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Fractions Q5

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Intern
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Fractions Q5 [#permalink] New post 02 Jan 2010, 01:21
If S and T are non-zero numbers and 1/S+1/T=S+T , which of the following is necessarily true?
(A) ST=1
(B) S+T=1
(C) 1/S=T
(D) S/T=1
(E) none of the above

Please help me understand right answer.I marked A, but it's wrong.
Tuck Thread Master
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Re: Fractions Q5 [#permalink] New post 02 Jan 2010, 12:38
1/S+1/T=\frac{S+T}{ST}=S+T
S+T=(S+T)*ST

Well so far everything should be pretty obvious

Here are 2 possibilities: either (S+T)=0 OR ST=1. But you cant say that necessarily ST=1, it is one of possible solutions
Senior Manager
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Re: Fractions Q5 [#permalink] New post 02 Jan 2010, 19:52
1/S +1/T = (T+S)/TS = S + T => S + T = ST(S + T)
So we have ST = 1 and S+T =0. We also get 1/S =T

now taking the options one by one ---
A) ST=1 ----- possible
(B) S+T=1-----not possible
(C) 1/S=T-----possible
(D) S/T=1---need to check
(E) none of the above

now if S =3 and T = -3 then ST is not equal to 1 so option A and D are out
1/S is not equal to T and S/T is also not equal to 1 so option C and B are also out

so looks like E -none of the above

OA pls
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Re: Fractions Q5 [#permalink] New post 04 Jan 2010, 10:58
Thanks Shalva & kp1811.

OA is E.
Re: Fractions Q5   [#permalink] 04 Jan 2010, 10:58
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