It is currently 18 Nov 2017, 16:50

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

Is rst <= 1?

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

Hide Tags

Current Student
avatar
Status: Up again.
Joined: 31 Oct 2010
Posts: 526

Kudos [?]: 546 [0], given: 75

Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40
GMAT 2: 740 Q49 V42
Is rst <= 1? [#permalink]

Show Tags

New post 30 Dec 2010, 06:23
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

46% (01:23) correct 54% (02:09) wrong based on 124 sessions

HideShow timer Statistics

Is rst ≤ 1?

(1) rs + rt = 5
(2) r + st = 2
[Reveal] Spoiler: OA

_________________

My GMAT debrief: http://gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html

Kudos [?]: 546 [0], given: 75

Expert Post
4 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132617 [4], given: 12326

Re: Algebra DS [#permalink]

Show Tags

New post 30 Dec 2010, 06:48
4
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
gmatpapa wrote:
Is rst ≤ 1?

(1) rs + rt = 5
(2) r + st = 2


Is rst ≤ 1?

(1) rs + rt = 5 --> \(r=\frac{5}{s+t}\) --> question becomes: is \(\frac{5st}{s+t}\leq{1}\)? --> is \(\frac{st}{s+t}\leq{\frac{1}{5}}\)? Now, if \(s\) and \(t\) are large enough positive numbers (for example 2 and 3) then the asnwer will be NO but if one of them equals to zero then the answer will be YES. Not sufficient.

(2) r + st = 2 --> \(st=2-r\) --> question becomes: is \(r(2-r)\leq{1}\)? --> is \(2r-r^2\leq{1}\)? --> is \(r^2-2r+1\geq{0}\)? --> is \((r-1)^2\geq{0}\)? As square of some expression is always more than or equal to zero then the answer to this question is always YES. Sufficient.

Answer: B.

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 [?]: 132617 [4], given: 12326

Current Student
avatar
Status: Up again.
Joined: 31 Oct 2010
Posts: 526

Kudos [?]: 546 [0], given: 75

Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40
GMAT 2: 740 Q49 V42
Re: Algebra DS [#permalink]

Show Tags

New post 30 Dec 2010, 09:03
Yes it is clear. With your explanation I also learnt a situation where equation can be manipulated to check sufficiency. very useful.. Kudos!!
_________________

My GMAT debrief: http://gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html

Kudos [?]: 546 [0], given: 75

Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7736

Kudos [?]: 17780 [1], given: 235

Location: Pune, India
Re: Algebra DS [#permalink]

Show Tags

New post 30 Dec 2010, 20:49
1
This post received
KUDOS
Expert's post
gmatpapa wrote:
Is rst ≤ 1?

(1) rs + rt = 5
(2) r + st = 2
(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.


The question is testing you on the following concept:
If the sum of two non negative numbers is constant, their product is greatest when the numbers are equal. e.g. if a + b = 10, then ab is maximum when a = b = 5. Maximum value of ab = 5*5 = 25


Stmnt 1: Given rs + rt is constant, the maximum value of rs*rt will be when rs = rt = 5/2. Maximum value of \(r^2st= (5/2)*(5/2) = 25/4.\)
But we get no information about maximum value of rst so not sufficient.

Stmnt 2: Given r + st = 2, then maximum value of r*st will be when r = st = 1.
Maximum value of rst = 1 i.e. rst <= 1. Sufficient.

Answer (B).

Note here that though they haven't said that the numbers are non-negative, we can easily see that the product can be less than 1. We only need to worry about the product greater than 1. In that case, since the sum is positive and product we need is positive, we only need to worry about positive numbers.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17780 [1], given: 235

Manager
Manager
avatar
Joined: 02 Oct 2010
Posts: 145

Kudos [?]: 50 [0], given: 29

Re: Algebra DS [#permalink]

Show Tags

New post 19 Jan 2011, 22:12
Bunuel wrote:
gmatpapa wrote:
Is rst ≤ 1?

(1) rs + rt = 5
(2) r + st = 2


Is rst ≤ 1?

