inequalities

[queenisabella]

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

[killer1387]

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?

because its the properties of inequalities, however, while performing multiplication and division we need to care about the sign but while adding we just need to check the inequality sign. whereas we cant perform subtraction of inequality, for that we need to check the values.