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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:
  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.
Q. Which among the following options best represents the number of domestic cosmetic products that had both the approvals?
  • a)
    At least 10 and at most 80
  • b)
    At least 20 and at most 70
  • c)
    At least 20 and at most 50
  • d)
    At least 10 and at most 60
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A speciality supermarket sells 320 products. Each of these products wa...
To solve this problem, we can use a Venn diagram to represent the relationships between the different categories of products.

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

We know that the total number of products is 320, so C + N = 320.

We also know that each product is either cosmetic or nutrition, so C + N = 320.

Similarly, each product is either foreign or domestic, so F + D = 320.

Finally, each product has at least one of the two approvals, so the total number of products is the sum of products with either approval (C + N) minus the products with both approvals. Since we don't have any information about the overlap between these two categories, we'll assume it to be zero.

So, the total number of products is C + N = 320.

Using the above equations, we can solve for C and N:

C + N = 320
C + N = 320

Subtracting the second equation from the first equation, we get:

0 = 0

This means that the value of C and N can be anything as long as their sum is 320.

Therefore, there is not enough information given in the problem to determine the specific values of C, N, F, and D.
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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 70 cosmetic products did not have EU approval, then how many nutrition products had both the approvals?

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?

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?

Read the passage carefully and answer the following questions:Around 2700 years ago, the Greek poet Archilochus wrote: “the fox knows many things; the hedgehog one big thing.” In the 1950s, philosopher Isaiah Berlin used that sentence as the basis of his essay “The Hedgehog and the Fox.” In it, Berlin divides great thinkers into two categories: hedgehogs, who have one perspective on the world, and foxes, who have many different viewpoints. Although Berlin later claimed the essay was not intended to be serious, it has become a foundational part of thinking about the distinction between specialists and generalists.A generalist is a person who is a competent jack of all trades, with lots of divergent useful skills and capabilities. Specialist, on the other hand, is someone with distinct knowledge and skills related to a single area. The generalist and the specialist are on the same continuum; there are degrees of specialization in a subject. There’s a difference between someone who specializes in teaching history and someone who specializes in teaching the history of the American Civil war, for example. Likewise, there is a spectrum for how generalized or specialized a certain skill is. Some skills — like the ability to focus, to read critically, or to make rational decisions — are of universal value. Others are a little more specialized but can be used in many different careers. Examples of these skills would be design, project management, and fluency in a foreign language.Generalists have the advantage of interdisciplinary knowledge, which fosters creativity and a firmer understanding of how the world works. They have a better overall perspective and can generally perform second-order thinking in a wider range of situations than the specialist can. Generalists often possess transferable skills, allowing them to be flexible with their career choices and adapt to a changing world. Managers and leaders are often generalists because they need a comprehensive perspective of their entire organization. And an increasing number of companies are choosing to have a core group of generalists on staff, and hire freelance specialists only when necessary. The métiers at the lowest risk of automation in the future tend to be those which require a diverse, nuanced skill set.When their particular skills are in demand, specialists experience substantial upsides. The scarcity of their expertise means higher salaries, less competition, and more leverage. The downside is that specialists are vulnerable to change. Many specialist jobs are disappearing as technology changes. Stockbrokers, for example, face the possibility of replacement by AI in coming years. That doesn’t mean no one will hold those jobs, but demand will decrease. Many people will need to learn new work skills, and starting over in a new field will put them back decades. That’s a serious knock, both psychologically and financially.What’s the safest option, the middle ground? By many accounts, it’s being a specialist in one area, while retaining a few general iterative skills-a generalizing specialist. Many great thinkers are (or wer e) generalizing specialists. Shakespeare, Da Vinci, Kepler, and Boyd excelled by branching out from their core competencies. These men knew how to learn fast, picking up the key ideas and then returning to their specialties. Unlike their forgotten peers, they didn’t continue studying one area past the point of diminishing returns; they got back to work — and the results were extraordinary.Q.Which of the following statements CANNOT be inferred from the passage?

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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?a)At least 10 and at most 80b)At least 20 and at most 70c)At least 20 and at most 50d)At least 10 and at most 60Correct answer is option 'D'. 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.Which among the following options best represents the number of domestic cosmetic products that had both the approvals?a)At least 10 and at most 80b)At least 20 and at most 70c)At least 20 and at most 50d)At least 10 and at most 60Correct answer is option 'D'. 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.Which among the following options best represents the number of domestic cosmetic products that had both the approvals?a)At least 10 and at most 80b)At least 20 and at most 70c)At least 20 and at most 50d)At least 10 and at most 60Correct answer is option 'D'. 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.Which among the following options best represents the number of domestic cosmetic products that had both the approvals?a)At least 10 and at most 80b)At least 20 and at most 70c)At least 20 and at most 50d)At least 10 and at most 60Correct answer is option 'D'. Can you explain this answer?.
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