NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 12:28 It is currently 26 Apr 2024, 12:28
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

What is the slope of line l that does not pass through the origin?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
avatar
L
TheUltimateWinner
CEO
CEO
Joined: 23 Feb 2015
Posts: 2519
Own Kudos [?]: 2096 [5]
Given Kudos: 1976
Concentration: Finance, Technology
Schools: Harvard '24 Judge '23 LBS '24 McCombs '24 Mendoza Tepper '24 Ross '24 Cox Marshall '24 Fisher Kelley '24 Jones McDonough '24 Owen '24 Terry BU Simon '24 Katz GWU Mason Babson Gabelli Foster '24 Goizueta '24 Scheller Stern '23 CBS '23 Booth '23 Haas '25 Wharton '25 Stanford '26 Johnson'23 Fuqua '23 Kellogg '23 Kenan-Flagler'23 INSEAD Aug 22 intake Olin '23 Said '23 Sloan '23 Carey Arizona "22 Yale '23 UC Davis Madison '23 Anderson '23 Carroll Carlson '23 Darden '23
Send PM
GMAT ToolKit User CAT Tests
What is the slope of line l that does not pass through the origin? [#permalink] New post   02 Aug 2020, 09:24
2
Kudos
3
Bookmarks
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

62% (01:25) correct 38% (01:34) wrong based on 119 sessions
Hide Show timer Statistics
What is the slope of line \(l\) that does not pass through the origin?
1) The \(y\)-intercept of line \(l\) is half its \(x\)-intercept.
2) The \(y\)-intercept of line \(l\) is three units less than its \(x\)-intercept.
ShowHide Answer
Official Answer
A
User avatar
L
yashikaaggarwal
Senior Moderator - Masters Forum
Joined: 19 Jan 2020
Posts: 3137
Own Kudos [?]: 2769 [2]
Given Kudos: 1510
Location: India
Schools: Cranfield (A) Warwick MiM "23 (M)
GPA: 4
WE:Analyst (Internet and New Media)
Send PM
Re: What is the slope of line l that does not pass through the origin? [#permalink] New post   03 Aug 2020, 05:45
2
Kudos
1) The y-intercept of line l is half its x-intercept.
let x = 0 in y = mx + c
y = c
then X = 2C when Y = 0
0= mx+c
mx = -c
m(2C) = -c
2m = -1
m = -1/2
slope is -1/2
(sufficient)

2) The y-intercept of line l is three units less than its x-intercept.
let x = 0 in y = mx + c
y = c
then X = C+3 when Y = 0
0= mx+c
mx = -c
m(C+3) = -c
mc + 3m = -c
c(m+1) = -3m
no value for m
(Insufficient)

IMO A
User avatar
L
IanStewart
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4128
Own Kudos [?]: 9247 [0]
Given Kudos: 91
 Q51  V47
Send PM
Re: What is the slope of line l that does not pass through the origin? [#permalink] New post   03 Aug 2020, 09:37
Expert Reply
To find the x-intercept of a line y = mx + b, we replace y with zero and solve for x. So if we solve 0 = mx + b for x, the value of x we'll find is the x-intercept. b is the y-intercept, so if Statement 1 is true, b = 0.5x, and 0 = mx + 0.5x, and since the x-intercept is nonzero (the line does not pass through the origin), we can divide both sides by x to find m = -0.5, and Statement 1 is sufficient.

Statement 2 is not sufficient, as any numerical examples will show. If the x-intercept is 2, say, then the slope of the line will be positive, but if x = 5, say, then it will be negative, so Statement 2 cannot be sufficient.
User avatar
P
Lipun
Manager
Manager
Joined: 05 Jan 2020
Posts: 148
Own Kudos [?]: 132 [0]
Given Kudos: 288
Send PM
Re: What is the slope of line l that does not pass through the origin? [#permalink] New post   09 Aug 2020, 10:49
IanStewart wrote:
To find the x-intercept of a line y = mx + b, we replace y with zero and solve for x. So if we solve 0 = mx + b for x, the value of x we'll find is the x-intercept. b is the y-intercept, so if Statement 1 is true, b = 0.5x, and 0 = mx + 0.5x, and since the x-intercept is nonzero (the line does not pass through the origin), we can divide both sides by x to find m = -0.5, and Statement 1 is sufficient.

Statement 2 is not sufficient, as any numerical examples will show. If the x-intercept is 2, say, then the slope of the line will be positive, but if x = 5, say, then it will be negative, so Statement 2 cannot be sufficient.


Hi IanStewart sir,

Can you please explain as to why are we not considering the absolute values of the intercepts while evaluating statement 1? If we consider absolute value of the intercepts, then the slope can be 1/2 or -1/2.

