CAT Exam > CAT Questions > A speciality supermarket sells 320 products. ...
Start Learning for Free
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:
The following facts are also known:
- There were equal numbers of domestic and foreign products.
- Half of the domestic products were FDA approved cosmetic products.
- None of the foreign products had both the approvals, while 60 domestic products had both the approvals.
- There were 140 nutrition products, half of them were foreign products.
- There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products.
Q. If 50 nutrition products did not have EU approval, then how many domestic cosmetic products did not have EU approval?
Correct answer is '50'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
A speciality supermarket sells 320 products. Each of these products wa...
, FDA (Food and Drug Administration) approval or CE (Conformité Européene) approval.
Let's represent the four categories of products as follows:
C = Cosmetic products
N = Nutrition products
F = Foreign products
D = Domestic products
We know that:
- The total number of products is 320, so C + N = 320.
- Each product is either a cosmetic or a nutrition product, so C + N = 320 is a complete partition of the set of 320 products.
- Each product is either a foreign or a domestic product, so F + D = 320 is also a complete partition of the set of 320 products.
- Each product has at least one of the two approvals, FDA or CE, so we can represent this as the union of the two sets:
FDA ∪ CE = C + N + F + D = 320
We want to find out how many products have both FDA and CE approvals.
We can start by applying the inclusion-exclusion principle:
|FDA ∪ CE| = |FDA| + |CE| - |FDA ∩ CE|
We don't know |FDA| or |CE|, but we do know that every product has at least one of the two approvals, so:
|FDA ∪ CE| = 320
We also know that each product has at least one approval, so:
|FDA ∩ CE| ≥ 0
Putting it all together, we get:
320 = |FDA| + |CE| - |FDA ∩ CE|
|FDA ∩ CE| ≤ |FDA|, and ≤ |CE|
|FDA ∩ CE| ≥ 0
We want to find |FDA ∩ CE|, so we need to find a way to express |FDA| and |CE| in terms of the information we have. We can do this by using the fact that every product has at least one approval.
Let's define:
FC = Products that are foreign and have FDA approval
NC = Products that are domestic and have FDA approval
FE = Products that are foreign and have CE approval
NE = Products that are domestic and have CE approval
We know that every product has at least one approval, so:
C = FC ∪ NC ∪ FE ∪ NE
F = FC ∪ FE
D = NC ∪ NE
We can use these relationships to express |FDA| and |CE| in terms of FC, NC, FE, and NE:
|FDA| = |FC| + |NC|
|CE| = |FE| + |NE|
Now we can use the inclusion-exclusion principle to find |FDA ∩ CE|:
320 = |FDA| + |CE| - |FDA ∩ CE|
320 = |FC| + |NC| + |FE| + |NE| - |FDA ∩ CE|
We don't know |FDA ∩ CE|, but we can find an upper bound for it using the fact that each product has at least one approval:
|FDA ∩ CE| ≤ min(|FDA|, |CE|) = min(|FC| + |NC|, |FE| + |NE|)
We can also find a lower bound for |FDA ∩ CE| using the fact that each product has at least one approval:
|FDA ∩ CE| ≥ max(0, 320 - |FC| -
Let's represent the four categories of products as follows:
C = Cosmetic products
N = Nutrition products
F = Foreign products
D = Domestic products
We know that:
- The total number of products is 320, so C + N = 320.
- Each product is either a cosmetic or a nutrition product, so C + N = 320 is a complete partition of the set of 320 products.
- Each product is either a foreign or a domestic product, so F + D = 320 is also a complete partition of the set of 320 products.
- Each product has at least one of the two approvals, FDA or CE, so we can represent this as the union of the two sets:
FDA ∪ CE = C + N + F + D = 320
We want to find out how many products have both FDA and CE approvals.
We can start by applying the inclusion-exclusion principle:
|FDA ∪ CE| = |FDA| + |CE| - |FDA ∩ CE|
We don't know |FDA| or |CE|, but we do know that every product has at least one of the two approvals, so:
|FDA ∪ CE| = 320
We also know that each product has at least one approval, so:
|FDA ∩ CE| ≥ 0
Putting it all together, we get:
320 = |FDA| + |CE| - |FDA ∩ CE|
|FDA ∩ CE| ≤ |FDA|, and ≤ |CE|
|FDA ∩ CE| ≥ 0
We want to find |FDA ∩ CE|, so we need to find a way to express |FDA| and |CE| in terms of the information we have. We can do this by using the fact that every product has at least one approval.
Let's define:
FC = Products that are foreign and have FDA approval
NC = Products that are domestic and have FDA approval
FE = Products that are foreign and have CE approval
NE = Products that are domestic and have CE approval
We know that every product has at least one approval, so:
C = FC ∪ NC ∪ FE ∪ NE
F = FC ∪ FE
D = NC ∪ NE
We can use these relationships to express |FDA| and |CE| in terms of FC, NC, FE, and NE:
|FDA| = |FC| + |NC|
|CE| = |FE| + |NE|
Now we can use the inclusion-exclusion principle to find |FDA ∩ CE|:
320 = |FDA| + |CE| - |FDA ∩ CE|
320 = |FC| + |NC| + |FE| + |NE| - |FDA ∩ CE|
We don't know |FDA ∩ CE|, but we can find an upper bound for it using the fact that each product has at least one approval:
|FDA ∩ CE| ≤ min(|FDA|, |CE|) = min(|FC| + |NC|, |FE| + |NE|)
We can also find a lower bound for |FDA ∩ CE| using the fact that each product has at least one approval:
|FDA ∩ CE| ≥ max(0, 320 - |FC| -
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
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: There were equal numbers of domestic and foreign products. Half of the domestic products were FDA approved cosmetic products. None of the foreign products had both the approvals, while 60 domestic products had both the approvals. There were 140 nutrition products, half of them were foreign products. There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products.Q.If 50 nutrition products did not have EU approval, then how many domestic cosmetic products did not have EU approval?Correct answer is '50'. Can you explain this answer?
