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M18-19

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Re: M18-19  [#permalink]

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New post 12 Dec 2017, 07:02
1
omavsp wrote:
Hey,

Can someone please clarify how did we get (S+T)(ST−1)=0?

here is the explanation again:

Cross-multiply: S+T=(S+T)∗ST

(S+T)(ST−1)=0

Thank you!


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

Re-arrange: \(0=(S+T)*ST-(S+T)\);

Factor out S + T: \(0=(S+T)(ST - 1)\).

Hope it's clear.
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Re: M18-19  [#permalink]

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New post 10 Jun 2018, 09:33
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Re: M18-19  [#permalink]

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New post 13 Jun 2018, 05:57
omavsp wrote:
Hey,

Can someone please clarify how did we get (S+T)(ST−1)=0?

here is the explanation again:

Cross-multiply: S+T=(S+T)∗ST

(S+T)(ST−1)=0

Thank you!



Not sure if u still want the clarification, posting it here anyway.
after you cross multiply S+T=(S+T)∗ST you bring all the expressions on one side.
ST (S+T) - (S+T) = 0
Factoring out S+T you get :
(S+T) (ST-1) = 0

Please kudo if that helped.
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Re: M18-19  [#permalink]

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New post 17 Oct 2018, 02:34
manhasnoname wrote:
when you have an equation (x-3)(x-2) = 0; x is either 3 or 2.

(S+T)(ST-1) = 0; => S+T = 0; or ST = 1;

ST = 1 should be the answer. However, S = 1/T is the same. So looks like there is more than one correct answer to this question!!


Hello manhasnoname and Nipson,
The below is one of the explanations by Bunuel in one of his posts. Reading and understanding them carefully will clear your doubts for the question in discussion, which is a MUST be true question.

“MUST BE TRUE" questions:
These questions ask which of the following MUST be true, or which of the following is ALWAYS true no matter what set of numbers you choose. Generally for such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.

As for "COULD BE TRUE" questions:
The questions asking which of the following COULD be true are different: if you can prove that a statement is true for one particular set of numbers, it will mean that this statement could be true and hence is a correct answer.

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Re: M18-19  [#permalink]

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New post 30 Jan 2019, 01:04
I think the problem can be solved by observation without much substitution:

If you closely observe, Option A and Option C are the same.
When you substitute numbers in Option B and Option D, none of them fit in right except for 1. Option B can't be right as neither S nor T can be 0.
If I assume the number to be 1, Options A and C are equal contenders. Thus, incorrect.

What remains is Option E which is the right answer. :)
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Re: M18-19  [#permalink]

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New post 21 Feb 2019, 13:06
Bunuel wrote:
Official Solution:

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


\(\frac{1}{S} + \frac{1}{T} = S + T\);

\(\frac{T+S}{ST}=S+T\)\(\rightarrow\);

Cross-multiply: \(S+T=(S+T)*ST\);

\((S+T)(ST-1)=0\). Either \(S+T=0\) or \(ST=1\). Now, notice that if \(S+T=0\) is true then none of the options must be true.


Answer: E



I think this is a HIGH QUALITY question.

Bunuel, just a question - how do we decide when to cancel out numbers/variables and when not to?
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Re: M18-19  [#permalink]

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New post 21 Feb 2019, 20:47
siddharthsinha123 wrote:
Bunuel wrote:
Official Solution:

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


\(\frac{1}{S} + \frac{1}{T} = S + T\);

\(\frac{T+S}{ST}=S+T\)\(\rightarrow\);

Cross-multiply: \(S+T=(S+T)*ST\);

\((S+T)(ST-1)=0\). Either \(S+T=0\) or \(ST=1\). Now, notice that if \(S+T=0\) is true then none of the options must be true.


Answer: E



I think this is a HIGH QUALITY question.

Bunuel, just a question - how do we decide when to cancel out numbers/variables and when not to?


Say you have ax = ay. Only when you know that a ≠ 0, you can divide by a and get x = y.
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Re: M18-19  [#permalink]

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New post 21 Feb 2019, 22:02
Bunuel wrote:
siddharthsinha123 wrote:
Bunuel wrote:
Official Solution:

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


\(\frac{1}{S} + \frac{1}{T} = S + T\);

\(\frac{T+S}{ST}=S+T\)\(\rightarrow\);

Cross-multiply: \(S+T=(S+T)*ST\);

\((S+T)(ST-1)=0\). Either \(S+T=0\) or \(ST=1\). Now, notice that if \(S+T=0\) is true then none of the options must be true.


Answer: E



I think this is a HIGH QUALITY question.

Bunuel, just a question - how do we decide when to cancel out numbers/variables and when not to?


Say you have ax = ay. Only when you know that a ≠ 0, you can divide by a and get x = y.


Thanks Bunuel,

Is there a link or a specific topic under "ALL YOU NEED FOR QUANT ! ! !" where i can find this concept?

Thanks
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Re: M18-19  [#permalink]

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New post 21 Feb 2019, 22:22
1
siddharthsinha123 wrote:
Thanks Bunuel,

Is there a link or a specific topic under "ALL YOU NEED FOR QUANT ! ! !" where i can find this concept?

Thanks
Sid


7. Algebra



For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
_________________

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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Re: M18-19   [#permalink] 21 Feb 2019, 22:22

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