if x and y are positive is 4x > 3y ? (1) x > y - x (2)

Oldest

Best Reply

Author

Message

TAGS:

Senior Manager

Joined: 28 Aug 2010

Posts: 280

Followers: 3

Kudos [?]: 20 [1] , given: 11

if x and y are positive is 4x > 3y ? (1) x > y - x (2) [#permalink]

14 Dec 2010, 18:22

This post received
KUDOS

00:00

Question Stats:

57% (01:37) correct

42% (00:53) wrong

based on 0 sessions

if x and y are positive is 4x > 3y ?

(1) x > y - x
(2) x/y < 1

Can someone provide good pointers into handling such question. I also have a doubt about the ans. thanks

[Reveal] Spoiler: OA

_________________

Verbal:new-to-the-verbal-forum-please-read-this-first-77546.html
Math: new-to-the-math-forum-please-read-this-first-77764.html
Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html
-------------------------------------------------------------------------------------------------
Ajit

Veritas Prep GMAT Instructor

Joined: 16 Oct 2010

Posts: 3113

Location: Pune, India

Followers: 572

Kudos [?]: 2017 [1] , given: 92

Re: if x and y are positive is 4x > 3y [#permalink]

14 Dec 2010, 19:48

This post received
KUDOS

ajit257 wrote:

if x and y are positive is 4x > 3y ?

(1) x > y - x
(2) x/y < 1

Can someone provide good pointers into handling such question. I also have a doubt about the ans. thanks

Since x and y are positive, you can multiply/divide the inequality by them. Now, another thing is that it is hard to wrap your head around a question if it has more than one variables. So try to get the variables together so that you can consider them a single variable.
is 4x > 3y ?
I can change this to: is x/y > 3/4?

Stmnt 1: x > y - x
2x > y
x/y > 1/2
So we know that x/y is greater than 1/2 but we do not know whether it is greater than 3/4. Not sufficient.

Stmnt 2: x/y < 1
So we know that x/y is less than 1 but we still do not know whether x/y is greater than or less than 3/4. Not sufficient.

Using both statements, we know x/y is greater than 1/2 and less than 1 but we still do not know whether it is greater than or less than 3/4. Not sufficient.

Answer (E).
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save 10% on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Current Student

Status: Bring the Rain

Joined: 17 Aug 2010

Posts: 410

Location: United States (MD)

Concentration: Strategy, Marketing

Schools: Michigan (Ross) - Class of 2014

GMAT 1: 730 Q49 V39

GPA: 3.13

WE: Corporate Finance (Aerospace and Defense)

Followers: 6

Kudos [?]: 42 [0], given: 46

Re: if x and y are positive is 4x > 3y [#permalink]

14 Dec 2010, 19:53

This is how I would have done it:

Question: is 4x>3y
Or is (x/y)>(3/4)?

Stmt1 -- Given x>y-x
Hence, 2x>y or (x/y)>(1/2) --INSUFF

Stmt 2 -- Given (x/y)<1 --INSUFF

Together 1/2<x/y<1 INSUFF

My answer would be E
_________________

Go Blue!

Find out what's new at GMAT Club - latest features and updates

Manager

Status: Preparing for GMAT - March 2011

Joined: 21 May 2010

Posts: 150

Location: London

Schools: INSEAD, RSM, HEC, St. Gallen, IF, IESE

WE 1: Finance 6 years

Followers: 5

Kudos [?]: 8 [0], given: 0

Re: if x and y are positive is 4x > 3y [#permalink]

17 Dec 2010, 04:41

thanks VeritasPrepKarishma
_________________

In The World Full Of Duplicates,, I Am The Only Masterpiece..
Girl Power
beat-the-beast-with-non-native-speaker-108349.html

Senior Manager

Joined: 28 Aug 2010

Posts: 280

Followers: 3

Kudos [?]: 20 [0], given: 11

Re: if x and y are positive is 4x > 3y [#permalink]

