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Sum of two numbers x, y = 1050. What is the maximum value of the HCF between x and y?
- a)350
- b)700
- c)1050
- d)525
- e)900
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Sum of two numbers x, y = 1050. What is the maximum value of the HCF b...
x = 525 and y = 525 works best.
If the question states x, y have to be distinct, then the best solution would be x = 350, y = 700, HCF = 350.
So the HCF is 525.
The question is "What is the maximum value of the HCF between x and y?"
Hence the answer is "525"
If the question states x, y have to be distinct, then the best solution would be x = 350, y = 700, HCF = 350.
So the HCF is 525.
The question is "What is the maximum value of the HCF between x and y?"
Hence the answer is "525"
Most Upvoted Answer
Sum of two numbers x, y = 1050. What is the maximum value of the HCF b...
Solution:
To find the maximum value of the HCF between x and y, we need to find the highest common factor of the two numbers.
Let's assume that x and y have a common factor d, where d is the HCF of x and y. Then we can write:
x = a * d
y = b * d
Where a and b are two integers. Since x + y = 1050, we can substitute the above equations and get:
a * d + b * d = 1050
d * (a + b) = 1050
Since d is a factor of both x and y, it must also be a factor of 1050. Therefore, we need to find the maximum factor of 1050 that can divide both x and y.
The prime factorization of 1050 is:
1050 = 2 * 3 * 5 * 7 * 5
To find the maximum factor of 1050 that can divide x and y, we need to find the highest value of d such that d is a factor of 1050 and a + b = 1050 / d.
Let's start with the highest factor of 1050, which is 1050 itself. If d = 1050, then a + b = 1, which is not possible since a and b are integers. Therefore, we need to try the next highest factor of 1050, which is 525.
If d = 525, then a + b = 2. The only possible values of a and b that satisfy this equation are a = 1 and b = 1. Therefore, the maximum value of the HCF of x and y is:
HCF(x, y) = d = 525
Therefore, the correct answer is option D, 525.
To find the maximum value of the HCF between x and y, we need to find the highest common factor of the two numbers.
Let's assume that x and y have a common factor d, where d is the HCF of x and y. Then we can write:
x = a * d
y = b * d
Where a and b are two integers. Since x + y = 1050, we can substitute the above equations and get:
a * d + b * d = 1050
d * (a + b) = 1050
Since d is a factor of both x and y, it must also be a factor of 1050. Therefore, we need to find the maximum factor of 1050 that can divide both x and y.
The prime factorization of 1050 is:
1050 = 2 * 3 * 5 * 7 * 5
To find the maximum factor of 1050 that can divide x and y, we need to find the highest value of d such that d is a factor of 1050 and a + b = 1050 / d.
Let's start with the highest factor of 1050, which is 1050 itself. If d = 1050, then a + b = 1, which is not possible since a and b are integers. Therefore, we need to try the next highest factor of 1050, which is 525.
If d = 525, then a + b = 2. The only possible values of a and b that satisfy this equation are a = 1 and b = 1. Therefore, the maximum value of the HCF of x and y is:
HCF(x, y) = d = 525
Therefore, the correct answer is option D, 525.
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Sum of two numbers x, y = 1050. What is the maximum value of the HCF between x and y?a)350b)700c)1050d)525e)900Correct answer is option 'D'. Can you explain this answer?
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Sum of two numbers x, y = 1050. What is the maximum value of the HCF between x and y?a)350b)700c)1050d)525e)900Correct answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Sum of two numbers x, y = 1050. What is the maximum value of the HCF between x and y?a)350b)700c)1050d)525e)900Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sum of two numbers x, y = 1050. What is the maximum value of the HCF between x and y?a)350b)700c)1050d)525e)900Correct answer is option 'D'. Can you explain this answer?.
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