December 09, 2018 December 09, 2018 07:00 AM PST 09:00 AM PST Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT. December 10, 2018 December 10, 2018 10:00 PM PST 11:00 PM PST Practice the one most important Quant section  Integer properties, and rapidly improve your skills.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 25 Dec 2009
Posts: 78

In the xyplane, if line k has negative slope and passes
[#permalink]
Show Tags
17 Jan 2010, 08:19
Question Stats:
63% (02:00) correct 37% (02:08) wrong based on 427 sessions
HideShow timer Statistics
In the xyplane, if line k has negative slope and passes through the point (5,r) , is the xintercept of line k positive? (1) The slope of line k is 5. (2) r > 0 OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/inthexypla ... 35197.html
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 51035

Re: In the xyplane, if line k has negative slope and passes
[#permalink]
Show Tags
17 Jan 2010, 12:14
GMATMadeeasy wrote: In the xyplane, if line k has negative slope and passes through the point (5,r) , is the xintercept of line k positive?(1) The slope of line k is 5. (2) r> 0 What is the answer and why ? I am for B but it is not OG answer. Based on second condition r > 0, xintercept for this line is negative, so we can determine definitively sign of xintercept. Let the \(x\) intercept be the point \((x,0)\). Slope \(m\) is rise over run and for two points \((5,r)\) and \((x,0)\) would be \(m=\frac{r0}{5x}=\frac{r}{5x}\) > \(x=\frac{r5m}{m}\). Question: is \(x>0\)? > is \(x=\frac{r5m}{m}>0\)? (1) \(m=5\) > \(x=\frac{r5m}{m}=\frac{r+25}{5}>0\)? \(x=\frac{r+25}{5}=\frac{r}{5}5>0\)? We can not determine whether \(\frac{r}{5}5>0\) or not. Not sufficient. (2) \(r>0\) and \(m<0\) > \(x=\frac{r5m}{m}=\frac{r}{m}5>0\)? \(\frac{r}{m}\) is some positive value (as \(m<0\)) but we don't know whether it's more than \(5\) or not. Not sufficient. (1)+(2) \(x=\frac{r}{5}5\) and \(r>0\) > \(r=5x+25>0\) > \(x>5\). \(x\) can be positive as well as negative. Not sufficient. Answer: E. This can be done by visualizing the question. Statement (2) tells us that the point \((5,r)\), as \(r>0\), is in the II quadrant. Line with negative slope through the point in the II quadrant can have \(x\) intercept positive as well as negative. Taken together: as we don't know the exact location of the point \((5,r)\) in II quadrant we can not say even knowing the slope whether the \(x\) intercept would be positive or negative.
_________________
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? Extrahard Quant Tests with Brilliant Analytics




Senior Manager
Joined: 22 Dec 2009
Posts: 305

Re: In the xyplane, if line k has negative slope and passes
[#permalink]
Show Tags
20 Feb 2010, 03:14
GMATMadeeasy wrote: In the xyplane, if line k has negative slope and passes through the point (5,r) , is the xintercept of line k positive?(1) The slope of line k is 5. (2) r> 0 What is the answer and why ? I am for B but it is not OG answer. Based on second condition r > 0, xintercept for this line is negative, so we can determine definitively sign of xintercept. Best Approach to use a graph!
Attachments
OG 12 DS Question.png [ 27.25 KiB  Viewed 16280 times ]
_________________
Cheers! JT........... If u like my post..... payback in Kudos!!
Do not post questions with OAPlease underline your SC questions while postingTry posting the explanation along with your answer choice For CR refer Powerscore CR BibleFor SC refer Manhattan SC Guide
~~Better Burn Out... Than Fade Away~~




CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2595
Location: Malaysia
Concentration: Technology, Entrepreneurship
GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35

Re: In the xyplane, if line k has negative slope and passes
[#permalink]
Show Tags
20 Jan 2010, 04:50
Letme give you one alternate solution and correct me if m wrong. Suppose line is y=mx+c 1. put value of y and x as 5,r we get r =25+c now put y=x=0 in ymxc which gives c This i hav done to check the side on which origin lies. This is dependent on value of c 2. r>0 For r >0, we cannot say anything about value of C even using r=25+c also. thus we cannot c on which side origin lies. For +ve intercept it should lie on left side of line and vice versa. Thus ans E
_________________
Fight for your dreams :For all those who fear from Verbal lets give it a fight
Money Saved is the Money Earned
Jo Bole So Nihaal , Sat Shri Akaal
Support GMAT Club by putting a GMAT Club badge on your blog/Facebook
GMAT Club Premium Membership  big benefits and savings
Gmat test review : http://gmatclub.com/forum/670to710alongjourneywithoutdestinationstillhappy141642.html



Manager
Joined: 25 Dec 2009
Posts: 78

Re: In the xyplane, if line k has negative slope and passes
[#permalink]
Show Tags
27 Jan 2010, 02:41
yes, good way too Gurpreet. lets play with it further to strenghtne the concepts . If I modify the second statement to 2. r < 0 , let's try to solve it in two ways i.e. First by visualising it and second, by using the basic equation y = mx +c Using the second method, The equation is r = 25+c and we know r < 0, so only possibility is c < 25 , so this can tell definitely the answer. Am I correct ? But if we want to visualise it, is there any possibility it can pass through First quadrant ? Second quadrant i can imagine easy . Also, How a line can make more than 180° angle ? I am from good maths background but do not remember exacly how a line makes more than 180° . So little help will break the code.



CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2595
Location: Malaysia
Concentration: Technology, Entrepreneurship
GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35

Re: In the xyplane, if line k has negative slope and passes
[#permalink]
Show Tags
27 Jan 2010, 04:17
GMATMadeeasy wrote: yes, good way too Gurpreet. lets play with it further to strenghtne the concepts . If I modify the second statement to 2. r < 0 , let's try to solve it in two ways i.e. First by visualising it and second, by using the basic equation y = mx +c Using the second method, The equation is r = 25+c and we know r < 0, so only possibility is c < 25 , so this can tell definitely the answer. Am I correct ? But if we want to visualise it, is there any possibility it can pass through First quadrant ? Second quadrant i can imagine easy . Also, How a line can make more than 180° angle ? I am from good maths background but do not remember exacly how a line makes more than 180° . So little help will break the code. r = 25+c and r>0 is given that means 25+c >0 => 25> c => 25 <c thus we cannot determine whether c is ve or +ve r25c should have same or different sign with C to know whether that number is on same or diff side of origin.
_________________
Fight for your dreams :For all those who fear from Verbal lets give it a fight
Money Saved is the Money Earned
Jo Bole So Nihaal , Sat Shri Akaal
Support GMAT Club by putting a GMAT Club badge on your blog/Facebook
GMAT Club Premium Membership  big benefits and savings
Gmat test review : http://gmatclub.com/forum/670to710alongjourneywithoutdestinationstillhappy141642.html