Question Description
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: There were equal numbers of domestic and foreign products. Half of the domestic products were FDA approved cosmetic products. None of the foreign products had both the approvals, while 60 domestic products had both the approvals. There were 140 nutrition products, half of them were foreign products. There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products.Q.If 50 nutrition products did not have EU approval, then how many domestic cosmetic products did not have EU approval?Correct answer is '50'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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: There were equal numbers of domestic and foreign products. Half of the domestic products were FDA approved cosmetic products. None of the foreign products had both the approvals, while 60 domestic products had both the approvals. There were 140 nutrition products, half of them were foreign products. There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products.Q.If 50 nutrition products did not have EU approval, then how many domestic cosmetic products did not have EU approval?Correct answer is '50'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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: There were equal numbers of domestic and foreign products. Half of the domestic products were FDA approved cosmetic products. None of the foreign products had both the approvals, while 60 domestic products had both the approvals. There were 140 nutrition products, half of them were foreign products. There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products.Q.If 50 nutrition products did not have EU approval, then how many domestic cosmetic products did not have EU approval?Correct answer is '50'. Can you explain this answer?.
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: There were equal numbers of domestic and foreign products. Half of the domestic products were FDA approved cosmetic products. None of the foreign products had both the approvals, while 60 domestic products had both the approvals. There were 140 nutrition products, half of them were foreign products. There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products.Q.If 50 nutrition products did not have EU approval, then how many domestic cosmetic products did not have EU approval?Correct answer is '50'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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: There were equal numbers of domestic and foreign products. Half of the domestic products were FDA approved cosmetic products. None of the foreign products had both the approvals, while 60 domestic products had both the approvals. There were 140 nutrition products, half of them were foreign products. There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products.Q.If 50 nutrition products did not have EU approval, then how many domestic cosmetic products did not have EU approval?Correct answer is '50'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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: There were equal numbers of domestic and foreign products. Half of the domestic products were FDA approved cosmetic products. None of the foreign products had both the approvals, while 60 domestic products had both the approvals. There were 140 nutrition products, half of them were foreign products. There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products.Q.If 50 nutrition products did not have EU approval, then how many domestic cosmetic products did not have EU approval?Correct answer is '50'. Can you explain this answer?.
Solutions for 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: There were equal numbers of domestic and foreign products. Half of the domestic products were FDA approved cosmetic products. None of the foreign products had both the approvals, while 60 domestic products had both the approvals. There were 140 nutrition products, half of them were foreign products. There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products.Q.If 50 nutrition products did not have EU approval, then how many domestic cosmetic products did not have EU approval?Correct answer is '50'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of 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: There were equal numbers of domestic and foreign products. Half of the domestic products were FDA approved cosmetic products. None of the foreign products had both the approvals, while 60 domestic products had both the approvals. There were 140 nutrition products, half of them were foreign products. There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products.Q.If 50 nutrition products did not have EU approval, then how many domestic cosmetic products did not have EU approval?Correct answer is '50'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
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: There were equal numbers of domestic and foreign products. Half of the domestic products were FDA approved cosmetic products. None of the foreign products had both the approvals, while 60 domestic products had both the approvals. There were 140 nutrition products, half of them were foreign products. There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products.Q.If 50 nutrition products did not have EU approval, then how many domestic cosmetic products did not have EU approval?Correct answer is '50'. Can you explain this answer?, a detailed solution for 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: There were equal numbers of domestic and foreign products. Half of the domestic products were FDA approved cosmetic products. None of the foreign products had both the approvals, while 60 domestic products had both the approvals. There were 140 nutrition products, half of them were foreign products. There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products.Q.If 50 nutrition products did not have EU approval, then how many domestic cosmetic products did not have EU approval?Correct answer is '50'. Can you explain this answer? has been provided alongside types of 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: There were equal numbers of domestic and foreign products. Half of the domestic products were FDA approved cosmetic products. None of the foreign products had both the approvals, while 60 domestic products had both the approvals. There were 140 nutrition products, half of them were foreign products. There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products.Q.If 50 nutrition products did not have EU approval, then how many domestic cosmetic products did not have EU approval?Correct answer is '50'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice 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: There were equal numbers of domestic and foreign products. Half of the domestic products were FDA approved cosmetic products. None of the foreign products had both the approvals, while 60 domestic products had both the approvals. There were 140 nutrition products, half of them were foreign products. There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products.Q.If 50 nutrition products did not have EU approval, then how many domestic cosmetic products did not have EU approval?Correct answer is '50'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup