If r > s + t , is r positive? (1) s > t (2) r/(s+t) > 1

The red part is not correct: \(\frac{r}{s+t}>1\) can be true for \(r>s+t\) (consider \(r=2\) and \(s+t=1\)) as well for \(r<s+t\) (consider \(r=-2\) and \(s+t=-1\)).

If r > s + t , is r positive?

(1) s > t. This does not tell us much, consider \(r=2\), \(s=1\), \(t=0\) and \(r=-2\), \(s=-1\), \(t=-2\). Not sufficient.

(2) r/(s+t) > 1 --> first of all notice that this means that \(r\) and \(s+t\) must be either both positive or both negative. If they are both negative, then we can multiply the given inequality by negative \(s+t\), flip the sign because multiplication by negative value and get \(r<s+t\), which contradicts given info that \(r>s+t\). So, the assumption that both \(r\) and \(s+t\) are negative is wrong, which leaves us only one case: both \(r\) and \(s+t\) are positive --> \(r>0\). Sufficient.

Answer: B.

Hope it's clear.