(1) rs + rt = 5 --> \(r=\frac{5}{s+t}\) --> question becomes: is \(\frac{5st}{s+t}\leq{1}\)? --> is \(\frac{st}{s+t}\leq{\frac{1}{5}}\)? Now, if \(s\) and \(t\) are large enough positive numbers (for example 2 and 3) then the asnwer will be NO but if one of them equals to zero then the answer will be YES. Not sufficient.

(2) r + st = 2 --> \(st=2-r\) --> question becomes: is \(r(2-r)\leq{1}\)? --> is \(2r-r^2\leq{1}\)? --> is \(r^2-2r+1\geq{0}\)? --> is \((r-1)^2\geq{0}\)? As square of some expression is always more than or equal to zero then the answer to this question is always YES. Sufficient.

Answer: B.

Hope it's clear.


Hello Bunnel,

In the second statement you have concluded that rst > = 0 which does not state that it has to be >=1. which the Q has asked to find... since it can have values from 0 to 1.
Please correct me if I am wrong..

Kudos [?]: 50 [0], given: 29

Current Student
avatar
Status: Up again.
Joined: 31 Oct 2010
Posts: 526

Kudos [?]: 546 [0], given: 75

Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40
GMAT 2: 740 Q49 V42
Re: Algebra DS [#permalink]

Show Tags

New post 19 Jan 2011, 22:41
jullysabat wrote:
Bunuel wrote:
gmatpapa wrote:
Is rst ≤ 1?

(1) rs + rt = 5
(2) r + st = 2


Is rst ≤ 1?

(1) rs + rt = 5 --> \(r=\frac{5}{s+t}\) --> question becomes: is \(\frac{5st}{s+t}\leq{1}\)? --> is \(\frac{st}{s+t}\leq{\frac{1}{5}}\)? Now, if \(s\) and \(t\) are large enough positive numbers (for example 2 and 3) then the asnwer will be NO but if one of them equals to zero then the answer will be YES. Not sufficient.

(2) r + st = 2 --> \(st=2-r\) --> question becomes: is \(r(2-r)\leq{1}\)? --> is \(2r-r^2\leq{1}\)? --> is \(r^2-2r+1\geq{0}\)? --> is \((r-1)^2\geq{0}\)? As square of some expression is always more than or equal to zero then the answer to this question is always YES. Sufficient.

Answer: B.

Hope it's clear.


Hello Bunnel,

In the second statement you have concluded that rst > = 0 which does not state that it has to be >=1. which the Q has asked to find... since it can have values from 0 to 1.
Please correct me if I am wrong..


Hi,

Let me answer that before Bunuel the Boss comes. If you see, What has been concluded is not \(rst >= 0\) but \((r-1)^2>=0\). Follow the procedure Bunuel has demonstrated. The statement has been manipulated, leading to mean that the question: Is \(rst< = 1\) is the same as Is \((r-1)^2 > =0\).

Hope its clear!
_________________

My GMAT debrief: http://gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html

Kudos [?]: 546 [0], given: 75

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132617 [0], given: 12326

Re: Is rst <= 1? [#permalink]

Show Tags

New post 22 Feb 2014, 14:23

Kudos [?]: 132617 [0], given: 12326

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15704

Kudos [?]: 282 [0], given: 0

Premium Member
Re: Is rst <= 1? [#permalink]

Show Tags

New post 10 Nov 2015, 01:38
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 [?]: 282 [0], given: 0

BSchool Forum Moderator
avatar
P
Joined: 12 Aug 2015
Posts: 2213

Kudos [?]: 869 [0], given: 602

GMAT ToolKit User Premium Member
Re: Is rst <= 1? [#permalink]

Show Tags

New post 13 Mar 2016, 07:27
Its a classic problem where we have to substitute an equality into an inequality to get the answer..
_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 869 [0], given: 602

Re: Is rst <= 1?   [#permalink] 13 Mar 2016, 07:27
Display posts from previous: Sort by

Is rst <= 1?

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


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®.