R>S.sana.noor wrote:If RT > ST and R>S, then which of the following must be true?
a) T > 0
b) S > 0
c) R > 0
d) T < 0
e) RS > 0
the OA is A
It is also given that RT>ST, a condition that RESTRICTS the value of T.
There are three cases to consider: T=0, T<0, and T>0.
T=0:
If we multiply each side of R>S by T=0, then RT=ST=0, which contradicts the condition that RT>ST.
Thus, T≠0.
T<0:
Multiplying each side of an inequality by a negative value requires that we flip the inequality.
Thus, if we multiply each side of R>S by T<0, then RT<ST, which also contradicts the condition that RT>ST.
Thus, it is not possible that T<0.
Since it is not possible that T=0 or that T<0, it must be true that T>0.
The correct answer is A.
