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An Egyptian fraction has a numerator equal to 1 and it's denominator is a positive integer. What is the maximum number of different Egyptian fractions such that their sum is equal to 1 and their denominators are equal to 10 or less?
a) 3
b) 5
c) 7
d) 9
Correct answer is a. Please explain how?
a) 3
b) 5
c) 7
d) 9
Correct answer is a. Please explain how?
Most Upvoted Answer
An Egyptian fraction has a numerator equal to 1 and it's denominator i...
Solution:
Let's start by understanding what an Egyptian fraction is. An Egyptian fraction is a fraction where the numerator is always 1 and the denominator is a positive integer. The sum of multiple Egyptian fractions can be equal to 1.
To find the maximum number of different Egyptian fractions with denominators equal to 10 or less that sum up to 1, we need to find a combination that satisfies this condition.
1. Fractions with Denominators 2, 3, 4, 5, 6, 7, 8, 9, and 10:
Let's consider the Egyptian fractions with denominators 2, 3, 4, 5, 6, 7, 8, 9, and 10. We need to find a combination of these fractions that sum up to 1.
2. Fractions with Denominators 2 and 3:
We start by considering the fraction with a denominator of 2, which is 1/2. Now, we subtract this fraction from 1, which gives us 1/2. We can see that we still need to find fractions that sum up to 1/2.
Next, we consider the fraction with a denominator of 3, which is 1/3. We subtract this fraction from 1/2, which gives us 1/6. Now, we still need to find fractions that sum up to 1/6.
3. Fractions with Denominators 4 and 5:
Continuing the process, we consider the fraction with a denominator of 4, which is 1/4. We subtract this fraction from 1/6, which gives us 1/12. Now, we still need to find fractions that sum up to 1/12.
Next, we consider the fraction with a denominator of 5, which is 1/5. We subtract this fraction from 1/12, which gives us 1/60. Now, we still need to find fractions that sum up to 1/60.
4. Fractions with Denominators 6, 7, 8, 9, and 10:
Continuing the process further, we consider the fraction with a denominator of 6, which is 1/6. We subtract this fraction from 1/60, which gives us 1/360. Now, we still need to find fractions that sum up to 1/360.
Next, we consider the fraction with a denominator of 7, which is 1/7. We subtract this fraction from 1/360, which gives us 1/2520. Now, we still need to find fractions that sum up to 1/2520.
We continue this process with denominators 8, 9, and 10. However, we can see that the fractions become very small and the sum of fractions with larger denominators will be even smaller. Since the denominators are limited to 10 or less, it is not possible to find additional fractions that sum up to 1.
5. Final Combination:
Therefore, the maximum number of different Egyptian fractions such that their sum is equal to 1 and their denominators are equal to 10 or less is 3. These fractions are
Let's start by understanding what an Egyptian fraction is. An Egyptian fraction is a fraction where the numerator is always 1 and the denominator is a positive integer. The sum of multiple Egyptian fractions can be equal to 1.
To find the maximum number of different Egyptian fractions with denominators equal to 10 or less that sum up to 1, we need to find a combination that satisfies this condition.
1. Fractions with Denominators 2, 3, 4, 5, 6, 7, 8, 9, and 10:
Let's consider the Egyptian fractions with denominators 2, 3, 4, 5, 6, 7, 8, 9, and 10. We need to find a combination of these fractions that sum up to 1.
2. Fractions with Denominators 2 and 3:
We start by considering the fraction with a denominator of 2, which is 1/2. Now, we subtract this fraction from 1, which gives us 1/2. We can see that we still need to find fractions that sum up to 1/2.
Next, we consider the fraction with a denominator of 3, which is 1/3. We subtract this fraction from 1/2, which gives us 1/6. Now, we still need to find fractions that sum up to 1/6.
3. Fractions with Denominators 4 and 5:
Continuing the process, we consider the fraction with a denominator of 4, which is 1/4. We subtract this fraction from 1/6, which gives us 1/12. Now, we still need to find fractions that sum up to 1/12.
