How many pairs. M p positive integers \( m\) and \( n\) satisfy the equation \( \Large \frac{1}{m} \)+\( \Large \frac{4}{n} \)= \( \Large \frac{1}{12} \)
Where \( n\) is an odd integer less than 60?
Correct Answer: Description for Correct answer:
\( \Large \frac{1}{m} + \frac{4}{n} = \frac{1}{12}\)
\( \Large \frac{1}{m} = \frac{1}{12} - \frac{4}{n}\)
For m to be positive, we have
\( \Large \frac{1}{12} > \frac{4}{n} \)
n > 48
For n = 49, 51 and 57, we get positive integer value of m.
There are three pairs of m and n which satisfy the given equation.
Option (d) is correct.
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