Help Distress NGO Volunteers Venn Diagram

CAT 2005 Slot 1 · DILR · Hard · DILR

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Passage / data set

37 volunteers work in 3 projects: Tsunami Relief (TR), Flood Relief (FR), Earthquake Relief (ER).

  • Max volunteers are in FR.
  • FR alone == volunteers in both FR and ER.
  • ER alone =2×= 2 \times all three projects.
  • Total TR =17= 17.
  • TR alone =ER alone−1= ER \text{ alone} - 1.
  • 10 volunteers in TR are in at least one more project (so TR alone =17−10=7= 17 - 10 = 7).

Question 1 of 4

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. A.

    1

  2. B.

    3

  3. C.

    4

  4. D.

    5

Answer

C

Explanation

TR alone =7= 7. ER alone =TR alone+1=8= TR \text{ alone} + 1 = 8. All three =ER alone/2=4= ER \text{ alone} / 2 = 4. Let FR & TR only =x= x, ER & TR only =y= y. Since n(TR)=17  ⟹  7+4+x+y=17  ⟹  x+y=6n(TR) = 17 \implies 7 + 4 + x + y = 17 \implies x + y = 6. Since n(FR)n(FR) is maximum, solving constraints yields minimum x=4x = 4.

Question 2 of 4

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

  1. A.

    Twenty volunteers are involved in FR.

  2. B.

    Four volunteers are involved in all the three projects.

  3. C.

    Twenty three volunteers are involved in exactly one project.

  4. D.

    No need for any additional information.

Answer

A

Explanation

Knowing total FR =20= 20 determines x=4x = 4 and y=2y = 2, fixing all regions uniquely.

Question 3 of 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?

  1. A.

    The lowest number of volunteers is now in TR project.

  2. B.

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

  3. C.

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

  4. D.

    None of the above.

Answer

B

Explanation

Calculating new totals after redistribution shows FR has at least 18 and ER has at most 17. Thus FR project has more volunteers than ER project.

Question 4 of 4

After the withdrawal of volunteers, as indicated in Question 89, 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. A.

    ER

  2. B.

    FR

  3. C.

    TR

  4. D.

    Cannot be determined

Answer

D

Explanation

Setting FR&ER=TR&ERFR \& ER = TR \& ER requires 5=y+2  ⟹  y=35 = y + 2 \implies y = 3. However, yy can only be 0, 1, or 2 from previous equations, leading to inconsistent data. Thus it cannot be determined.

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