunteers involved in the TR project alone is one less than the number of volunteers involved in ER project alone.

• Ten volunteers involved in the TR project are also involved in at least one more project.

1. Based on the information given above, the minimum number of volunteers involved in both FR and TR projects, but not in the ER project is

(1) 1

(2) 3

(3) 4

(4) 5

2. Which of the following additional information would enable to find the exact number of volunteers involved in various projects?

(1) Twenty volunteers are involved in FR.

(2) Four volunteers are involved in all the three projects.

(3) Twenty three volunteers are involved in exactly one project.

(4) No need for any additional information.

3. After some time, the volunteers who were involved in all the three projects were asked to withdraw from one project. As a result, one of the volunteers opted out of the TR project, and one opted out of the ER project, while the remaining ones involved in all the three projects opted out of the FR project. Which of the following statements, then, necessarily follows?

(1) The lowest number of volunteers is now in TR project.

(2) More volunteers are now in FR project as compared to ER project.

(3) More volunteers are now in TR project as compared to ER project.

(4) None of the above.

4. After the withdrawal of volunteers, as indicated in Question 3, some new volunteers joined the NGO. Each one of them was allotted only one project in a manner such that, the number of volunteers working in one project alone for each of the three projects became identical. At that point, it was also found that the number of volunteers involved in FR and ER projects was the same as the number of volunteers involved in TR and ER projects. Which of the projects now has the highest number of volunteers?

(1) ER

(2) FR

(3) TR

(4) Cannot be determined

This was exactly how the CAT set went. In case of confusion, use your best judgment.

The solution:

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