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 andndash; 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.How many foreign products were FDA approved cosmetic products?Correct answer is '40'. Can you explain this answer?

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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. How many foreign products were FDA approved cosmetic products?

Correct answer is '40'. Can you explain this answer?

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CAT 2022 Slot 2: Past Year Question Paper

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A speciality supermarket sells 320 products. Each of these products wa...

(organic or vegan).

Let's define the following variables:

- C = number of cosmetic products
- N = number of nutrition products
- F = number of foreign products
- D = number of domestic products
- O = number of organic products
- V = number of vegan products

From the problem statement, we know that:

- C + N = 320 (since there are 320 products in total)
- C + F = O + F (since each product has at least one of the two approvals)
- N + D = V + D (same reasoning as above)

We can simplify the last two equations to:

- C = O - V
- N = V - F

Now we have three equations and six variables, which means we need to use more information to solve the problem. One possible approach is to use the fact that each variable is non-negative (since we're counting products).

Let's start with O and V. We know that each product has at least one of the two approvals, so:

- O + V - (C + N) >= 0

Substituting C and N from the earlier equations, we get:

- O + V - 320 >= 0
- O + V >= 320

Since O and V are non-negative, their sum must be at least 320.

Next, let's look at F and D. We know that there are no products that are both foreign and domestic, so:

- F + D <= 320="">

Now we can use the equation N = V - F to eliminate F:

- N + D <= 320="" +="" v="">
- N + D - V <= 320="">

Since N, D, and V are non-negative, their sum must be at most 320.

Finally, let's use the equation C = O - V to eliminate V:

- C + N = 320
- C + N - O <= v="">
- (O - V) + N - O <= v="">
- C - O + N <= 0="">

Since C, O, and N are non-negative, their sum must be at least 0.

Putting everything together, we have the following system of inequalities:

- O + V >= 320
- N + D - V <= 320="">
- C - O + N <= 0="">
- C, N, F, D, O, V >= 0

We want to find the maximum possible value of V, since that corresponds to the maximum number of products with the vegan approval. We can rewrite the second inequality as:

- V <= n="" +="" d="" -="" 320="">

Now we can substitute C = O - V and N = V - F to get:

- O - V + V - F = 320 - D
- O - F = 320 - D

This tells us that the difference between the number of organic products and the number of foreign products is equal to the complement of the number of domestic products (i.e., the number of non-domestic products). Since we want to maximize V, we want to minimize F. The smallest possible value of F is 0 (since it's non-negative), which gives us:

- O = 320 - D
- V <= n="" +="" d="" -="" 320="">
- C = O - V =

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A speciality supermarket sells 320 products. Each of these products wa...

I think the correct answer is 40

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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?

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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.How many cosmetic products did not have FDA approval?

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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.Which among the following options best represents the number of domestic cosmetic products that had both the approvals?

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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.How many foreign products were FDA approved cosmetic products?Correct answer is '40'. Can you explain this answer?

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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.How many foreign products were FDA approved cosmetic products?Correct answer is '40'. 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.How many foreign products were FDA approved cosmetic products?Correct answer is '40'. 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.How many foreign products were FDA approved cosmetic products?Correct answer is '40'. Can you explain this answer?.

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