1. Each decimal digit is greater than 5

m,n >0.6

This is sufficient.

Note: Give attention to "greater than". If it was greater than equal to 5, we could have m=n=0.5. In that scenario, m+n=1, not >1

2. For second statement, you should know this

AM >= GM

Arithmetic Mean of 2 numbers is greater than equal to Geometric Mean of 2 numbers.

So,

\(\frac{(m+n)}{2}\) >= \(\sqrt{mn}\)

We know that mn > \(\frac{1}{2}\)

So \(\sqrt{mn}\) > \(\frac{1}{\sqrt{2}}\)

Substitute this in our original equation

\(\frac{(m+n)}{2}\) >= \(\frac{1}{\sqrt{2}}\)

m+n >= \(\sqrt{2}\)

Hence, m+n >1

This is sufficient.

D.

Additional Lesson: AM >= GM >= HM (Harmonic Mean)

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