17 Dec 2010, 09:11

Karishma,
Thanks! I do have a small doubt though...when should you solve such questions using algebraic approach and when should you take the intuitive approach. I always get caught up in this dilemma.
_________________

Veritas Prep GMAT Instructor

Joined: 16 Oct 2010

Posts: 3113

Location: Pune, India

Followers: 572

Kudos [?]: 2017 [1] , given: 92

Re: if x and y are positive is 4x > 3y [#permalink]

17 Dec 2010, 19:36

This post received
KUDOS

ajit257 wrote:

First of all, one method is not better than the other. They both have their pros and cons. I like logical approach for most questions since it helps in finding the answer very quickly. On the other hand, using the algebraic approach, you don't need to think very much. Just make equations and solve. Also the probability that you will overlook something is less using algebraic approach. Ideally, you need to be comfortable with both. Different questions demand a different approach but during the exam, pick the one which comes first to mind and with which you are comfortable. For inequality questions, I prefer to use algebra since using logic too takes time.. It isn't as intuitive as in the case of arithmetic... Numbers between 0 and 1 behave in a different manner and those between 1 and infinity behave in a different manner. Similarly negative number follow their own rules too.... So if I can see simple straight forward algebra, I use it for inequalities. Else you have to use logic, plug in number etc....
_________________

Intern

Joined: 15 Jul 2010

Posts: 3

Followers: 0

Kudos [?]: 0 [0], given: 11

Re: if x and y are positive is 4x > 3y [#permalink]

28 Dec 2010, 00:32

Hi,
Can anyone plz explain the above question using graphical method.

Thanks
Animesh

Veritas Prep GMAT Instructor

Joined: 16 Oct 2010

Posts: 3113

Location: Pune, India

Followers: 572

Kudos [?]: 2017 [1] , given: 92

Re: if x and y are positive is 4x > 3y [#permalink]

28 Dec 2010, 09:53

This post received
KUDOS

animeshsen wrote:

Hi,
Can anyone plz explain the above question using graphical method.

Thanks
Animesh

Look at the diagrams below.

Attachment:

Ques5.jpg [ 43.99 KiB | Viewed 1936 times ]

The first one shows the region asked in the question stem: is 4x > 3y? or is 4x - 3y > 0? (The Green region in the first diagram. If you have a doubt on how the regions were drawn, let me know. I will guide you to the related blog.)
The second and third show the statements 1 and 2 respectively
1. x > y - x or 2x - y > 0 (shown by the Red region)
2. x/y < 1 or x - y < 0 (shown by the Blue region)
Since Red and Blue regions have points that are not in Green region, a point satisfying 2x - y > 0 or x - y < 0 doesn't necessarily satisfy 4x - 3y > 0. So each alone is not sufficient.
Look at the last diagram now. Using both 1 and 2 together, we get the points that satisfy both inequalities: 2x - y > 0 and x - y < 0. (Region where Red and Blue overlap) Even here, some points will lie in Green region, some will not. Hence, even together, the statements are not enough. Answer (E).

I intend to take this question in detail on the Veritas Blog. If interested, go to http://www.veritasprep.com/blog/ and search for "Quarter Wit Quarter Wisdom" in the upcoming days.
_________________

Intern

Joined: 15 Jul 2010

Posts: 3

Followers: 0

Kudos [?]: 0 [0], given: 11

Re: if x and y are positive is 4x > 3y [#permalink]

29 Dec 2010, 00:33

Thanks Karishma,
The explanation is really nice and what exactly I wanted.... Can you please tell me more about solving inequalities using graphs(some links..etc)

thanks
Animesh

Veritas Prep GMAT Instructor

Joined: 16 Oct 2010

Posts: 3113

Location: Pune, India

Followers: 572

Kudos [?]: 2017 [0], given: 92

Re: if x and y are positive is 4x > 3y [#permalink]