Manager
Joined: 25 Dec 2009
Posts: 78

Re: In the xyplane, if line k has negative slope and passes
[#permalink]
Show Tags
27 Jan 2010, 05:17
Let's take it a step further. Adding one more question that will take discussion further . (Source: GMATprep)
Lnes n and p lie in the xy plane . Is the slope of line n less than the slope of line p?
1. Lines n and p intersect at the point (5,1) 2. The y intercept of line n is greater than the y intercept of line p.
1. Clearly insufficient : For equation n y=m1.x+c1 and for equation p y=m2.x+c2 => First equation of line :1 = 5.m1+c1 Second equation of line: 1= 5.m2+c2
Clearly, m1 and m2 Can take any vset of values that m1>m2 and m1<m2, both are possible
2. Insufficent again : y=m1.x+c1 and y=m2.x+c2 => given is c1 > c2 => m1 and m2 can take any set of values again
1 and 2 statement togather :
First line : 1 = 5.m1+c1 Second Line: 1= 5.m2+c2
From this we can conclude that 5.m1+c1 = 5.m2+c2 or 5 (m1  m2) = c2  c1 now we are given c1 > c2 , I beleive that Statement refers to absolute values so c1 could be 4 and c2 as 3 => c2c1 gives 1 or c1 could be 4 and c2 as 3 => c2c1 gives 7 or c1 could be 4 and c2 as 3 => c2c1 gives 7 or c1 could be 4 and c2 3 => c2c1 gives 1
that means m1 and m2 can be greater or lesser than each other.So both together not sufficinet.
If I ignore my assumption that the values are absolute : In that case, c2c1 has to be negative if c1 > c2 . so m1  m2 has to be negative too .
m1  m2 < 0 or m1 < m2 , Sufficient
Question 1 : Which of the case one should assume ? answer is C that both together are sufficient that means we can't assume absolute values.
Question 2 : Sloe 1 and slope 2 , generally speaking 1 is greater than 2 but slope if we look at 2 is greater than 1.
What is the rule one should follow ?



Intern
Joined: 15 Nov 2009
Posts: 4

Re: In the xyplane, if line k has negative slope and passes
[#permalink]
Show Tags
30 Jan 2010, 09:58
I still cant visualize.
In stmt 2: we know that like passes through second quadrant and it has negative slope. How can it intercept at positive x?
Negative slope always goes bottom to top from left to right.
Please help me visualizing this, I am sure i am missing something.



Manager
Joined: 26 May 2005
Posts: 189

Re: In the xyplane, if line k has negative slope and passes
[#permalink]
Show Tags
11 Feb 2010, 21:46
jshah wrote: I still cant visualize.
In stmt 2: we know that like passes through second quadrant and it has negative slope. How can it intercept at positive x?
Negative slope always goes bottom to top from left to right.
Please help me visualizing this, I am sure i am missing something. take a line that is passing through the origin and bisects the II quadrant and IV quadrant. Now draw parallel lines above and below that line .. one will have positive x intercept and other will have negative x intercept and the original line will have 0 xintecept.



Manager
Joined: 25 Dec 2009
Posts: 78

Re: In the xyplane, if line k has negative slope and passes
[#permalink]
Show Tags
15 Feb 2010, 09:14
@testprep2010 : Your response is E. I do not understand what values such posts bring. 1. This is OG question so answer is known. 2. The post does not just ask to answer just an option 3. How do I know your answer is wrong or right ? 4. Even if everyone votes A for this, it will not change the answer. I feel sad why people put thier time answering like this on these forums.



Senior Manager
Joined: 22 Dec 2009
Posts: 305

Re: In the xyplane, if line k has negative slope and passes
[#permalink]
Show Tags
20 Feb 2010, 09:15
Thanks Bunuel.. for the Kudos! A kudos from u.. means a lot!
_________________
Cheers! JT........... If u like my post..... payback in Kudos!!
Do not post questions with OAPlease underline your SC questions while postingTry posting the explanation along with your answer choice For CR refer Powerscore CR BibleFor SC refer Manhattan SC Guide
~~Better Burn Out... Than Fade Away~~



Intern
Status: Princess of Economics
Joined: 13 Nov 2011
Posts: 7
Location: Canada
Concentration: Economics

Re: In the xyplane, if line k has negative slope and passes
[#permalink]
Show Tags
16 Nov 2011, 00:37
Bunuel, how do you know from statement 2 that m<0? Statement 2 only says that r>0. Could you please explain it to me? Thank you!



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8649
Location: Pune, India

Re: In the xyplane, if line k has negative slope and passes
[#permalink]
Show Tags
16 Nov 2011, 21:36
MariaBez wrote: Bunuel, how do you know from statement 2 that m<0? Statement 2 only says that r>0. Could you please explain it to me? Thank you! The question stem tells you that line k has negative slope so m < 0. Also, you may want to look at the diagram made by jeeteshsingh in the first reply to this question. It uses both the statements together and shows you two possible cases (through two different dotted lines). In one case, line k has positive x intercept; in the second case it has negative x intercept. Hence both statements together are not sufficient.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Intern
Status: Princess of Economics
Joined: 13 Nov 2011
Posts: 7
Location: Canada
Concentration: Economics

Re: In the xyplane, if line k has negative slope and passes
[#permalink]
Show Tags
17 Nov 2011, 21:53
VeritasPrepKarishma, thank you for your reply! I got it. Yeah, m<0 is given to us.



