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CAT 2025 Lesson : DILR: Mar '25 to Apr '25 - Venn vs Table - 13 Mar 2025
Details for Questions 1 to 4 are provided 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.
1) Among the students surveyed who supported proposal A, what percentage preferred Sunita for student union president?
Answer:
2) What percentage of the students surveyed who did not support proposal A preferred Ragini as student union president?
Answer:
3) What percentage of the students surveyed who supported both proposals A and B preferred Sunita as student union president?
(1) 25
(2) 20
(3) 50
(4) 40
4) How many of the students surveyed supported proposal B, did not support proposal A and preferred Ragini as student union president?
(1) 40
(2) 150
(3) 210
(4) 200
Details for Questions 5 to 9 are provided below
A speciality supermarket sells 320 products. Each of these products was either a cosmetic product or a nutrition product. Each of these products was also either a foreign product or a domestic product. Each of these products had at least one of the two approvals – FDA or EU.
The following facts are also known:
1. There were equal numbers of domestic and foreign products.
2. Half of the domestic products were FDA approved cosmetic products.
3. None of the foreign products had both the approvals, while 60 domestic products had both the approvals.
4. There were 140 nutrition products, half of them were foreign products.
5. There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products.
5) How many foreign products were FDA approved cosmetic products?
Answer:
6) How many cosmetic products did not have FDA approval?
(1) 10
(2) 60
(3) 50
(4) Cannot be determined
7) Which among the following options best represents the number of domestic cosmetic products that had both the approvals?
(1) At least 10 and at most 80
(2) At least 20 and at most 70
(3) At least 10 and at most 60
(4) At least 20 and at most 50
8) If 70 cosmetic products did not have EU approval, then how many nutrition products had both the approvals?
(1) 50
(2) 30
(3) 10
(4) 20
9) If 50 nutrition products did not have EU approval, then how many domestic cosmetic products did not have EU approval?
Answer:
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.
1) Among the students surveyed who supported proposal A, what percentage preferred Sunita for student union president?
Answer:
2) What percentage of the students surveyed who did not support proposal A preferred Ragini as student union president?
Answer:
3) What percentage of the students surveyed who supported both proposals A and B preferred Sunita as student union president?
(1) 25
(2) 20
(3) 50
(4) 40
4) How many of the students surveyed supported proposal B, did not support proposal A and preferred Ragini as student union president?
(1) 40
(2) 150
(3) 210
(4) 200
Details for Questions 5 to 9 are provided below
A speciality supermarket sells 320 products. Each of these products was either a cosmetic product or a nutrition product. Each of these products was also either a foreign product or a domestic product. Each of these products had at least one of the two approvals – FDA or EU.
The following facts are also known:
1. There were equal numbers of domestic and foreign products.
2. Half of the domestic products were FDA approved cosmetic products.
3. None of the foreign products had both the approvals, while 60 domestic products had both the approvals.
4. There were 140 nutrition products, half of them were foreign products.
5. There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products.
5) How many foreign products were FDA approved cosmetic products?
Answer:
6) How many cosmetic products did not have FDA approval?
(1) 10
(2) 60
(3) 50
(4) Cannot be determined
7) Which among the following options best represents the number of domestic cosmetic products that had both the approvals?
(1) At least 10 and at most 80
(2) At least 20 and at most 70
(3) At least 10 and at most 60
(4) At least 20 and at most 50
8) If 70 cosmetic products did not have EU approval, then how many nutrition products had both the approvals?
(1) 50
(2) 30
(3) 10
(4) 20
9) If 50 nutrition products did not have EU approval, then how many domestic cosmetic products did not have EU approval?
Answer:
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