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CAT 2019 Slot 2 — DILR Question 26

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Passage / Data

Answer the following questions based on the information given below.

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.

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

Answer & solution

Answer: 64

Solution
  Sunita Ragini
Only proposal A k p
Only proposal B l q
Both A and B m r
Neither A nor B n s

From (1), k + m + p + r = 250 and l + m + q + r = 250

From (4), l + m = 0.2 × 250 = 50

From (6), l = 0 ⇒ m = 50

∴ q + r = 200

From (2), k + l + m + n = 200 and hence p + q + r + s = 300

From (3), p + r = 0.3 × 300 = 90 ⇒ k + m = 160

As l = 0 and k + l + m + n = 200, n = 40

∴ k = 110

From (7), n + s = 100 ⇒ s = 60

∴ p + q + r = 240 and p + r = 90 ⇒ q = 150

∴ q + r = 200 ⇒ r = 50 and hence p = 40

Thus, we have

  Sunita Ragini
Only proposal A 110 40
Only proposal B 0 150
Both A and B 50 50
Neither A nor B 40 60

Among 250 students who supported proposal A, 110 + 50 = 160 students preferred Sunita for student union president which is equivalent to 64%.

Answer: 64.

CAT 2019 Slot 2 DILR Q26: Among the students surveyed who supported proposal A, what percentage preferred Sunita for student union presi — Solution | TheCATExam