If x and y are positive, is 4x > 3y? : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 20 Jan 2017, 14:46

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x and y are positive, is 4x > 3y?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 06 Apr 2010
Posts: 144
Followers: 3

Kudos [?]: 658 [1] , given: 15

If x and y are positive, is 4x > 3y? [#permalink]

### Show Tags

26 Aug 2010, 09:07
1
KUDOS
00:00

Difficulty:

45% (medium)

Question Stats:

61% (02:23) correct 39% (01:10) wrong based on 140 sessions

### HideShow timer Statistics

If x and y are positive, is 4x > 3y?

(1) x > y - x
(2) x/y < 1
[Reveal] Spoiler: OA
Current Student
Joined: 29 Apr 2010
Posts: 228
Schools: Sloan R1, McCombs R1, Ross R1 (w/int), Haas R2, Kellogg R2
WE 1: Product Engineering/Manufacturing
Followers: 3

Kudos [?]: 35 [0], given: 26

### Show Tags

26 Aug 2010, 09:29
I found this easy to make X alone on each equation:

So we need to determine, is x>3y/4?

1) Simplifies to x>y/2. Not sufficient
2) Simplifies to x<y. Not sufficient

Combined: Simplifies to y/2<x<y. Not sufficient.

Ans: E
Math Expert
Joined: 02 Sep 2009
Posts: 36583
Followers: 7087

Kudos [?]: 93280 [0], given: 10555

### Show Tags

26 Aug 2010, 09:58
udaymathapati wrote:
If x and y are positive, is 4x > 3y?
(1) x > y - x
(2) x/y < 1

Given: $$x>0$$ and $$y>0$$. Question: is $$4x>3y$$?

(1) $$x>y-x$$ --> $$2x>y$$ --> $$4x>2y$$, not sufficient to say whether $$4x$$ is more than $$3y$$.

(2) $$\frac{x}{y}<1$$ --> as $$y>0$$ we can cross multiply --> $$x<y$$ --> $$4x<4y$$, not sufficient to say whether $$4x$$ is more than $$3y$$.

(1)+(2) We know that $$4x$$ is more than $$2y$$ but less than $$4y$$ --> $$2y<4x<4y$$, but from this we can not find the relationship between $$4x$$ and $$3y$$ (we have $$2y---3y---4y$$, $$4x$$ is somewhere between endpoints but we can not say whether it's between $$2y$$ and $$3y$$, equal to $$3y$$ or between $$3y$$ and $$4y$$). Not sufficient.

_________________
Manager
Joined: 06 Apr 2010
Posts: 83
Followers: 2

Kudos [?]: 37 [1] , given: 2

### Show Tags

03 Sep 2010, 06:22
1
KUDOS
udaymathapati wrote:
If x and y are positive, is 4x > 3y?
(1) x > y - x
(2) x/y < 1

from the stem: $$x/y>3/4$$?
1) $$2x>y$$
$$x/y > 1/2$$
not sufficient as $$x/y$$ could be greater or smaller than $$3/4$$
2) $$x/y < 1$$
not sufficient for the same reason
both:
$$1/2 < x/y < 1$$
still not sufficient for the same reason
Senior Manager
Joined: 28 Aug 2010
Posts: 260
Followers: 6

Kudos [?]: 553 [1] , given: 11

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

### Show Tags

14 Dec 2010, 17:22
1
KUDOS
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
_________________

Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html
-------------------------------------------------------------------------------------------------
Ajit

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7125
Location: Pune, India
Followers: 2137

Kudos [?]: 13673 [5] , given: 222

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

### Show Tags

14 Dec 2010, 18:48
5
KUDOS
Expert's post
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.

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Senior Manager Status: Bring the Rain Joined: 17 Aug 2010 Posts: 406 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: 7 Kudos [?]: 45 [1] , given: 46 Re: if x and y are positive is 4x > 3y [#permalink] ### Show Tags 14 Dec 2010, 18:53 1 This post received KUDOS 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 _________________ Senior Manager Joined: 28 Aug 2010 Posts: 260 Followers: 6 Kudos [?]: 553 [0], given: 11 Re: if x and y are positive is 4x > 3y [#permalink] ### Show Tags 17 Dec 2010, 08:11 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. _________________ 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: 7125 Location: Pune, India Followers: 2137 Kudos [?]: 13673 [3] , given: 222 Re: if x and y are positive is 4x > 3y [#permalink] ### Show Tags 17 Dec 2010, 18:36 3 This post received KUDOS Expert's post ajit257 wrote: 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. 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.... _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Intern
Joined: 15 Jul 2010
Posts: 2
Followers: 0

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

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

### Show Tags

27 Dec 2010, 23:32
Hi,
Can anyone plz explain the above question using graphical method.

Thanks
Animesh
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7125
Location: Pune, India
Followers: 2137

Kudos [?]: 13673 [2] , given: 222

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

### Show Tags

28 Dec 2010, 08:53
2
KUDOS
Expert's post
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 6230 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.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 15 Jul 2010 Posts: 2 Followers: 0 Kudos [?]: 0 [0], given: 11 Re: if x and y are positive is 4x > 3y [#permalink] ### Show Tags 28 Dec 2010, 23:33 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: 7125 Location: Pune, India Followers: 2137 Kudos [?]: 13673 [1] , given: 222 Re: if x and y are positive is 4x > 3y [#permalink] ### Show Tags 29 Dec 2010, 19:18 1 This post received KUDOS Expert's post 1 This post was BOOKMARKED 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.. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Manager
Joined: 17 Dec 2010
Posts: 98
Location: Australia
GMAT 1: 690 Q48 V37
GPA: 3.37
WE: Engineering (Consulting)
Followers: 1

Kudos [?]: 23 [0], given: 15

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

### Show Tags

29 Dec 2010, 19:25
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

Math Expert
Joined: 02 Sep 2009
Posts: 36583
Followers: 7087

Kudos [?]: 93280 [0], given: 10555

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

### Show Tags

30 Dec 2010, 03:23
You can also check the following topic: "Graphic approach to problems with inequalities" by Walker - graphic-approach-to-problems-with-inequalities-68037.html
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7125
Location: Pune, India
Followers: 2137

Kudos [?]: 13673 [1] , given: 222

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

### Show Tags

03 Jan 2011, 10:29
1
KUDOS
Expert's post
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/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13468
Followers: 575

Kudos [?]: 163 [0], given: 0

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

### Show Tags

21 May 2014, 19:24
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 Club Legend
Joined: 09 Sep 2013
Posts: 13468
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: If x and y are positive, is 4x > 3y? [#permalink]

### Show Tags

10 Feb 2016, 21:06
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 x and y are positive, is 4x > 3y?   [#permalink] 10 Feb 2016, 21:06
Similar topics Replies Last post
Similar
Topics:
4 If x and y are positive integers, is (4^x)*(1/3)^y < 1? 6 21 Jan 2015, 01:58
What is the value of (4x-y)*1/(3y)? 1 27 May 2012, 08:13
6 Is x > 3y ? 9 16 Aug 2011, 14:17
1 If -3/4*x+3y-1/2=3/2*y-1/4*x what is the value of x? 3 28 Jan 2011, 04:10
60 If xy 0, is x > y? (1) 4x = 3y (2) |y - x| = x - y 24 12 Nov 2009, 08:45
Display posts from previous: Sort by

# If x and y are positive, is 4x > 3y?

 Powered by phpBB © phpBB Group and phpBB SEO 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®.