CAT 2019 Slot 2 — DILR Question 28
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.
- 250 students supported proposal A and 250 students supported proposal B.
- Among the 200 students who preferred Sunita as student union president, 80% supported proposal A.
- Among those who preferred Ragini, 30% supported proposal A.
- 20% of those who supported proposal B preferred Sunita.
- 40% of those who did not support proposal B preferred Ragini.
- Every student who preferred Sunita and supported proposal B also supported proposal A.
- Among those who preferred Ragini, 20% did not support any of the proposals.
How many of the students surveyed supported proposal B, did not support proposal A and preferred Ragini as student union president?
Answer & solution
- A
200
- B
40
150
- D
210
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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
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Out of 250 students who supported proposal B, 150 did not support proposal A and preferred Ragini as student union president.
Hence, option (c).