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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]

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New post 11 Feb 2013, 09:39
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]

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New post 18 Mar 2013, 11:06
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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]

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New post 18 Mar 2013, 11:12
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]

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New post 18 Mar 2013, 11:14
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]

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New post 27 Dec 2015, 08:46
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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.



Bunuel,

Not able to understand the highlighted part. Kindly explain in detail...

Thx,
Arun

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

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New post 27 Dec 2015, 08:51
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Expert's post
ArunpriyanJ 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.



Bunuel,

Not able to understand the highlighted part. Kindly explain in detail...

Thx,
Arun


\(S+T=(S+T)*ST\)

\((S+T)*ST-(S+T)=0\)

Factor s+t: \((S+T)(ST-1)=0\)

Hope it's clear.
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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Extra-hard Quant Tests with Brilliant Analytics

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

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New post 07 Sep 2016, 07:06
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also the OA can be crosschecked by plugging value of S=1 and T=-1
in this case 1/S+1/T= S+T
but \(ST\neq{-1}\), \(1/S\neq{T}\) since S+T=0 here.

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

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Re: If S and T are non-zero numbers and   [#permalink] 16 Nov 2017, 03:16

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