CAT 2019 LRDI Questions with Answers 11

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

Show Answer
ANSWER: 64

Question 2:
What percentage of the students surveyed who did not support proposal A preferred Ragini as student union president?

Show Answer
ANSWER: 84

Question 3:
What percentage of the students surveyed who supported both proposals A and B preferred Sunita as student union president?

  1. 50
  2. 40
  3. 20
  4. 25
Show Answer
OPTION: 1

Question 4:
How many of the students surveyed supported proposal B, did not support proposal A and preferred Ragini as student union president?

  1. 200
  2. 150
  3. 210
  4. 40
Show Answer
OPTION: 2

The set of students who like Sunita and Ragini are disjoint sets.

Hence, the Venn diagram can be drawn as follows

There are 500 students in all.

From statement (2)

Sunita = 200. Hence, Ragini = 300.

From statement (1) A (Sunita) + A (Ragini) = 250 and B (Sunita) + B (Ragini) = 250.

From (2), A (Sunita) = 160. Hence, A (Ragini) = 90.

From (4), B (Sunita) = 20 % of 250 = 50. Hence, B (Ragini) = 200.

From (6), g (Sunita) = 50 and hence, b (Sunita) = 0 and a (Sunita) = 110. Hence, n (Sunita) = 40.

From (7), n (Ragini) = 60

It is given that 250 support B, hence the other 250 do not support B.

From (5), (a + n) of Ragini = 40 % of 250 = 100. Hence, a (Ragini) = 40.

Thus, the final solution is as follows.

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