Logical 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. |
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: |

✖ A. |
1 |

✖ B. |
3 |

✔ C. |
4 |

✖ D. |
5 |

**Solution:**

Option(**C**) is correct

Consider the Venn diagram shown below.

17 volunteers are involved in the TR project and 10 in TR are also involved in other projects. Thus, 7 volunteers are involved only in TR.

∴ 8 volunteers are involved in ER alone.

∴ 4 volunteers are involved in all the three projects.

Let *x* people be involved in FR alone.

∴ Number of people involved in FR and ER but not TR = *x* – 4

Now, *a* + *b* + 4 = 10

∴ *a* + *b* = 6

Also, 7 + *a* + *b* + 4 + *x* + *x* – 4 + 8 = 37

∴ 2*x* = 16 or *x* = 8

Number of Volunteers involved in FR > Number of Volunteers involved in TR

And Number of Volunteers involved in FR > Number of Volunteers involved in ER

∴ 16 + *a* > 17 and 16 + *a* > 16 + *b* or *a* > *b*

∴ *a* and *b* can be (6, 0), (5, 1), (4, 2)

The minimum number of volunteers involved in both FR and TR projects, but not in the ER Project = minimum value of *a* = 4

Hence, **option C** is the correct choice.