|
Author |
Message |
|
TAGS:
|
|
|
Manager
Joined: 28 Jul 2011
Posts: 212
Followers: 0
Kudos [?]:
14
[0], given: 11
|
If r > s + t , is r positive? (1) s > t (2) r/(s+t) > 1 [#permalink]
 23 May 2012, 20:59
Question Stats:
52% (01:58) correct
47% (01:01) wrong based on 0 sessions
If r > s + t , is r positive? (1) s > t (2) r/(s+t) > 1 not sure why the answer in book is " B"
|
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11519
Followers: 1795
Kudos [?]:
9546
[1] , given: 826
|
Re: if r > s + t , is r positive? [#permalink]
24 May 2012, 00:11
1
This post received
KUDOS
sdpkind wrote: 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
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. Answer: B. Hope it's clear.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Intern
Joined: 20 Mar 2011
Posts: 2
Followers: 0
Kudos [?]:
0
[0], given: 1
|
Re: if r > s + t , is r positive? [#permalink]
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
So,B
|
|
|
|
|
|
Manager
Joined: 16 Feb 2012
Posts: 211
Concentration: Finance, Economics
Followers: 4
Kudos [?]:
15
[0], given: 93
|
Re: If r > s + t , is r positive? (1) s > t (2) r/(s+t) > 1 [#permalink]
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!
_________________
Kudos if you like the post!
Failing to plan is planning to fail.
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11519
Followers: 1795
Kudos [?]:
9546
[0], given: 826
|
Re: If r > s + t , is r positive? (1) s > t (2) r/(s+t) > 1 [#permalink]
24 May 2012, 03:03
Stiv wrote: 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. Hope it's clear.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Senior Manager
Joined: 24 Aug 2009
Posts: 280
Schools: Harvard, Columbia, Stern, Booth, LSB,
Followers: 2
Kudos [?]:
129
[0], given: 216
|
Re: If r > s + t , is r positive? (1) s > t (2) r/(s+t) > 1 [#permalink]
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)>0Now 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
|
|
|
|
|
|
Director
Joined: 22 Mar 2011
Posts: 608
WE: Science (Education)
Followers: 43
Kudos [?]:
267
[0], given: 43
|
Re: If r > s + t , is r positive? (1) s > t (2) r/(s+t) > 1 [#permalink]
09 Oct 2012, 16:26
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" (1) Take t = -2, \,\,s = -1,and r = -1. \,\,-1 > -1 + (-2) = -3.Or, t = 0, \,\,s = 1, \,\,r = 2. \,\,2 > 1 + 0.Not sufficient. (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]
09 Oct 2012, 16:26
|
|
|
|
|
|
|
|
|
|
|
close