Next, we consider the fraction with a denominator of 5, which is 1/5. We subtract this fraction from 1/12, which gives us 1/60. Now, we still need to find fractions that sum up to 1/60.
4. Fractions with Denominators 6, 7, 8, 9, and 10:
Continuing the process further, we consider the fraction with a denominator of 6, which is 1/6. We subtract this fraction from 1/60, which gives us 1/360. Now, we still need to find fractions that sum up to 1/360.
Next, we consider the fraction with a denominator of 7, which is 1/7. We subtract this fraction from 1/360, which gives us 1/2520. Now, we still need to find fractions that sum up to 1/2520.
We continue this process with denominators 8, 9, and 10. However, we can see that the fractions become very small and the sum of fractions with larger denominators will be even smaller. Since the denominators are limited to 10 or less, it is not possible to find additional fractions that sum up to 1.
5. Final Combination:
Therefore, the maximum number of different Egyptian fractions such that their sum is equal to 1 and their denominators are equal to 10 or less is 3. These fractions are
Community Answer
An Egyptian fraction has a numerator equal to 1 and it's denominator i...
The answer is A
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An Egyptian fraction has a numerator equal to 1 and it's denominator is a positive integer. What is the maximum number of different Egyptian fractions such that their sum is equal to 1 and their denominators are equal to 10 or less? a) 3b) 5c) 7d) 9Correct answer is a. Please explain how?
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An Egyptian fraction has a numerator equal to 1 and it's denominator is a positive integer. What is the maximum number of different Egyptian fractions such that their sum is equal to 1 and their denominators are equal to 10 or less? a) 3b) 5c) 7d) 9Correct answer is a. Please explain how? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about An Egyptian fraction has a numerator equal to 1 and it's denominator is a positive integer. What is the maximum number of different Egyptian fractions such that their sum is equal to 1 and their denominators are equal to 10 or less? a) 3b) 5c) 7d) 9Correct answer is a. Please explain how? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An Egyptian fraction has a numerator equal to 1 and it's denominator is a positive integer. What is the maximum number of different Egyptian fractions such that their sum is equal to 1 and their denominators are equal to 10 or less? a) 3b) 5c) 7d) 9Correct answer is a. Please explain how?.
An Egyptian fraction has a numerator equal to 1 and it's denominator is a positive integer. What is the maximum number of different Egyptian fractions such that their sum is equal to 1 and their denominators are equal to 10 or less? a) 3b) 5c) 7d) 9Correct answer is a. Please explain how? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about An Egyptian fraction has a numerator equal to 1 and it's denominator is a positive integer. What is the maximum number of different Egyptian fractions such that their sum is equal to 1 and their denominators are equal to 10 or less? a) 3b) 5c) 7d) 9Correct answer is a. Please explain how? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An Egyptian fraction has a numerator equal to 1 and it's denominator is a positive integer. What is the maximum number of different Egyptian fractions such that their sum is equal to 1 and their denominators are equal to 10 or less? a) 3b) 5c) 7d) 9Correct answer is a. Please explain how?.
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An Egyptian fraction has a numerator equal to 1 and it's denominator is a positive integer. What is the maximum number of different Egyptian fractions such that their sum is equal to 1 and their denominators are equal to 10 or less? a) 3b) 5c) 7d) 9Correct answer is a. Please explain how?, a detailed solution for An Egyptian fraction has a numerator equal to 1 and it's denominator is a positive integer. What is the maximum number of different Egyptian fractions such that their sum is equal to 1 and their denominators are equal to 10 or less? a) 3b) 5c) 7d) 9Correct answer is a. Please explain how? has been provided alongside types of An Egyptian fraction has a numerator equal to 1 and it's denominator is a positive integer. What is the maximum number of different Egyptian fractions such that their sum is equal to 1 and their denominators are equal to 10 or less? a) 3b) 5c) 7d) 9Correct answer is a. Please explain how? theory, EduRev gives you an
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