This problem seems beyond the scope of the GMAT.
That said, here is one approach:
1/m = 1/12 - 4/n.
Since m must be positive, 1/12 must be greater than 4/n:
1/12 > 4/n
n > 48.
Since n must be an odd integer less than 60, test odd integers between 48 and 60 to see which yield integer values for m.
n=49:
1/m = 1/12 - 4/49
1/m = 1/(12*49)
Here, m = 12*49.
n=51:
1/m = 1/12 - 4/51
1/m = 3/(12*51)
1/m = 1/(4*51).
Here, m = 4*51.
n=53:
1/m = 1/12 - 4/53
1/m = 5/(12*53).
Here, m is not an integer.
n=55
1/m = 1/12 - 4/55
1/m = 7/(12*55).
Here, m is not an integer.
n=57:
1/m = 1/12 - 4/57
1/m = 9/(12*57)
1/m = 1/(3*19).
Here, m = 3*19.
n=59:
1/m = 1/12 - 4/59
1/m = 11/(12*59).
Here, m is not an integer.
Only the 3 options in red are viable.
The correct answer is B.
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