source: manhattan prep

If r + s > 2t, is r > t ?

(1) t > s

(2) r > s

The OA is D.. however and answer solution included below. QUESTION - how can add the 2 equations together to get the answer? Why can perform these operations unless we know that all these variables are > 0?


(1) SUFFICIENT: We can combine the given inequality r + s > 2t with the first statement by adding the two inequalities:

r + s > 2t
t > s
r + s + t > 2t + s
r > t

(2) SUFFICIENT: We can combine the given inequality r + s > 2t with the second statement by adding the two inequalities:

r + s > 2t
r > s
2r + s > 2t + s
2r > 2t
r > t