CAT 2019 - Slot 2 - Logical Reasoning and Data Interpretation - Students in a college are discussing two proposals
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.
Q. 1:: Among the students surveyed who supported proposal A, what percentage preferred Sunita for student union president?
Q. 2: What percentage of the students surveyed who did not support proposal A preferred Ragini as student union president?
Q. 3: What percentage of the students surveyed who supported both proposals A and B preferred Sunita as student union president?
1. 25
2. 40
3. 20
4. 50
Q. 4: How many of the students surveyed supported proposal B, did not support proposal A and preferred Ragini as student union president?
1.150
2. 40
3. 200
4. 210
1. 64
2. 84
3. Option 4
4. Option 1
As per question it is clear that a student can not prefer both Ragini and Sunita simultaneously. So on the basis of information given , table can be formed as given below:
Now from point 2 it is clear that 200 students preferred Sunita so no of students who preferred Ragini = 500 – 200 = 300
No of students who preferred Sunita and supported proposal A = 80% of 200 = 160
From point 3) , no of students who preferred Ragini and supported proposal A = 30% of 300 = 90
From point 4) No of students who preferred Sunita and supported proposal B = 20% of 250 = 50
From point 6) No of students who preferred Sunita and supported proposal A and B both = 50
From point 7) no of students who preferred Ragini and didn’t supported any proposal = 20% of 300 = 60
Now the complete table can be formed as given below:
No of surveyed who supported proposal A, percentage of students who Preferred Sunita for student union president = 160/250 *100 = 64%
No of the students surveyed who did not support proposal A Preferred Ragini as student union president = 300 – 90 = 210
Required percentage = 210/250*100 = 84%
No of students who supported both proposals = 100
No of the students surveyed who supported both proposals A and B and Preferred Sunita as student union president = 50
Thus required % tage = 50/100 *100 = 50 %
No of the students surveyed supported proposal B, did not support proposal A and preferred Ragini as student union president = no of students who supported proposal B and preferred Ragini – no of students who supported proposal A and B and preferred Ragini = 200 – 50 = 150
Now all the question can be answered.
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