How many pairs of positive integers m, n satisfy 1/m + 4/n = 1/12 where n is an odd integer less than 60?
Explanation:
1/m + 4/n = 1/12
∴ 1/m = 1/12 – 4/n
∴ m = 12n/(n – 48)
As, m is a positive integer, n should be greater than 48 and moreover since n is a positive odd integer lesser than 60, n can take values 49, 51, 53, 55, 57 and 59.
If n = 49, 51, 57 then m is a positive integer.
If n = 53, 55, 59 then m is not an integer.
∴ 3 pairs of values of m and n satisfy the given equation.
Hence, option (e).
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