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:

Re: If r > s + t , is r positive? (1) s > t (2) r/(s+t) > 1 [#permalink]

Show Tags

23 May 2012, 22:48

1.S>T

S=1,T=-5;S+T=1-5=-4 and since R>S+T,R should be greater than -4, which can be positive or negative. Not sufficient.

2. R/(S+T) > 1

For R/(S+T) to be greater than 1, R should be greater than S+ T. Two cases: 1. R and S+T should be positive.this case is valid as R > S + T(from stem) 2. R and S+T should be negative. This case is not valid as the fraction would be less than 1 because of R > S + T and it would violate R/(S+T) >1

S=1,T=-5;S+T=1-5=-4 and since R>S+T,R should be greater than -4, which can be positive or negative. Not sufficient.

2. R/(S+T) > 1

For R/(S+T) to be greater than 1, R should be greater than S+ T. Two cases: 1. R and S+T should be positive.this case is valid as R > S + T(from stem) 2. R and S+T should be negative. This case is not valid as the fraction would be less than 1 because of R > S + T and it would violate R/(S+T) >1

So,B

The red part is not correct: \(\frac{r}{s+t}>1\) can be true for \(r>s+t\) (consider \(r=2\) and \(s+t=1\)) as well for \(r<s+t\) (consider \(r=-2\) and \(s+t=-1\)).

If r > s + t , is r positive?

(1) s > t. This does not tell us much, consider \(r=2\), \(s=1\), \(t=0\) and \(r=-2\), \(s=-1\), \(t=-2\). Not sufficient.

(2) r/(s+t) > 1 --> first of all notice that this means that \(r\) and \(s+t\) must be either both positive or both negative. If they are both negative, then we can multiply the given inequality by negative \(s+t\), flip the sign because multiplication by negative value and get \(r<s+t\), which contradicts given info that \(r>s+t\). So, the assumption that both \(r\) and \(s+t\) are negative is wrong, which leaves us only one case: both \(r\) and \(s+t\) are positive --> \(r>0\). Sufficient.

Re: If r > s + t , is r positive? (1) s > t (2) r/(s+t) > 1 [#permalink]

Show Tags

24 May 2012, 02:55

It's not quite clear. I don't understand your explanation about the second statement. How can I be sure that r is positive? Since I don't know the signs of the variables I cannot perform any action in the equation (so, I cannot tell with certainty whether r is positive or negative). Please, try to explain again. Thank you!
_________________

It's not quite clear. I don't understand your explanation about the second statement. How can I be sure that r is positive? Since I don't know the signs of the variables I cannot perform any action in the equation (so, I cannot tell with certainty whether r is positive or negative). Please, try to explain again. Thank you!

\(\frac{r}{s+t}>1\) means that either both \(r\) and \(s+t\) are positive or both \(r\) and \(s+t\) are negative.

Suppose they are both negative. In this case if we multiply both parts by negative \(s+t\) we'll get \(r<s+t\) (flip the sign when multiplying by a negative value), which contradicts given info that \(r>s+t\).

So, the assumption that both \(r\) and \(s+t\) are negative is wrong, which leaves us only one case: both \(r\) and \(s+t\) are positive --> \(r>0\).

Re: If r > s + t , is r positive? (1) s > t (2) r/(s+t) > 1 [#permalink]

Show Tags

09 Oct 2012, 12:29

kuttingchai wrote:

If r > s + t , is r positive?

(1) s > t (2) r/(s+t) > 1

not sure why the answer in book is "B"

I think most of us will face problem with statement 2. So i am explaining statement 2 only

From stem r>s+t ---> r-(s+t) >0 2) r/(s+t) >1 ----> r/(s+t) -1>0--->[r- (s+t)]/(s+t) >0 ----equation (A) From stem , its given that r-(s+t) >0 Thus the Numerator of equation (A) is positive, which means Denominator has to be positive as well because the ratio of Numerator/denominator is positive i.e. (s+t)>0

Now see the stem which says r > s + t r>0 (see the red color highlighted portion) r is positive Sufficient Answer B

I hope this will help many.
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

(2) \(\frac{r}{s+t}>1\) is equivalent to \(\frac{r}{s+t}-1>0\) or \(\frac{r-(s+t)}{s+t}>0\). Since the numerator is positive (from the stem, \(r > s + t\)), the fraction is positive only if the denominator is also positive, which means \(s + t > 0.\) Since \(r>s+t>0,\) it follows that \(r>0.\) Sufficient.

Answer B.
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: If r > s + t , is r positive? (1) s > t (2) r/(s+t) > 1 [#permalink]

Show Tags

02 Sep 2014, 07:39

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: If r > s + t , is r positive? (1) s > t (2) r/(s+t) > 1 [#permalink]

Show Tags

18 Mar 2016, 04:43

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: If r > s + t , is r positive? (1) s > t (2) r/(s+t) > 1 [#permalink]

Show Tags

02 Apr 2016, 03:28

If r > s + t , is r positive?

(1) s > t s+t>2t r>s+t => r>2t but no inf about sign of t so we cnt predict sign of r. Insufficient. (2) r/(s+t) > 1 (r-(s+t))/(s+t) >0 => +ve/(s+t) >0 => (s+t) is positive. r is >(s+t) => r is positive. Sufficient.

gmatclubot

Re: If r > s + t , is r positive? (1) s > t (2) r/(s+t) > 1
[#permalink]
02 Apr 2016, 03:28

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...