It is currently 23 Feb 2018, 00:52

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

In the xy-coordinate plane, line l passes through the point (-3, 0).

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

Hide Tags

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43891
In the xy-coordinate plane, line l passes through the point (-3, 0). [#permalink]

Show Tags

New post 12 Nov 2014, 09:09
1
This post received
KUDOS
Expert's post
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

77% (00:50) correct 23% (00:44) wrong based on 147 sessions

HideShow timer Statistics

Tough and Tricky questions: Coordinate Geometry.



In the xy-coordinate plane, line \(l\) passes through the point \((-3, 0)\). Does line \(l\) pass through the point \((0, \frac{3}{4})\)?


(1) The slope of line \(l\) is \(\frac{1}{4}\).

(2) Line \(l\) passes through the point \((5, 2)\).

Kudos for a correct solution.
[Reveal] Spoiler: OA

_________________

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

1 KUDOS received
Current Student
avatar
Joined: 07 Oct 2014
Posts: 160
GMAT 1: 710 Q48 V39
WE: Sales (Other)
Re: In the xy-coordinate plane, line l passes through the point (-3, 0). [#permalink]

Show Tags

New post 12 Nov 2014, 09:19
1
This post received
KUDOS
In the xy-coordinate plane, line l passes through the point (-3, 0). Does line l pass through the point (0, \frac{3}{4})?


(1) The slope of line l is \frac{1}{4}.

(2) Line l passes through the point (5, 2).


1). With this slope, the line increases height by 1/4 for each movement towards a higher X value. -3 to 0 is 3 movements. 3*1/4 = 3/4. sufficient.

2) delta y over delta x is slope. (2-0) / (5-(-3)) = 2/8 = 1/4 = same as 1) = sufficient.

Answer is D?
1 KUDOS received
Manager
Manager
avatar
Joined: 10 Sep 2014
Posts: 98
Re: In the xy-coordinate plane, line l passes through the point (-3, 0). [#permalink]

Show Tags

New post 12 Nov 2014, 09:49
1
This post received
KUDOS
statement 1: sufficient
no need for calculations, since we are given a starting point, we can use the slope to draw the line and see if it passes through (0, 3/4).

statement 2: sufficient
we now have 2 points on of the line and with this we can figure out the slope and figure out if it passes through (0, 3/4). again, no need for calculations :)

Answer D!
Manager
Manager
avatar
Joined: 22 Sep 2012
Posts: 141
Concentration: Strategy, Technology
WE: Information Technology (Computer Software)
Re: In the xy-coordinate plane, line l passes through the point (-3, 0). [#permalink]

Show Tags

New post 12 Nov 2014, 19:16
Statement 1: The slope of line l is 1/4 .

We can find out the equation of the line , 1/4(x+3)=y, and therefore by replacing x by 0 and y by 3/4, we know that the line passes through the point. Sufficient

Statement 2: Line l passes through the point (5, 2).

Similarly, we can find the equation of the line and then equate it with (0,3/4). Sufficient

D) should be the answer
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43891
Re: In the xy-coordinate plane, line l passes through the point (-3, 0). [#permalink]

Show Tags

New post 13 Nov 2014, 08:14
Expert's post
2
This post was
BOOKMARKED
Bunuel wrote:

Tough and Tricky questions: Coordinate Geometry.



In the xy-coordinate plane, line \(l\) passes through the point \((-3, 0)\). Does line \(l\) pass through the point \((0, \frac{3}{4})\)?


(1) The slope of line \(l\) is \(\frac{1}{4}\).

(2) Line \(l\) passes through the point \((5, 2)\).

Kudos for a correct solution.


Official Solution:


We start by writing the equation of line \(l\) in slope-intercept form: \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. We are asked if the line passes through \((0, \frac{3}{4})\). Recall that the y-intercept is the point where the line crosses the y-axis, or, equivalently, the point on the line where \(x = 0\). Therefore, \((0, \frac{3}{4})\) is a potential y-intercept. We must determine if, in the equation of line \(l\), \(b\) is equal to \(\frac{3}{4}\).

Statement 1 gives us the slope of the line, which we can plug into the equation: \(y = \frac{1}{4}x + b\). In the prompt, we are also given a point on the line: \((-3, 0)\). Plugging in this point makes the equation: \(0 = \frac{1}{4}(-3) + b\). This simplifies to \(b = \frac{3}{4}\), and so line \(l\) does pass through the point \((0, \frac{3}{4})\). Statement 1 is sufficient to answer the question. Eliminate answer choices B, C, and E. The correct answer choice must be A or D.

Statement 2 tells us that line \(l\) passes through the point \((5, 2)\). Along with the x-intercept, \((-3, 0)\), we now have two points on the line, which is enough to find the slope. As we saw with statement 1, knowing the slope and one point on the line is enough to find the y-intercept. Since we can find the y-intercept, we know that we can find the answer to the question, even though we do not yet know whether the answer is yes or no. Therefore, statement 2 is also sufficient to answer the question.

Answer choice D is correct.

Recall that when we are given two points, we can always find the slope: \(slope = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}\). In this case, since our two points are \((-3, 0)\) and \((5, 2)\), \(m = \frac{0 - 2}{-3 - 5} = \frac{-2}{-8} = \frac{1}{4}\). We saw in examining statement 1 that if line \(l\) has slope equal to \(\frac{1}{4}\) and passes through the point \((-3, 0)\), it will have a y-intercept of \(\frac{3}{4}\), as desired.


Answer: D.
_________________

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

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13792
Premium Member
Re: In the xy-coordinate plane, line l passes through the point (-3, 0). [#permalink]

Show Tags

New post 15 May 2017, 18:31
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

Re: In the xy-coordinate plane, line l passes through the point (-3, 0).   [#permalink] 15 May 2017, 18:31
Display posts from previous: Sort by

In the xy-coordinate plane, line l passes through the point (-3, 0).

  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®.