The line 3x + 4y = 8 passes through all of the quadrants in : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

It is currently 05 Dec 2016, 08:38
GMAT Club Tests

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The line 3x + 4y = 8 passes through all of the quadrants in

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

Hide Tags

3 KUDOS received
Manager
Manager
avatar
Joined: 02 Nov 2009
Posts: 138
Followers: 3

Kudos [?]: 162 [3] , given: 97

The line 3x + 4y = 8 passes through all of the quadrants in [#permalink]

Show Tags

New post 09 Oct 2012, 11:28
3
This post received
KUDOS
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

71% (01:32) correct 29% (00:42) wrong based on 280 sessions

HideShow timer Statistics

The line 3x + 4y = 8 passes through all of the quadrants in the coordinate plane except:

A. I
B. II
C. III
D. IV
E. II and IV.
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Oct 2012, 12:56, edited 3 times in total.
Edited the question and added the OA.
Expert Post
5 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35867
Followers: 6839

Kudos [?]: 89945 [5] , given: 10382

Re: The line 3x + 4y = 8 passes through all of the quadrants in [#permalink]

Show Tags

New post 09 Oct 2012, 13:21
5
This post received
KUDOS
Expert's post
venmic wrote:
The line 3x + 4y = 8 passes through all of the quadrants in the coordinate plane except:

A. I
B. II
C. III
D. IV
E. II and IV.


Notice that if both x and y are negative, then both 3x and 4y will be negative. The sum of two negative values (3x and 4y) cannot give positive result (8). Thereore the line does not pass through the third quadrant, where both x and y are negative.

Answer: C.

Check the diagram below:
Attachment:
graph.png
graph.png [ 6.97 KiB | Viewed 6349 times ]
Hope it's clear.
_________________

New to the Math Forum?
Please read this: 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

1 KUDOS received
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 98

Kudos [?]: 866 [1] , given: 43

Re: The line 3x + 4y = 8 passes through all of the quadrants in [#permalink]

Show Tags

New post 09 Oct 2012, 15:14
1
This post received
KUDOS
venmic wrote:
The line 3x + 4y = 8 passes through all of the quadrants in the coordinate plane except:

A. I
B. II
C. III
D. IV
E. II and IV.


This is a line which doesn't pass through the origin. We know because there is a free term (which doesn't contain neither \(x,\) nor \(y\)).
In this case, we can use the intercept form of the line equation: divide through the equation by the free term 8. We get:
\(\frac{3x}{8}+\frac{4y}{8}=1\) or \(\frac{x}{8/3}+\frac{y}{8/2}=1\), and finally \(\frac{x}{2\frac{2}{3}}+\frac{y}{2}=1\).

Now, we can easily see that the \(x\) intercept is \(2\frac{2}{3}\) and the \(y\) intercept is \(2.\)
So, our line passes through the points \((2\frac{2}{3},0)\) and \((0,2)\). Sketch the line through these two points.
It is a decreasing line which doesn't pass through the third quadrant.

Answer C.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 12874
Followers: 559

Kudos [?]: 157 [0], given: 0

Premium Member
Re: The line 3x + 4y = 8 passes through all of the quadrants in [#permalink]

Show Tags

New post 25 Jan 2014, 03:54
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

Intern
Intern
User avatar
Joined: 14 May 2014
Posts: 45
Followers: 0

Kudos [?]: 40 [0], given: 1

Re: The line 3x + 4y = 8 passes through all of the quadrants in [#permalink]

Show Tags

New post 21 May 2014, 05:50
Line : 3x + 4y = 8

Given line can be written as

x/(8/3) + y/(8/4) = 1

Comparing with the intercept form of the equation of line we get x axis intercept as 8/3 and y axis intercept as 8/4 = 2.

So this line cut an intercept of 8/3 on x axis and 2 on y axis.

Attachment:
File comment: intercept
gmat234.jpg
gmat234.jpg [ 18.45 KiB | Viewed 4743 times ]


From fig.. Line does not pass through quadrant III. Hence answer is C
_________________

Help me with Kudos if it helped you "

Mathematics is a thought process.

1 KUDOS received
Intern
Intern
avatar
Joined: 08 Apr 2016
Posts: 3
Followers: 0

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

The line 3x + 4y = 8 passes through all of the quadrants in [#permalink]

Show Tags

New post 22 Apr 2016, 03:34
1
This post received
KUDOS
The easiest method would be to find and x and y intercept of this line

To find x intercept put y = 0 in 3x+4y = 8 which will give x = 8/3
To find y intercept put x = 0 in 3x+4y = 8 which will give y = 2

Therefore we have 2 points on the line (8/3, 0) and (0, 2). The first point lies on +ve X-axis and second on +ve Y-axis.
You can quickly (and roughly) plot these 2 points to verify that a line joining these 2 points will pass through 1st, 2nd and 4th Quadrant. Hence it cannot pass through 3rd Quadrant.

Answer is C
Director
Director
User avatar
Joined: 04 Jun 2016
Posts: 656
GMAT 1: 750 Q49 V43
Followers: 45

Kudos [?]: 177 [0], given: 36

The line 3x + 4y = 8 passes through all of the quadrants in [#permalink]

Show Tags

New post 14 Jul 2016, 01:30
venmic wrote:
The line 3x + 4y = 8 passes through all of the quadrants in the coordinate plane except:

A. I
B. II
C. III
D. IV
E. II and IV.


The general form of line is ax+by+c=0
your equation become 3x+4y-8=0
Slope (m)=-a/b =-3/4
Slope is negative; meaning Line will like be this \ not like this | or not like this / (i hope you get what i am trying to say)
Y intercept=-c/b=-(-8)/4=2
Y intercept is 2; meaning line will start at Quadrant II ; Then touch the positive Y axis at 2; Then pass through Quadrant I ; Then touch X axis and then enter Quadrant IV
The line will never pass through Quadrant III (SEE ATTACHED FILE)

Hence C is the answer.

Image
_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016.

The line 3x + 4y = 8 passes through all of the quadrants in   [#permalink] 14 Jul 2016, 01:30
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic If -3x+4y=28 and 3x-2y=8, what is the product of x and y? Bunuel 2 14 Jul 2016, 00:47
3 Experts publish their posts in the topic The slope of the line passing through the point (5,5) is 5/6. All of Bunuel 2 16 May 2016, 01:43
6 In a rectangular coordinate system, if a line passes through the point vatsavayi 4 23 Oct 2014, 00:17
25 Experts publish their posts in the topic In the coordinate plane, line k passes through the origin an Bunuel 12 19 Feb 2014, 00:17
42 Experts publish their posts in the topic If P and Q are two points on the line 3x + 4y =-15 such that kobinaot 19 21 Oct 2010, 05:47
Display posts from previous: Sort by

The line 3x + 4y = 8 passes through all of the quadrants in

  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 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®.