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While multiplying three real numbers, Ashok took one of the numbers as 73 instead of 37. As a result, the product went up by 720. Then the minimum possible value of the sum of squares of the other two numbers is
[2018]
  • a)
    40
  • b)
    20
  • c)
    30
  • d)
    10
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
While multiplying three real numbers, Ashok took one of the numbers as...
Let the other two numbers be y and z.
73yz – 37yz = 720
yz = 20
Minimum possible sum of the squares of the other two numbers would occur when y = z
If y = z, then y2 = 20 = z2
Hence, y2 + z2 = 40
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Most Upvoted Answer
While multiplying three real numbers, Ashok took one of the numbers as...
To solve this problem, let's assume the three real numbers to be a, b, and c.

Let's first write down the given information:
1. The original product of the three numbers is abc.
2. Ashok took one of the numbers as 73 instead of 37, so the new product is (73bc) = 720 + abc.

Now, let's find the original product of the three numbers:
Original product = abc

And the new product after Ashok's mistake:
New product = (73bc) = 720 + abc

We can subtract the original product from the new product to get the increase in the product:
Increase in product = (73bc) - abc = 720

Simplifying the equation, we get:
72bc = 720

Dividing both sides by 72, we get:
bc = 10

Now, we need to find the minimum possible value of the sum of squares of the other two numbers, which is a^2 + b^2.

To minimize the sum of squares, we need to minimize the individual squares.

Since the product bc is a constant value of 10, to minimize the value of b^2, we need to minimize the value of b. Similarly, to minimize the value of a^2, we need to minimize the value of a.

The smallest possible value for b is 1, and the smallest possible value for c is 10 (since the product bc = 10).

Substituting these values in the equation, we get:
a^2 + b^2 = a^2 + 1

Since we want to minimize the sum of squares, we need to minimize the value of a. The smallest possible value for a is 0.

Substituting a = 0 in the equation, we get:
a^2 + b^2 = 0 + 1 = 1

Therefore, the minimum possible value of the sum of squares of the other two numbers is 1.

But we need to find the minimum possible value of a^2 + b^2, not a^2 + b^2 + c^2.

Since we know that c = 10, we can substitute the value of c in the equation:
a^2 + b^2 + c^2 = 1 + 10^2 = 101

Therefore, the minimum possible value of a^2 + b^2 is 1.

Hence, the correct answer is option A) 40.
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Directions: Read the following information carefully and answer the given question.A minimum viable product (MVP) is a development technique in which a new product or website is developed with sufficient features to satisfy early adopters. The final, complete set of features is only designed and developed after considering feedback from the product's initial users. This technique helps them in making the final product much better. With the help of MVP concept, the research or the marketing team will come to know where the product is lacking and or what are its strengths or weaknesses.MVP has three distinct features. One is that it will have enough features for consumers to purchase the product (it becomes easier for the company to market it), the other is that it will have some sort of a feedback mechanism wherein users would be able to send their feedback about the product. And, lastly it should have enough future benefits for consumers who choose to adopt the product first (Google gave free upgrade of its OS to all Nexus users). The idea is to get feedback from the consumers which will in turn help in making the desired changes in the final product. MVP actually tests the usage scenario that is much more helpful for the company to make changes to the final product.The developing team of an MVP will not waste any time on anything beyond the bare minimum, and build every other feature over time as they assess the customers' wishes and preferences as they start using the product. The product may change even dramatically or even get abandoned as feedback from users may significantly diverge from the original project. However, the developing teams will not waste any resources (efforts, time, money, advertising) on a product that no one really wants, needs, or likes. The catch to this development technique is that it assumes that early adopters can see the vision or promise of the final product and provide the valuable feedback needed to guide developers forward.The whole focus is learning during product development by collecting information from customers that are validated already. Observing users as they utilize the product is much more reliable than trying to validate marketing hypotheses with questionnaires or forecasts. A common pitfall is to release a bare-bone product that is so much below the users' expectations that is not viable at all. In general, the MVP technique is particularly viable for technically-oriented products used by technical users who are often keen on providing practical insights on how to improve or update the product. The concept of MVP has, in fact, been widely adopted by many verticals in the informatics industry. For example, many video games today spend many months (sometimes years) as early access products and are slowly developed as the community grows. Some popular franchises, such as Farmville, fully leveraged the concept of MVP by implementing new gameplay features over time while progressively improving overall user experience.Q. Which of the following statements is the author most likely to disagree about?

