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# Fractions Q5

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Intern
Joined: 07 Oct 2009
Posts: 33

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02 Jan 2010, 02:21
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

Joined: 20 Aug 2009
Posts: 306
Location: Tbilisi, Georgia
Schools: Stanford (in), Tuck (WL), Wharton (ding), Cornell (in)

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02 Jan 2010, 13:38
$$1/S+1/T=\frac{S+T}{ST}=S+T$$
$$S+T=(S+T)*ST$$

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
Joined: 30 Aug 2009
Posts: 287
Location: India
Concentration: General Management

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02 Jan 2010, 20:52
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
Intern
Joined: 07 Oct 2009
Posts: 33

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04 Jan 2010, 11:58
Thanks Shalva & kp1811.

OA is E.
Re: Fractions Q5   [#permalink] 04 Jan 2010, 11:58
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# Fractions Q5

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