Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

(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.

The correct answer is E

Question: I understand the way of the equation, however, what I would have done is interfere at the following step: S+T = (S+T)*ST -> (S+T)/(S+T)=ST -> ST = 1

Is there some rule which forbids me to take this step? Or is the only option to realize so, that you perform the above given equation as well and realise that "S+T = 0" negates all other options than E.... ??

Thanks in advance, best regards

P.S. Sry if the format is terrible, this is the first question I am copying out of somewhere.

If S and T are non-zero numbers and 1S+1T=S+T, which of the following must be true? A. ST=1 B. S+T=1 C. 1/S=T D. S/T=1 E. none of the above Explanation provided: 1/S + 1/T = S+T; T+S/ST = S+T→; 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. The correct answer is E Question: I understand the way of the equation, however, what I would have done is interfere at the following step: S+T = (S+T)*ST -> (S+T)/(S+T)=ST -> ST = 1 Is there some rule which forbids me to take this step? Or is the only option to realize so, that you perform the above given equation as well and realise that "S+T = 0" negates all other options than E.... ?? Thanks in advance, best regards P.S. Sry if the format is terrible, this is the first question I am copying out of somewhere.

Yes, this is not correct way of cancelling. I'll show you one example. 5* 0 = 3*0 if we cancel 0 on both side, we get 5=3. is it correct? No.

The crux (and the rule) is, we can cancel out a term only when we know its not 0. So the way it is done in explanation is absolutely correct and the right method.

If S and T are non-zero numbers and 1S+1T=S+T, which of the following must be true?

A. ST=1 B. S+T=1 C. 1/S=T D. S/T=1 E. none of the above

Explanation provided:

1/S + 1/T = S+T;

T+S/ST = S+T→;

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.

The correct answer is E

Question: I understand the way of the equation, however, what I would have done is interfere at the following step: S+T = (S+T)*ST -> (S+T)/(S+T)=ST -> ST = 1

Is there some rule which forbids me to take this step? Or is the only option to realize so, that you perform the above given equation as well and realise that "S+T = 0" negates all other options than E.... ??

Thanks in advance, best regards

P.S. Sry if the format is terrible, this is the first question I am copying out of somewhere.

There was this fun derivation that my math teacher showed us in school. Just to demonstrate how cancelling of 0 could yield wrong results. He claimed that he could prove that 1=2 and hence all numbers are equal.

It goes as below:

Let, \(a=b\)

Multiplying both sides by a, We get

\(a^2 = ab\)

Subtracting \(b^2\) from both sides

\(a^2 - b^2 = ab - b^2\)

\((a+b)(a-b) = b(a-b)\)

Cancelling \((a-b)\) on both sides,

\(a+b = b\)

Since \(a=b\)

\(a+a = a\)

\(2a = a\)

\(2=1\)
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Yes, this is not correct way of cancelling. I'll show you one example. 5* 0 = 3*0 if we cancel 0 on both side, we get 5=3. is it correct? No.

The crux (and the rule) is, we can cancel out a term only when we know its not 0. So the way it is done in explanation is absolutely correct and the right method.

Hope it helps

Thanks - lol I am an idiot - ...! I even thought of the zero number things, but mistakenly memorized the prompt as telling me that the respective equation could not be "0", though it only said that each number alone is non-zero....

Thanks guys!
_________________

Exhaust your body, proceed your mind, cultivate your soul.

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.

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

Show Tags

07 Nov 2012, 00:19

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.

Bunuel, in your solution I need to ask one thing. Inequalities, there is a rule that if you dont know the sign of denominator, then dont cross multiply. In your solution, how can you be so sure of the sign of ST. Please let me know if i am missing something
_________________

In this step: s+t = (s+t)st can't we just cancel (s+t) and get ---> st =1?

thanks, -K

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).

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.

Bunuel, in your solution I need to ask one thing. Inequalities, there is a rule that if you dont know the sign of denominator, then dont cross multiply. In your solution, how can you be so sure of the sign of ST. Please let me know if i am missing something

We are concerned with the sign when we cross-multiply an inequality because this operation might affect (flip) its sign (> to <, for example) but it's always safe to cross-multiply an equation.
_________________

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

Show Tags

10 Feb 2013, 05:03

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, Since S+T=0 OR ST=1 and the question asks whatmust be true, the answer is E ? Another way to answer the question. . Is my reasoning right?
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

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.

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

Show Tags

10 Feb 2013, 06:04

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..
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

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

Show Tags

10 Feb 2013, 13:55

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.
_________________

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

Show Tags

10 Feb 2013, 18:17

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
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

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

Show Tags

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.
_________________