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If S and T are non-zero numbers and

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Re: If S and T are non-zero numbers and [#permalink] New post 11 Feb 2013, 07:59
Sachin9 wrote:
Vips0000 wrote:
Sachin9 wrote:
I get it Vippss. But in all other cases, the generalization will hold good right?

Rules are good, generalizations are not :)
Enjoy and practice kudos :-p


why on earth do u need kudos :shock: u already done with ur gmat. .

Retake bro.. Coming soon :-)
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Re: If S and T are non-zero numbers and [#permalink] New post 11 Feb 2013, 08:39
you hav a 720 and you gonna re-take
:shock: :shock: :shock: :shock: :shock: :shock: :shock: :shock: :shock: :shock: :shock: :shock: :shock: :shock: :shock: :shock: :shock: :shock:

Good luck mate :)
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Re: If S and T are non-zero numbers and [#permalink] New post 18 Mar 2013, 10:06
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.

Answer: E.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Please pay attention to the rule #3. Thank you.



Hello Bunuel,

How did u get S+T=(S+T)*ST --> (S+T)(ST-1)=0 ??

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.
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Re: If S and T are non-zero numbers and [#permalink] New post 18 Mar 2013, 10:12
Expert's post
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.

Answer: E.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Please pay attention to the rule #3. Thank you.



Hello Bunuel,

How did u get S+T=(S+T)*ST --> (S+T)(ST-1)=0 ??

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.


Check here: if-s-and-t-are-non-zero-numbers-and-141887.html#p1140729

Hope it helps.
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Re: If S and T are non-zero numbers and [#permalink] New post 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.

Answer: E.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Please pay attention to the rule #3. Thank you.



Hello Bunuel,

How did u get S+T=(S+T)*ST --> (S+T)(ST-1)=0 ??

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).
"

therefore
1/S+1/T = S+T
(S+T) = (S+T) (ST)
0= (S+T) (ST) - (S+T)
0 = (S+T) (ST-1)

(S+T)=0 or ST = 1

Thank you
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Re: If S and T are non-zero numbers and [#permalink] New post 12 Jul 2014, 16:12
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Re: If S and T are non-zero numbers and   [#permalink] 12 Jul 2014, 16:12
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