Let me know if my understanding is incorrect.

Regards
Lipun
User avatar
L
IanStewart
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4128
Own Kudos [?]: 9247 [0]
Given Kudos: 91
 Q51  V47
Send PM
Re: What is the slope of line l that does not pass through the origin? [#permalink] New post   09 Aug 2020, 12:16
Expert Reply
Lipun wrote:
Hi IanStewart sir,

Can you please explain as to why are we not considering the absolute values of the intercepts while evaluating statement 1? If we consider absolute value of the intercepts, then the slope can be 1/2 or -1/2.


I'm not sure I understand your question - why is it that you think we need to use absolute value here? Intercepts can be positive or negative. If Statement 1 is true, then one intercept is half of the other, so they must have the same sign. If a line's x-intercept and y-intercept have the same sign, the line's slope is automatically negative, so the slope cannot be 1/2.
User avatar
L
Mo2men
RSM Erasmus Moderator
Joined: 26 Mar 2013
Posts: 2461
Own Kudos [?]: 1360 [0]
Given Kudos: 641
Concentration: Operations, Strategy
Schools: Erasmus (II)
Send PM
Reviews Badge
Re: What is the slope of line l that does not pass through the origin? [#permalink] New post   09 Aug 2020, 16:46
IanStewart wrote:
Lipun wrote:
Hi IanStewart sir,

Can you please explain as to why are we not considering the absolute values of the intercepts while evaluating statement 1? If we consider absolute value of the intercepts, then the slope can be 1/2 or -1/2.


I'm not sure I understand your question - why is it that you think we need to use absolute value here? Intercepts can be positive or negative. If Statement 1 is true, then one intercept is half of the other, so they must have the same sign. If a line's x-intercept and y-intercept have the same sign, the line's slope is automatically negative, so the slope cannot be 1/2.



Hi IanStewart

Actually I had same question. According to statement 1, y intercept is half x intercept. For example, if y =1, then x=2 or y=-1 then x =-2 but why does it have to be same sign. We still could have y =1 and x=-2. I solved it conceptually because nothing in statement 1 indicates we have same sign. Where did I go wrong?

Thanks
User avatar
L
firas92
Current Student
Joined: 16 Jan 2019
Posts: 631
Own Kudos [?]: 1444 [0]
Given Kudos: 144
Location: India
Concentration: General Management
Schools: Tepper '23 (M$) Foster '23 (D)
GMAT 1: 740 Q50 V40
WE:Sales (Other)
Send PM
Reviews Badge
What is the slope of line l that does not pass through the origin? [#permalink] New post   09 Aug 2020, 17:38
Hi Lipun Mo2men

I don't understand why absolute values need to come into the picture.

Consider this, if the x-intercept of the line is \(a\), then the y intercept must be \(\frac{a}{2}\)


So the line passes through the points \((a,0)\) and \((0,\frac{a}{2})\)

We have a formula to calculate the slope of a line passing through the points \((x1,y1)\) and \((x2,y2)\)

\(Slope=\frac{y2-y1}{x2-x1}\)

Using this formula,

Slope of line \(l\) = \(\frac{\frac{a}{2}-0}{0-a}=-\frac{1}{2}\)

Hope this is clear

Posted from my mobile device
User avatar
L
IanStewart
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4128
Own Kudos [?]: 9247 [1]
Given Kudos: 91
 Q51  V47
Send PM
Re: What is the slope of line l that does not pass through the origin? [#permalink] New post   10 Aug 2020, 09:54
1
Kudos
Expert Reply
Mo2men wrote:
Hi IanStewart

Actually I had same question. According to statement 1, y intercept is half x intercept. For example, if y =1, then x=2 or y=-1 then x =-2 but why does it have to be same sign. We still could have y =1 and x=-2. I solved it conceptually because nothing in statement 1 indicates we have same sign. Where did I go wrong?


The solution firas92 posted above is correct. You can't have y = 1 and x = -2, because 1 is not half of -2; -1 is half of -2.

I'm wondering if perhaps you and Lipun are interpreting Statement 1 to mean "the distance from the y-intercept to the origin is half of the distance from the x-intercept to the origin," or something similar. If Statement 1 did say that, then you would both be correct. But that's not what it says - it is describing the intercepts themselves, and intercepts are coordinates, not distances, so they can be positive or negative. If you divide an intercept by 2, the sign won't change.
GMAT Club Bot
gmatclubot
Re: What is the slope of line l that does not pass through the origin? [#permalink]
10 Aug 2020, 09:54
Moderator:
Bunuel
Math Expert
92948 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions