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How many pairs of positive integers m, n satisfy 1/m + 4/n = 1/12 where n is an odd integer less than 60?
- a)7
- b)5
- c)3
- d)6
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
How many pairs of positive integers m, n satisfy 1/m + 4/n = 1/12 wher...
Since m and n are both positive and their sum is equal to
Hence the value of both there fractions must be less than
Therefore n-can take values > 48 and odd
N = {49, 51, 53, 55, 57, 59}
Now we have to check which values of ‘n’ will give integral values of ‘m’.
Equation:
For m to be on integer (n - 48) should be a multiple of 12n
The above condition is satisfied for
N = 49, 51, 57
Corresponding values of m
N = 49
M = 12 × 49
N = 51
Equation:
For m to be on integer (n - 48) should be a multiple of 12n
The above condition is satisfied for
N = 49, 51, 57
Corresponding values of m
N = 49
M = 12 × 49
N = 51
Most Upvoted Answer
How many pairs of positive integers m, n satisfy 1/m + 4/n = 1/12 wher...
Problem: How many pairs of positive integers m, n satisfy 1/m * 4/n = 1/12 where n is an odd integer less than 60?
Given:
- The equation: 1/m * 4/n = 1/12
- n is an odd integer less than 60
To find: The number of pairs of positive integers m, n that satisfy the given equation.
Approach:
1. Multiply both sides of the equation by 12mn to eliminate the fractions.
2. Simplify the equation to obtain 48 = mn.
3. Find the number of pairs (m, n) that satisfy the equation within the given constraints.
Solution:
1. Multiply both sides of the equation by 12mn:
12mn * (1/m * 4/n) = 12mn * (1/12)
4n = mn
48 = mn (dividing both sides by 4)
2. Simplify the equation to obtain 48 = mn.
- We know that n is an odd integer less than 60.
- Since m and n are positive integers, the possible values for m and n are:
- m = 1, n = 48
- m = 2, n = 24
- m = 3, n = 16
- m = 4, n = 12
- m = 6, n = 8
- m = 8, n = 6
- m = 12, n = 4
- m = 16, n = 3
- m = 24, n = 2
- m = 48, n = 1
3. Count the number of pairs (m, n) that satisfy the given equation:
- There are 3 pairs (m, n) that satisfy the equation: (m=3, n=16), (m=4, n=12), (m=16, n=3)
Answer: The correct answer is option 'C' as there are 3 pairs of positive integers (m, n) that satisfy the given equation.
Given:
- The equation: 1/m * 4/n = 1/12
- n is an odd integer less than 60
To find: The number of pairs of positive integers m, n that satisfy the given equation.
Approach:
1. Multiply both sides of the equation by 12mn to eliminate the fractions.
2. Simplify the equation to obtain 48 = mn.
3. Find the number of pairs (m, n) that satisfy the equation within the given constraints.
Solution:
1. Multiply both sides of the equation by 12mn:
12mn * (1/m * 4/n) = 12mn * (1/12)
4n = mn
48 = mn (dividing both sides by 4)
2. Simplify the equation to obtain 48 = mn.
- We know that n is an odd integer less than 60.
- Since m and n are positive integers, the possible values for m and n are:
- m = 1, n = 48
- m = 2, n = 24
- m = 3, n = 16
- m = 4, n = 12
- m = 6, n = 8
- m = 8, n = 6
- m = 12, n = 4
- m = 16, n = 3
- m = 24, n = 2
- m = 48, n = 1
3. Count the number of pairs (m, n) that satisfy the given equation:
- There are 3 pairs (m, n) that satisfy the equation: (m=3, n=16), (m=4, n=12), (m=16, n=3)
Answer: The correct answer is option 'C' as there are 3 pairs of positive integers (m, n) that satisfy the given equation.
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How many pairs of positive integers m, n satisfy 1/m + 4/n = 1/12 where n is an odd integer less than 60?a)7b)5c)3d)6Correct answer is option 'C'. Can you explain this answer?
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How many pairs of positive integers m, n satisfy 1/m + 4/n = 1/12 where n is an odd integer less than 60?a)7b)5c)3d)6Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about How many pairs of positive integers m, n satisfy 1/m + 4/n = 1/12 where n is an odd integer less than 60?a)7b)5c)3d)6Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many pairs of positive integers m, n satisfy 1/m + 4/n = 1/12 where n is an odd integer less than 60?a)7b)5c)3d)6Correct answer is option 'C'. Can you explain this answer?.
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