Students & Proposals Survey

CAT 2019 Slot 2 · DILR · Medium · Venn Diagrams

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Passage / data set

Students in a college are discussing two proposals -- A: a proposal by the authorities to introduce dress code on campus, and B: a proposal by the students to allow multinational food franchises to set up outlets on college campus.

A student does not necessarily support either of the two proposals. In an upcoming election for student union president, there are two candidates in fray: Sunita and Ragini. Every student prefers one of the two candidates. A survey was conducted among the students by picking a sample of 500 students. The following information was noted from this survey:

  1. 250 students supported proposal A and 250 students supported proposal B.
  2. Among the 200 students who preferred Sunita as student union president, 80% supported proposal A.
  3. Among those who preferred Ragini, 30% supported proposal A.
  4. 20% of those who supported proposal B preferred Sunita.
  5. 40% of those who did not support proposal B preferred Ragini.
  6. Every student who preferred Sunita and supported proposal B also supported proposal A.
  7. Among those who preferred Ragini, 20% did not support any of the proposals.

Question 1 of 4

Among the students surveyed who supported proposal A, what percentage preferred Sunita for student union president?

Answer

64

Explanation

Total Sunita = 200, Ragini = 300. Sunita supporting A = 80%×200=16080\% \times 200 = 160. Total supporting A = 250. Percentage of A supporters preferring Sunita =160250×100=64%= \frac{160}{250} \times 100 = 64\%.

Question 2 of 4

What percentage of the students surveyed who did not support proposal A preferred Ragini as student union president?

Answer

84

Explanation

Total not supporting A = 500−250=250500 - 250 = 250. Ragini not supporting A = 300−90=210300 - 90 = 210. Percentage =210250×100=84%= \frac{210}{250} \times 100 = 84\%.

Question 3 of 4

What percentage of the students surveyed who supported both proposals A and B preferred Sunita as student union president?

  1. A.

    25

  2. B.

    50

  3. C.

    40

  4. D.

    20

Answer

B

Explanation

Sunita supporters supporting B = 20%×250=5020\% \times 250 = 50. From condition 6, all 50 Sunita supporters who support B also support A. Thus, Sunita supporters supporting both A and B = 50. Total supporting both A and B = 100. Percentage = 50100×100=50%\frac{50}{100} \times 100 = 50\%.

Question 4 of 4

How many of the students surveyed supported proposal B, did not support proposal A and preferred Ragini as student union president?

  1. A.

    40

  2. B.

    210

  3. C.

    200

  4. D.

    150

Answer

D

Explanation

Ragini supporters supporting B = 250−50=200250 - 50 = 200. Ragini supporting both A and B = 90−40=5090 - 40 = 50. So, Ragini supporting B but not A = 200−50=150200 - 50 = 150.

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