Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 28 Oct 2016, 07:33

### 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

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Nov 2009
Posts: 138
Followers: 2

Kudos [?]: 151 [3] , given: 97

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

### Show Tags

09 Oct 2012, 12:28
3
KUDOS
5
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

72% (01:31) correct 28% (00:43) wrong based on 272 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, 13:56, edited 3 times in total.
Edited the question and added the OA.
Math Expert
Joined: 02 Sep 2009
Posts: 35336
Followers: 6650

Kudos [?]: 85933 [5] , given: 10263

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

### Show Tags

09 Oct 2012, 14:21
5
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.

Check the diagram below:
Attachment:

graph.png [ 6.97 KiB | Viewed 6119 times ]
Hope it's clear.
_________________
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 93

Kudos [?]: 846 [1] , given: 43

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

### Show Tags

09 Oct 2012, 16:14
1
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.

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12277
Followers: 542

Kudos [?]: 152 [0], given: 0

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

### Show Tags

25 Jan 2014, 04:54
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.
_________________
Intern
Joined: 14 May 2014
Posts: 45
Followers: 0

Kudos [?]: 39 [0], given: 1

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

### Show Tags

21 May 2014, 06:50
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 [ 18.45 KiB | Viewed 4513 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.

Intern
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

22 Apr 2016, 04:34
1
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.

Director
Joined: 04 Jun 2016
Posts: 656
GMAT 1: 750 Q49 V43
Followers: 40

Kudos [?]: 155 [0], given: 36

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

### Show Tags

14 Jul 2016, 02:30
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
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)

_________________

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, 02:30
Similar topics Replies Last post
Similar
Topics:
If -3x+4y=28 and 3x-2y=8, what is the product of x and y? 2 14 Jul 2016, 01:47
2 The slope of the line passing through the point (5,5) is 5/6. All of 2 16 May 2016, 02:43
6 In a rectangular coordinate system, if a line passes through the point 4 23 Oct 2014, 01:17
24 In the coordinate plane, line k passes through the origin an 12 19 Feb 2014, 01:17
42 If P and Q are two points on the line 3x + 4y =-15 such that 19 21 Oct 2010, 06:47
Display posts from previous: Sort by