It is currently 17 Nov 2017, 16:25

Close

GMAT Club Daily Prep

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the ratio of r to s?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Manager
Manager
avatar
Joined: 10 Feb 2011
Posts: 112

Kudos [?]: 370 [1], given: 10

What is the ratio of r to s? [#permalink]

Show Tags

New post 15 Mar 2011, 16:48
1
This post received
KUDOS
7
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

69% (00:37) correct 31% (00:51) wrong based on 320 sessions

HideShow timer Statistics

What is the ratio of r to s?

(1) r + s = 7
(2) r^2 – s^2 = 7
[Reveal] Spoiler: OA

Last edited by Bunuel on 29 Jul 2013, 08:29, edited 1 time in total.
Edited the question.

Kudos [?]: 370 [1], given: 10

Director
Director
avatar
Joined: 01 Feb 2011
Posts: 726

Kudos [?]: 146 [0], given: 42

Re: 20. (M) What is the ratio of r to s? (1) r + s = 7 (2) r2 [#permalink]

Show Tags

New post 16 Mar 2011, 16:36
1. Not sufficient

(r , s could be 5 2 or 4 3 so on)

2. Not enough info to derive r/s . Not sufficient.

Together its sufficient to find r and s. Answer C.

Kudos [?]: 146 [0], given: 42

Intern
Intern
avatar
Joined: 12 Oct 2011
Posts: 6

Kudos [?]: 5 [0], given: 4

Location: Canada
Concentration: Finance, Entrepreneurship
WE: Asset Management (Mutual Funds and Brokerage)
Re: (M) What is the ratio of r to s? (1) r + s = 7 (2) r2 s2 = 7 [#permalink]

Show Tags

New post 29 Jul 2013, 08:27
For (2), I did the following:

r^2 - s^2 = 7
(r+s)(r-s) = 7
(4+3)(4-3) = 7 <--- I don't see any other possible combination of numbers that would give you 7

Thus, I fail to see how statement 2 is insufficient. Please help!

Kudos [?]: 5 [0], given: 4

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132516 [2], given: 12324

Re: (M) What is the ratio of r to s? (1) r + s = 7 (2) r2 s2 = 7 [#permalink]

Show Tags

New post 29 Jul 2013, 08:32
2
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
Startup wrote:
What is the ratio of r to s?

(1) r + s = 7
(2) r^2 – s^2 = 7


For (2), I did the following:

r^2 - s^2 = 7
(r+s)(r-s) = 7
(4+3)(4-3) = 7 <--- I don't see any other possible combination of numbers that would give you 7

Thus, I fail to see how statement 2 is insufficient. Please help!


Notice that we are not told that r and s are integers, so consider \(r^2=7\) and \(s=0\) OR \(r^2=8\) and \(s=1\)...
_________________

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132516 [2], given: 12324

Current Student
avatar
Joined: 18 May 2013
Posts: 40

Kudos [?]: 10 [0], given: 2

Concentration: Real Estate, Finance
GPA: 3.73
WE: Analyst (Real Estate)
Re: What is the ratio of r to s? [#permalink]

Show Tags

New post 15 Sep 2013, 23:14
Why can't R+S = 7 be solved to (-7/1) = (-S/R) and thus prove sufficiency in Statement 1?

Kudos [?]: 10 [0], given: 2

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132516 [0], given: 12324

Re: What is the ratio of r to s? [#permalink]

Show Tags

New post 16 Sep 2013, 02:07
stevennu wrote:
Why can't R+S = 7 be solved to (-7/1) = (-S/R) and thus prove sufficiency in Statement 1?


First of all: when a DS question asks about the value, then the statement is sufficient ONLY if you can get the single numerical value.

From r + s = 7 we cannot find the single numerical value of r/s, it can take infinitely many values:
...
r=-1 and s=8 --> r/s=-1/8;
r=1 and s=6 --> r/s=1/6;
r=2 and s=5 --> r/s=2/5;
...

Also notice that your example does not satisfy the equation at all: if r=1 and s=-7, then r + s = -6 not 7.

Hope this 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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132516 [0], given: 12324

Intern
Intern
avatar
Joined: 17 Jun 2013
Posts: 27

Kudos [?]: 2 [0], given: 7

Re: What is the ratio of r to s? [#permalink]

Show Tags

New post 16 Sep 2013, 20:13
I stumbled upon C) to be the right answer but I'm not quite sure how...
1) r+s=7
2)r^2 - s^2 = 7
(r+s)(r-s)=7
r-s=1

Is the question not asking for r/s = ?

