anjaneiya wrote:If S and T are non-zero numbers and (1/S)+(1/T)=S+T , which of the following is necessarily true?
1.ST=1
2.S+T=1
3.S/T=1
4.1/S=T
5. none of the above
source-gmatclub. pl explain...
Rewrite the left side of the equation over a common denominator:
1/S + 1/T = (T+S)/ST = (S+T)/ST.
Substitute into 1/S + 1/T = S+T:
(S+T)/ST = S+T.
The equation above works if S+T=0:
0/ST = 0
0=0.
The equation above also works if ST=1:
(S+T)/1 = S+T
S+T = S+T
Since we can determine only that S+T=0 or that ST=1, none of the answer choices must be true.
The correct answer is
E.
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