Manager
Joined: 12 Oct 2011
Posts: 197

Re: In the xyplane, if line k has negative slope and passes
[#permalink]
Show Tags
17 Dec 2011, 19:28
MariaBez wrote: Bunuel, how do you know from statement 2 that m<0? Statement 2 only says that r>0. Could you please explain it to me? Thank you! 'm' is the slope of the line in the equation y = m*x + c The question stem already states that the line has negative slope. Hence, m < 0.



Intern
Joined: 12 Mar 2012
Posts: 11

Re: In the xyplane, if line k has negative slope and passes
[#permalink]
Show Tags
21 Apr 2012, 03:16
GMATMadeeasy wrote: In the xyplane, if line k has negative slope and passes through the point (5,r) , is the xintercept of line k positive?(1) The slope of line k is 5. (2) r> 0 What is the answer and why ? I am for B but it is not OG answer. Based on second condition r > 0, xintercept for this line is negative, so we can determine definitively sign of xintercept. y=mx+c substitute (5,r)
r=5m+c
C= r+5m
1) m=5
y=mx+c
put y=0 to find x intercept
and m=5
0= 5x+r+5(5) 5x=r25
Dont know r so insufficient
2) r> 0, certainly not sufficient . . . 0= mx+r+5m , we do not know m and r
combine both 1 and 2 5X=r25 and r>0
r can be any thing so cannot determine X
Hence the answere is E



Intern
Joined: 03 Jul 2016
Posts: 1

Re: In the xyplane, if line k has negative slope and passes
[#permalink]
Show Tags
25 Sep 2016, 03:29
GMATMadeeasy wrote: In the xyplane, if line k has negative slope and passes through the point (5,r) , is the xintercept of line k positive?
(1) The slope of line k is 5. (2) r > 0 Hi, Can you please tell where I am wrong. I assumed eq of line as y=mx+c. Let x intercept be A(x,0) At point A, 0=mx+c =>x=c/m Hence, sign of x will depend on sign of c/m Since m is negative, i. if c<0, c/m <0 =>x<0 ii. if c>0, c/m >0 =>x>0 Statement 1 is not sufficient. As per statement 2, r>0 => 5m+c>0 =>5m>c =>5m<c =>5<c/m or c/m >5 => both c and m have same sign i.e. m,c<0 => x<0 => Statement 2 is sufficient



Director
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 505
Location: India

Re: In the xyplane, if line k has negative slope and passes
[#permalink]
Show Tags
23 Feb 2017, 03:56
PROMPT ANALYSIS The equation of the will be y = r + m(x+5) where m is the slope. X intercept is r/m 5 Superset The answer will be either yes or no. Translation In order to find the answer we need: 1# Exact value of m and r 2# Equations to solve m and r STATEMENT ANALYSIS St 1: m = 5. For this x intercept is r/5 5. Cannot say about the sign of the expression because r can be any real number.INSUFFICIENT. Hence option a and d eliminated. St 2: r>0. The value of r/m 5 will depend on the value of m, which can be any real number. INSUFFICIENT. Hence option b eliminated. St 1&st 2: r/5 5 will be positive for natural number r>25, these kind of constraints are not given. SO INSUFFICIENT. HEnce option c eliminated. Option E.
_________________
GMAT Mentors



Math Expert
Joined: 02 Sep 2009
Posts: 51035

Re: In the xyplane, if line k has negative slope and passes
[#permalink]
Show Tags
19 Jan 2018, 09:39




Re: In the xyplane, if line k has negative slope and passes &nbs
[#permalink]
19 Jan 2018, 09:39






