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

It is currently 25 Jul 2014, 01:04

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In the xy-plane, if line k has negative slope and passes

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
SVP
SVP
avatar
Joined: 17 Feb 2010
Posts: 1563
Followers: 12

Kudos [?]: 184 [0], given: 6

In the xy-plane, if line k has negative slope and passes [#permalink] New post 22 May 2010, 13:41
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

61% (02:45) correct 39% (02:01) wrong based on 36 sessions
In the xy-plane, if line k has negative slope and passes through the point (s, -2), is the x-intercept of the line k positive?

(1) s = 0
(2) The y-intercept of line k is negative
[Reveal] Spoiler: OA
Manager
Manager
avatar
Joined: 19 Feb 2009
Posts: 77
Location: chennai
Followers: 3

Kudos [?]: 16 [0], given: 0

Re: Is the x-intercept of the line k positive? [#permalink] New post 22 May 2010, 14:11
Can someone help me on how to approach and solve such problems. Thanks in advance.

In the xy-plane, if line k has negative slope and passes through the point (s, -2), is the x-intercept of the line k positive?

(1) s = 0
(2) The y-intercept of line k is negative

y=mx+c
given that m is -ve & the line passes through (s,-2)

the equation of the line will be
y= -mx+c ( substitute (s,-2) in the equation )
therefore,
y+2 =-m(x-s)
y+2=-mx+ms

question is x intercept of line is +ve.,
to find x intercept, put y=0. so the equation will be,x=(ms-2)/m;
Condition 1) if S=0; then x will be -ve

Condition 2) The y-intercept of line k is negative
we cant deducew any thing from it.


Ans - A)
Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18733
Followers: 3243

Kudos [?]: 22380 [3] , given: 2616

Re: Is the x-intercept of the line k positive? [#permalink] New post 22 May 2010, 14:57
3
This post received
KUDOS
Expert's post
seekmba wrote:
Can someone help me on how to approach and solve such problems. Thanks in advance.

In the xy-plane, if line k has negative slope and passes through the point (s, -2), is the x-intercept of the line k positive?

(1) s = 0
(2) The y-intercept of line k is negative


Drawing method:

(1) Line k passes through the point (0, -2) and has negative slope. Line k can be something like this:
Attachment:
1.png
1.png [ 9.16 KiB | Viewed 2125 times ]

So you can see that x intercept must be negative. Sufficient.

(2) The y-intercept of line k is negative and line has negative slope. Line k can be something like this:
Attachment:
2.png
2.png [ 9.87 KiB | Viewed 2125 times ]

Again you can see that when y-intercept is negative and slope is negative, then x-intercept must be negative too. Sufficient.

Answer: D.

Algebraic approach:

Equation of a line in point intercept form is y=mx+b, where: m is the slope of the line; b is the y-intercept of the line (the value of y for x=0); x is the independent variable of the function y.

X-intercept is the value of x for y=0 --> x_{intercept}=-\frac{b}{m}.

Question: is -\frac{b}{m}>0. As given that slope is negative (m<0), basically the question becomes is b>0?

(1) Line k passes through the point (0, -2) --> -2=0*m+b --> b=-2<0. Answer to the question is NO. Sufficient.

(2) The y-intercept of line k is negative --> as y-intercept is value of b, so we are directly told that b<0. Answer to the question is NO. Sufficient.

Answer: D.

For more on this issue refer to the Coordinate Geometry chapter of the Math book (link in my signature).

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

SVP
SVP
avatar
Joined: 17 Feb 2010
Posts: 1563
Followers: 12

Kudos [?]: 184 [0], given: 6

Re: Is the x-intercept of the line k positive? [#permalink] New post 24 May 2010, 05:37
Thanks so much Bunuel. I cannot believe how easily you explained it. I have some doubts in the graphs solution but totally understood the algebraic approach.

one question that I have though is:

In the graphs, I see the functions: f(x) = -x-2 and f(x) = -3x-1. How did you derive these formulas and how did you use them towards the question?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18733
Followers: 3243

Kudos [?]: 22380 [0], given: 2616

Re: Is the x-intercept of the line k positive? [#permalink] New post 24 May 2010, 05:58
Expert's post
seekmba wrote:
Thanks so much Bunuel. I cannot believe how easily you explained it. I have some doubts in the graphs solution but totally understood the algebraic approach.

one question that I have though is:

In the graphs, I see the functions: f(x) = -x-2 and f(x) = -3x-1. How did you derive these formulas and how did you use them towards the question?


These lines are just examples of what actual line k could be look like, f(x) = -x-2 and f(x) = -3x-1 do not represent the exact equations of the line k. I just needed to draw lines for statements 1 and 2 (each line satisfying the given statement) to illustrate the point that x-intercept must be negative.

f(x)=-x-2 is just one of the infinite lines with negative slope (m=-1<0) and with y-intercept equal to -2 (line passes through the pint (0,-2)).

f(x)=-3x-1 is just one of the infinite lines with negative slope (m=-3<0) and with negative y-intercept (y_{intercept}=b=-1<0).

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: Is the x-intercept of the line k positive?   [#permalink] 24 May 2010, 05:58
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic In the xy-plane, if line k has a negative slope and passes Val1986 7 06 Jun 2012, 22:04
2 Experts publish their posts in the topic In the xy-plane, if line k has negative slope and passes enigma123 2 15 May 2012, 20:26
9 Experts publish their posts in the topic In the xy-plane, if line k has negative slope and passes Lstadt 4 29 Feb 2012, 12:18
1 Experts publish their posts in the topic In the xy-plane, if line k has negative slope and passes GMATD11 4 26 Feb 2011, 06:21
8 Experts publish their posts in the topic In the xy-plane, if line k has negative slope and passes TeHCM 16 26 Dec 2005, 23:17
Display posts from previous: Sort by

In the xy-plane, if line k has negative slope and passes

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| 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®.