Kudos [?]: 2 [0], given: 7

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132516 [1], given: 12324

Re: What is the ratio of r to s? [#permalink]

Show Tags

New post 17 Sep 2013, 00:34
1
This post received
KUDOS
Expert's post
Ksterr wrote:
I stumbled upon C) to be the right answer but I'm not quite sure how...
1) r+s=7
2)r^2 - s^2 = 7
(r+s)(r-s)=7
r-s=1

Is the question not asking for r/s = ?


What is the ratio of r to s?

Questions asks to find the value of r/s.

(1) r + s = 7. Infinite pairs of (r, s) satisfies this equations. Not sufficient.

(2) r^2 – s^2 = 7. Infinite pairs of (r, s) satisfies this equations. Not sufficient.

(1)+(2) From (2) we know that (r - s)(r + s) = 7, since from (1) r + s = 7, then (r - s)*7 = 7, which gives r - s = 1. Solving r + s = 7 and r - s = 1 gives r = 4 and s = 3 --> r/s = 4/3. Sufficient.

Answer: C.

Hope it's clear.
_________________

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132516 [1], given: 12324

Intern
Intern
avatar
Joined: 13 Mar 2014
Posts: 1

Kudos [?]: [0], given: 0

Manhattan GMAT CAT Question [#permalink]

Show Tags

New post 20 May 2014, 21:00
I came across a question in one of my CAT practice exams and I thought I answered it correctly, but it turns out I was wrong. But I have no idea why my solution is not valid as I get the same answer as the solutions manual (just with a different approach). Can someone clarify this for me?

Thank you!

What is the ratio of r to s?

(1) r + s = 7

(2) r^2 – s^2 = 7

I answered (B) - statement 2 is sufficient. My reasoning was:

Numbers: 1, 2, 3, 4, 5, 6 etc
Their perfect square: 1, 4, 9, 16, 25 etc.
There is only one occasion in which the difference between two squared numbers is 7 and this 16-9 or 4^2 - 3^2. Thus the ratio of r/s would be 4/3.
Even if you use -1, -2, -3, -4, -5, -6 etc it makes no difference because you still get 4/3.

The solution states that you need both (answer C) in order to solve the problem (and they come up with 4/3 as well). Now using both statements is perfectly valid but why can't I get away with using only (2)?

Any help would be much appreciated!

Kudos [?]: [0], given: 0

1 KUDOS received
Director
Director
User avatar
Joined: 25 Apr 2012
Posts: 722

Kudos [?]: 864 [1], given: 724

Location: India
GPA: 3.21
WE: Business Development (Other)
Premium Member Reviews Badge
Re: Manhattan GMAT CAT Question [#permalink]

Show Tags

New post 20 May 2014, 21:56
1
This post received
KUDOS
zsoltvigh wrote:
I came across a question in one of my CAT practice exams and I thought I answered it correctly, but it turns out I was wrong. But I have no idea why my solution is not valid as I get the same answer as the solutions manual (just with a different approach). Can someone clarify this for me?

Thank you!

What is the ratio of r to s?

(1) r + s = 7

(2) r^2 – s^2 = 7

I answered (B) - statement 2 is sufficient. My reasoning was:

Numbers: 1, 2, 3, 4, 5, 6 etc
Their perfect square: 1, 4, 9, 16, 25 etc.
There is only one occasion in which the difference between two squared numbers is 7 and this 16-9 or 4^2 - 3^2. Thus the ratio of r/s would be 4/3.
Even if you use -1, -2, -3, -4, -5, -6 etc it makes no difference because you still get 4/3.

The solution states that you need both (answer C) in order to solve the problem (and they come up with 4/3 as well). Now using both statements is perfectly valid but why can't I get away with using only (2)?

Any help would be much appreciated!


Hello zsoltvigh,

Welcome to Gmatclub..

The Question is discussed here : what-is-the-ratio-of-r-to-s-110947.html#p1267783
As you scroll through the posts in the above link you will find the answer as C and not B....(Hint consider a case where s=0....and see what you get as ratio r/s what-is-the-ratio-of-r-to-s-110947.html#p1251159)

Note that when you have some doubts on questions especially from MGMAT Test or Veritas prep test, use the search option to check if the question has been discussed before.It will get you answers faster than waiting for response.....