Directions: Read the following information carefully and answer the given question.A minimum viable product (MVP) is a development technique in which a new product or website is developed with sufficient features to satisfy early adopters. The final, complete set of features is only designed and developed after considering feedback from the product's initial users. This technique helps them in making the final product much better. With the help of MVP concept, the research or the marketing team will come to know where the product is lacking and or what are its strengths or weaknesses.MVP has three distinct features. One is that it will have enough features for consumers to purchase the product (it becomes easier for the company to market it), the other is that it will have some sort of a feedback mechanism wherein users would be able to send their feedback about the product. And, lastly it should have enough future benefits for consumers who choose to adopt the product first (Google gave free upgrade of its OS to all Nexus users). The idea is to get feedback from the consumers which will in turn help in making the desired changes in the final product. MVP actually tests the usage scenario that is much more helpful for the company to make changes to the final product.The developing team of an MVP will not waste any time on anything beyond the bare minimum, and build every other feature over time as they assess the customers' wishes and preferences as they start using the product. The product may change even dramatically or even get abandoned as feedback from users may significantly diverge from the original project. However, the developing teams will not waste any resources (efforts, time, money, advertising) on a product that no one really wants, needs, or likes. The catch to this development technique is that it assumes that early adopters can see the vision or promise of the final product and provide the valuable feedback needed to guide developers forward.The whole focus is learning during product development by collecting information from customers that are validated already. Observing users as they utilize the product is much more reliable than trying to validate marketing hypotheses with questionnaires or forecasts. A common pitfall is to release a bare-bone product that is so much below the users' expectations that is not viable at all. In general, the MVP technique is particularly viable for technically-oriented products used by technical users who are often keen on providing practical insights on how to improve or update the product. The concept of MVP has, in fact, been widely adopted by many verticals in the informatics industry. For example, many video games today spend many months (sometimes years) as early access products and are slowly developed as the community grows. Some popular franchises, such as Farmville, fully leveraged the concept of MVP by implementing new gameplay features over time while progressively improving overall user experience.Q. Which of the following statements is true in context of the passage?

Directions: Read the following information carefully and answer the given question.A minimum viable product (MVP) is a development technique in which a new product or website is developed with sufficient features to satisfy early adopters. The final, complete set of features is only designed and developed after considering feedback from the product's initial users. This technique helps them in making the final product much better. With the help of MVP concept, the research or the marketing team will come to know where the product is lacking and or what are its strengths or weaknesses.MVP has three distinct features. One is that it will have enough features for consumers to purchase the product (it becomes easier for the company to market it), the other is that it will have some sort of a feedback mechanism wherein users would be able to send their feedback about the product. And, lastly it should have enough future benefits for consumers who choose to adopt the product first (Google gave free upgrade of its OS to all Nexus users). The idea is to get feedback from the consumers which will in turn help in making the desired changes in the final product. MVP actually tests the usage scenario that is much more helpful for the company to make changes to the final product.The developing team of an MVP will not waste any time on anything beyond the bare minimum, and build every other feature over time as they assess the customers' wishes and preferences as they start using the product. The product may change even dramatically or even get abandoned as feedback from users may significantly diverge from the original project. However, the developing teams will not waste any resources (efforts, time, money, advertising) on a product that no one really wants, needs, or likes. The catch to this development technique is that it assumes that early adopters can see the vision or promise of the final product and provide the valuable feedback needed to guide developers forward.The whole focus is learning during product development by collecting information from customers that are validated already. Observing users as they utilize the product is much more reliable than trying to validate marketing hypotheses with questionnaires or forecasts. A common pitfall is to release a bare-bone product that is so much below the users' expectations that is not viable at all. In general, the MVP technique is particularly viable for technically-oriented products used by technical users who are often keen on providing practical insights on how to improve or update the product. The concept of MVP has, in fact, been widely adopted by many verticals in the informatics industry. For example, many video games today spend many months (sometimes years) as early access products and are slowly developed as the community grows. Some popular franchises, such as Farmville, fully leveraged the concept of MVP by implementing new gameplay features over time while progressively improving overall user experience.Q. Which of the following limitations, if true, would hinder the proper adoption of a minimum viable product?

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While multiplying three real numbers, Ashok took one of the numbers as 73 instead of 37. As a result, the product went up by 720. Then the minimum possible value of the sum of squares of the other two numbers is[2018]a)40b)20c)30d)10Correct answer is option 'A'. Can you explain this answer?
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