### CAT 2005 Question Paper Question 59

Instructions

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 ofvolunteers involved in ER project alone.

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

Question 59

# 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?

Solution

FR is greater than ER, thus z is 4,5,6.

If z=4,

FR=20, ER= 18

If z=5,

FR=21, ER= 17

If z=6,

FR=22, ER= 16

Now even if we transfer one of the volunteers opted out of the TR project thus he will now be handling FR and ER, and one opted out of the ER project will be handling TR and FR, while the remaining ones involved in all the three projects opted out of the FR project.

The worst-case scenario will be when z=4. Now 2 are out of FR, 1 from ER and 1 from TR.

FR=20-2=18 and ER=18-1=17

So we can see that even if volunteers are withdrawn, the number of volunteers in FR are more as in, total if we calculate comes out to be more. Hence option B.