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Re: If S and T are non-zero numbers and [#permalink]

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11 Feb 2013, 00:59

Sachin9 wrote:

Vips0000 wrote:

Sachin9 wrote:

I understand what you are trying to say bunuel.. my question is that since the equation results in 2 soln and we have a OR .. . that is soln 1 OR soln 2 and the question asks for MUST be true..

So based on this reasoning, can we say the answer is E..?

For something must be true , we cannot have soln 1 OR soln 2.. we need to have 1 soln / soln1 AND soln2..

Hope you are getting what I am trying to ask..

I would say that don't generalize this point. You know that because there are two solutions, any of the given options need not be a MUST. But if u really have an option that says (s+t)(st-1)=0 then that MUST be true.

But if u really have an option that says (s+t)(st-1)=0 then that MUST be true.

Ididn;t understand this.. if (s+t)(st-1)=0 then either s+t=0 or st-1=0.. we still have a OR here

If the question were to be this: If S and T are non-zero numbers and \(\frac{1}{S} + \frac{1}{T} = S + T\), which of the following must be true?

A. \(ST = 1\) B. \(S + T = 1\) C. \(\frac{1}{S} = T\) D. \(\frac{S}{T} = 1\) E. None of the above F. (s+t)(st-1)=0

Then your generalization will go wrong as you have an ans choice F that must hold true.
_________________

If S and T are non-zero numbers and \(\frac{1}{S} + \frac{1}{T} = S + T\), which of the following must be true?

A. \(ST = 1\) B. \(S + T = 1\) C. \(\frac{1}{S} = T\) D. \(\frac{S}{T} = 1\) E. None of the above

OE:

\(\frac{1}{S} + \frac{1}{T} = S + T\) --> \(\frac{T+S}{ST}=S+T\) --> cross-multiply: \(S+T=(S+T)*ST\) --> \((S+T)(ST-1)=0\) --> either \(S+T=0\) or \(ST=1\). So, if \(S+T=0\) is true then none of the options must be true.

What did i miss in he below equation?? how come you got (S+T)(ST-1)=0 ?? Ca you please explain 1/S+1/T = S+T (S+T) = (S+T) (ST) divide both side by (S+T) we get 1=1(ST) therefore ST=1

Re: If S and T are non-zero numbers and [#permalink]

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18 Mar 2013, 10:14

kuttingchai wrote:

Bunuel wrote:

If S and T are non-zero numbers and \(\frac{1}{S} + \frac{1}{T} = S + T\), which of the following must be true?

A. \(ST = 1\) B. \(S + T = 1\) C. \(\frac{1}{S} = T\) D. \(\frac{S}{T} = 1\) E. None of the above

OE:

\(\frac{1}{S} + \frac{1}{T} = S + T\) --> \(\frac{T+S}{ST}=S+T\) --> cross-multiply: \(S+T=(S+T)*ST\) --> \((S+T)(ST-1)=0\) --> either \(S+T=0\) or \(ST=1\). So, if \(S+T=0\) is true then none of the options must be true.

What did i miss in he below equation?? how come you got (S+T)(ST-1)=0 ?? Ca you please explain 1/S+1/T = S+T (S+T) = (S+T) (ST) divide both side by (S+T) we get 1=1(ST) therefore ST=1

Thank you.

I think I got the answer

from your previous post I got " Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We can not divide by zero.

So, if you divide (reduce) s+t = (s+t)st by (s+t), you assume, with no ground for it, that (s+t) does not equal to zero thus exclude a possible solution (notice that both st=1 AND (s+t)=0 satisfy the equation). "

Re: If S and T are non-zero numbers and [#permalink]

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12 Jul 2014, 16:12

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Re: If S and T are non-zero numbers and [#permalink]

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26 Dec 2015, 11:34

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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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