If you don't find you are more than welcome to post it on the Forum
_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Kudos [?]: 864 [1], given: 724

Manager
Manager
User avatar
Joined: 20 Dec 2013
Posts: 130

Kudos [?]: 109 [0], given: 1

Re: What is the ratio of r to s? [#permalink]

Show Tags

New post 20 May 2014, 22:11
banksy wrote:
What is the ratio of r to s?

(1) r + s = 7
(2) r^2 – s^2 = 7


Statement I is insufficient:

r = 2, s = 5
r = 1, s = 6

Statement II is insufficient:
(r+s)(r-s) = 7
r = 4, s = 3
r = -4, s = 3

Combining is sufficient:
r + s = 7
(r+s) (r-s) = 7
r - s = 1, r + s = 7
We get definite values of r and s hence answer is C.
_________________

76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views

Perfect Scores
http://perfectscores.org
http://www.youtube.com/perfectscores

Kudos [?]: 109 [0], given: 1

Intern
Intern
avatar
Joined: 25 Mar 2014
Posts: 4

Kudos [?]: 2 [0], given: 13

WE: Information Technology (Computer Software)
Re: What is the ratio of r to s? [#permalink]

Show Tags

New post 20 May 2014, 23:39
It's better to use algerabic forumale rather than picking numbers as the exponent is 2.

Also R power 2 - S power 2 can be written as (R+S)(R-S).

I used statement 1 to deduct R-S.

Then Combine Statement1 and R-S to get the value of R.

Obviously we will get S value from any statement. No need to calculate as its a DS q.

I might belong to that band which assumes given variables are integers though it's not explicitly given.

Kudos!

Kudos [?]: 2 [0], given: 13

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132516 [0], given: 12324

Re: Manhattan GMAT CAT Question [#permalink]

Show Tags

New post 21 May 2014, 01:41
Expert's post
1
This post was
BOOKMARKED
zsoltvigh wrote:
I came across a question in one of my CAT practice exams and I thought I answered it correctly, but it turns out I was wrong. But I have no idea why my solution is not valid as I get the same answer as the solutions manual (just with a different approach). Can someone clarify this for me?

Thank you!

What is the ratio of r to s?

(1) r + s = 7

(2) r^2 – s^2 = 7

I answered (B) - statement 2 is sufficient. My reasoning was:

Numbers: 1, 2, 3, 4, 5, 6 etc
Their perfect square: 1, 4, 9, 16, 25 etc.
There is only one occasion in which the difference between two squared numbers is 7 and this 16-9 or 4^2 - 3^2. Thus the ratio of r/s would be 4/3.
Even if you use -1, -2, -3, -4, -5, -6 etc it makes no difference because you still get 4/3.

The solution states that you need both (answer C) in order to solve the problem (and they come up with 4/3 as well). Now using both statements is perfectly valid but why can't I get away with using only (2)?

Any help would be much appreciated!


Merging similar topics. Please refer to the discussion above.

P.S. please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 1, 2, and 3. Thank you.
_________________

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132516 [0], given: 12324

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15703

Kudos [?]: 281 [0], given: 0

Premium Member
Re: What is the ratio of r to s? [#permalink]

Show Tags

New post 16 Apr 2016, 01:23
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 281 [0], given: 0

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15703

Kudos [?]: 281 [0], given: 0

Premium Member
Re: What is the ratio of r to s? [#permalink]

Show Tags

New post 03 May 2017, 11:30
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 281 [0], given: 0

Director
Director
avatar
S
Joined: 12 Nov 2016
Posts: 794

Kudos [?]: 36 [0], given: 165

Re: What is the ratio of r to s? [#permalink]

Show Tags

New post 08 Sep 2017, 20:41
banksy wrote:
What is the ratio of r to s?

(1) r + s = 7
(2) r^2 – s^2 = 7


St 1

clearly insuff too many possibilities

St 2

rewrite

(r +s)(r-s) =7

more than one possibility as do not know whether r and s should be integers, negative numbers etc

St 1 and St 2

We have a system of linear equations because

7(r-s) =7

r +s =7
r-s =1

S =3

C

Kudos [?]: 36 [0], given: 165

Re: What is the ratio of r to s?   [#permalink] 08 Sep 2017, 20:41
Display posts from previous: Sort by

What is the ratio of r to s?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.