# Section-1: Venn Diagrams Solved QuestionLogical Reasoning Discussion

Common Information

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, FloodRelief (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.
 Q. Common Information Question: 3/4 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?
 ✖ A. The lowest number of volunteers is now in TR project. ✔ B. More volunteers are now in FR project as compared to ER project. ✖ C. More volunteers are now in TR project as compared to ER project. ✖ D. None of the above

Solution:
Option(B) is correct

Consider the Venn diagram shown below.

After the volunteers withdraw as mentioned, the number of volunteers working on different projects is as shown.

∴ Number of volunteers working on TR = 7 + 6 + 3 = 16

Number of volunteers working on FR = 14 + a

Number of volunteers working on ER = 15 + b

Considering the possible values of a and b,

14 + a > 15 + b

∴ More volunteers are now in FR than in ER

Hence, option B is the correct choice.