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# If S and T are non-zero numbers and

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Senior Manager
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 415
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Re: If S and T are non-zero numbers and  [#permalink]

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11 Feb 2013, 08:39
you hav a 720 and you gonna re-take

Good luck mate
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Manager
Joined: 28 Jul 2011
Posts: 153
Re: If S and T are non-zero numbers and  [#permalink]

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18 Mar 2013, 10:06
1
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.

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.
Math Expert
Joined: 02 Sep 2009
Posts: 62465
Re: If S and T are non-zero numbers and  [#permalink]

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18 Mar 2013, 10:12
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.

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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Manager
Joined: 28 Jul 2011
Posts: 153
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.

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
Manager
Joined: 03 Aug 2015
Posts: 51
Concentration: Strategy, Technology
Schools: ISB '18, SPJ GMBA '17
GMAT 1: 680 Q48 V35
Re: If S and T are non-zero numbers and  [#permalink]

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27 Dec 2015, 07:46
1
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.

Bunuel,

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

Thx,
Arun
Math Expert
Joined: 02 Sep 2009
Posts: 62465
Re: If S and T are non-zero numbers and  [#permalink]

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27 Dec 2015, 07:51
2
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.

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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Joined: 22 Apr 2015
Posts: 25
WE: Business Development (Internet and New Media)
Re: If S and T are non-zero numbers and  [#permalink]

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07 Sep 2016, 06:06
1
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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27 May 2019, 03:31
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Re: If S and T are non-zero numbers and   [#permalink] 27 May 2019, 03:31

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