Let’s assume the work done to be 1 unit.
Mary can do this work in m hours; therefore, Mary works at the rate of (\(\frac{1}{m}\)) units per hour.
Nadir can do this work in n hours; therefore, Nadir works at the rate of (\(\frac{1}{n}\)) units per hour.
If they work together, their combined rate = \(\frac{1}{m}\) + \(\frac{1}{n}\) = \(\frac{(m+n) }{ mn}\).
When work is constant, time and rates are reciprocal of each other. Therefore, the time taken by them when working together = \(\frac{mn }{ (m+n)}\).
From statement I alone, \(\frac{mn }{ (m+n)}\) > \(\frac{m}{2}\).
Note that m and n are positive values since they represent time. Therefore, we can cancel off m from both sides of the inequality. When we do this, we get,
\(\frac{n }{ (m+n)}\) > ½ or 2n>m+n or n>m.
Is m<n? Yes. Statement I alone is sufficient. Answer options B, C and E can be eliminated. Possible answer options are A or D.
From statement II alone, \(\frac{mn }{ (m+n)}\) < \(\frac{n}{2}\). Following a similar approach as we did in the previous statement, we can simplify the inequality as shown below:
\(\frac{m }{ (m+n)}\) < ½ or 2m < m + n or m<n.
Is m<n? Yes. Statement II alone is sufficient. Answer option A can be eliminated.
The correct answer option is D.
Hope that helps!
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