29 Dec 2010, 20:18

animeshsen wrote:

Thanks Karishma,
The explanation is really nice and what exactly I wanted.... Can you please tell me more about solving inequalities using graphs(some links..etc)

thanks
Animesh

Check out a couple of questions on gmat club where I have given graphical solutions:
http://gmatclub.com/forum/is-the-line-s-intercept-with-axis-x-greater-than-r-94505.html#p810874
http://gmatclub.com/forum/2-sums-with-modulus-and-inequality-both-103746.html#p808305
[url]
ps-triple-modul-1185.html#p807380[/url]
though the mod questions are higher level...

Also, as I mentioned before, check out Veritas blog:
http://www.veritasprep.com/blog/2010/12/quarter-wit-quarter-wisdom-bagging-the-graphs/
http://www.veritasprep.com/blog/2010/12/quarter-wit-quarter-wisdom-bagging-the-graphs-part-ii/
I will put up a part 3 discussing this question by the end of the week...

In addition, try solving questions using graphs and if you get stuck, pm me... Also, I think shrouded1 here uses graphs frequently too so you can check some of his/her solutions as well..
_________________

Manager

Joined: 17 Dec 2010

Posts: 100

Location: Australia

GMAT 1: 690 Q48 V37

GPA: 3.37

WE: Engineering (Consulting)

Followers: 1

Kudos [?]: 17 [0], given: 15

Re: if x and y are positive is 4x > 3y [#permalink]

29 Dec 2010, 20:25

I'm finding that the best way to get better at these problems is to see heaps and heaps of problems

I still get caught up with silly mistakes - I've really gotta start getting into some sample questions to start getting a feel for all of the different types of questions, and develop a logical system to approach all questions.
_________________

Kudos always appreciated if my post helped you

Intern

Joined: 15 Jul 2010

Posts: 3

Followers: 0

Kudos [?]: 0 [0], given: 11

Re: if x and y are positive is 4x > 3y [#permalink]

29 Dec 2010, 23:51

Wow Karishma,
Thanks so much....And thanks for the explanation too...
Kudos to you..
Animesh

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11611

Followers: 1801

Kudos [?]: 9597 [0], given: 829

Re: if x and y are positive is 4x > 3y [#permalink]

30 Dec 2010, 04:23

You can also check the following topic: "Graphic approach to problems with inequalities" by Walker - graphic-approach-to-problems-with-inequalities-68037.html
_________________

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

Veritas Prep GMAT Instructor

Joined: 16 Oct 2010

Posts: 3113

Location: Pune, India

Followers: 572

Kudos [?]: 2017 [0], given: 92

Re: if x and y are positive is 4x > 3y [#permalink]

03 Jan 2011, 11:29

animeshsen wrote:

Wow Karishma,
Thanks so much....And thanks for the explanation too...
Kudos to you..
Animesh

The post with the detailed solution is up:
http://www.veritasprep.com/blog/2011/01/quarter-wit-quarter-wisdom-bagging-the-graphs-part-iii/
_________________

Re: if x and y are positive is 4x > 3y [#permalink] 03 Jan 2011, 11:29

	Similar topics	Author	Replies	Last post
Similar Topics:	4x > 3y? 1 4x > 2y 2. x/y <1	jinesh	5	01 Feb 2006, 02:02
	If x and y are positive, is 4x > 3y? (1) x > y - x (2)	smily_buddy	7	07 Aug 2007, 13:13
	If x and y are positive is 4x>3y 1) X>Y-X 2) (X/Y)	hardaway7	2	29 Dec 2008, 11:24
	If x and y are positive, is 4x > 3y? (1) x > y - x (2)	Economist	2	22 Mar 2009, 23:22
	If x and y are positive, is 4x > 3y? (1) x > y - x (2)	udaymathapati	4	26 Aug 2010, 10:07

if x and y are positive is 4x > 3y ? (1) x > y - x (2)

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.