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The number of positive integer valued pairs (x, y), satisfying 4x – 17 y = 1 and x < 1000 is:
- a)55
- b)57
- c)59
- d)58
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The number of positive integer valued pairs (x, y), satisfying 4x &nda...
The integral values of x for which y is an integer are 13, 30, 47,……
The values are in the form 17n + 13, where n ≥ 0
17n + 13 < 1000
⇒ 17n < 987
⇒ n < 58.05
⇒ n can take values from 0 to 58
⇒ Number of values = 59
Most Upvoted Answer
The number of positive integer valued pairs (x, y), satisfying 4x &nda...
There are no positive integer valued pairs (x, y) that satisfy the inequality 4x< /><5x.>
To see why this is the case, suppose there exists a positive integer pair (x, y) that satisfies the inequality. Then, we have:
4x < y="" />< />
Since y is a positive integer, it must be at least one greater than 4x. This means that y = 4x + 1 or greater. However, if y = 4x + 1, then the inequality becomes:
4x < 4x="" +="" 1="" />< />
This is not possible for positive integer x, as there are no integers between consecutive integers. Therefore, there are no positive integer pairs (x, y) that satisfy the inequality 4x< /><5x.>
To see why this is the case, suppose there exists a positive integer pair (x, y) that satisfies the inequality. Then, we have:
4x < y="" />< />
Since y is a positive integer, it must be at least one greater than 4x. This means that y = 4x + 1 or greater. However, if y = 4x + 1, then the inequality becomes:
4x < 4x="" +="" 1="" />< />
This is not possible for positive integer x, as there are no integers between consecutive integers. Therefore, there are no positive integer pairs (x, y) that satisfy the inequality 4x< /><5x.>
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The number of positive integer valued pairs (x, y), satisfying 4x – 17 y = 1 and x < 1000 is:a)55b)57c)59d)58Correct answer is option 'C'. Can you explain this answer?
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The number of positive integer valued pairs (x, y), satisfying 4x – 17 y = 1 and x < 1000 is:a)55b)57c)59d)58Correct answer is option 'C'. Can you explain this answer? for CLAT 2025 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about The number of positive integer valued pairs (x, y), satisfying 4x – 17 y = 1 and x < 1000 is:a)55b)57c)59d)58Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CLAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of positive integer valued pairs (x, y), satisfying 4x – 17 y = 1 and x < 1000 is:a)55b)57c)59d)58Correct answer is option 'C'. Can you explain this answer?.
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