Last visit was: 06 Oct 2024, 20:03 It is currently 06 Oct 2024, 20:03
Decision Tracker
My Rewards
Unanswered
Active Topics
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

In the x-y coordinate plane, does line k have a positive x-intercept?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6797
Own Kudos [?]: 31560 [14]
Given Kudos: 799
Location: Canada
Send PM
In the x-y coordinate plane, does line k have a positive x-intercept? [#permalink] In the x-y coordinate plane, does line k have a positive x-intercept?   19 Oct 2018, 07:47
2
Kudos
12
Bookmarks
Expert Reply
Top Contributor
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

63% (01:48) correct 37% (02:10) wrong based on 249 sessions
Hide Show DIFFICULTY AND TIMER STATISTICS
In the x-y coordinate plane, does line k have a positive x-intercept?

(1) (slope of line k)(y-intercept of line k) > 0
(2) (slope of line k) - (y-intercept of line k) < 0

*kudos for all correct solutions
ShowHide Answer
Official Answer
A
User avatar
G
Salsanousi
Joined: 19 Oct 2013
Posts: 407
Own Kudos [?]: 321 [4]
Given Kudos: 117
Location: Kuwait
GPA: 3.2
WE:Engineering (Real Estate)
Send PM
GMAT ToolKit User
In the x-y coordinate plane, does line k have a positive x-intercept? [#permalink] In the x-y coordinate plane, does line k have a positive x-intercept?   Updated on: 19 Oct 2018, 09:39
1
Kudos
3
Bookmarks
GMATPrepNow
In the x-y coordinate plane, does line k have a positive x-intercept?

(1) (slope of line k)(y-intercept of line k) > 0
(2) (slope of line k) - (y-intercept of line k) < 0

*kudos for all correct solutions

If the slope is positive then the y-intercept is positive only way for this to be possible is when x-intercept is negative.

The same is true for the slope is negative and y-intercept is negative

The x-intercept is negative.

Sufficient.



For statement 2)

If slope is positive then y intercept must be a larger positive for the statement to hold true and be negative.

If both are positive then x-intercept is negative.

Now if slope is negative then y-intercept is a smaller negative or a positive number.


X-intercept then can be positivbe or negative

Insufficient.

The answer is best understood by a drawing.

Answer choice A.

Thanks to GMATinsight for pointing out a mistake in my solution, I originally choose D.

Posted from my mobile device
Attachments

File comment: For statement 2
Screen Shot 2018-10-19 at 7.37.39 PM.png
Screen Shot 2018-10-19 at 7.37.39 PM.png [ 31.78 KiB | Viewed 5493 times ]

File comment: For statement 1
Screen Shot 2018-10-19 at 7.37.33 PM.png
Screen Shot 2018-10-19 at 7.37.33 PM.png [ 24.96 KiB | Viewed 5493 times ]


Originally posted by Salsanousi on 19 Oct 2018, 08:17.
Last edited by Salsanousi on 19 Oct 2018, 09:39, edited 2 times in total.
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6059
Own Kudos [?]: 14256 [1]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: In the x-y coordinate plane, does line k have a positive x-intercept? [#permalink] In the x-y coordinate plane, does line k have a positive x-intercept?   19 Oct 2018, 09:04
1
Kudos
Expert Reply
GMATPrepNow
In the x-y coordinate plane, does line k have a positive x-intercept?

(1) (slope of line k)(y-intercept of line k) > 0
(2) (slope of line k) - (y-intercept of line k) < 0

*kudos for all correct solutions

Question: does line k have a positive x-intercept?

Statement 1: (slope of line k)(y-intercept of line k) > 0

Case 1: Both slope and y-intercept are +ve (Red Line)
Case 2: Both slope and y-intercept are -ve (Blue Line)


As per both cases, x-intercept is -ve hence
SUFFICIENT

Statement 2: (slope of line k) - (y-intercept of line k) < 0

i.e. (slope of line k) < (y-intercept of line k)
Case 1: Y-intercept = 3 and slope = 1 (Red Line)
Case 2: Y-intercept = 3 and slope = -1 (Blue Line)

X intercept in one case is +ve and in other case it's -ve hence
NOT SUFFICIENT

Answer: Option A
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6059
Own Kudos [?]: 14256 [0]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: In the x-y coordinate plane, does line k have a positive x-intercept? [#permalink] In the x-y coordinate plane, does line k have a positive x-intercept?   19 Oct 2018, 09:08
Expert Reply
Salsanousi
GMATPrepNow
In the x-y coordinate plane, does line k have a positive x-intercept?

(1) (slope of line k)(y-intercept of line k) > 0
(2) (slope of line k) - (y-intercept of line k) < 0

*kudos for all correct solutions

If the slope is positive then the y-intercept is positive only way for this to be possible is when x-intercept is negative.

The same is true for the slope is negative and y-intercept is negative

The x-intercept is negative.

Sufficient.



For statement 2)

If slope is positive then y intercept must be a larger positive for the statement to hold true and be negative.

If both are positive then x-intercept is negative.

Now if slope is negative then y-intercept must be a smaller negative.


X-intercept is negative.

Sufficient.

The answer is best understood by a drawing.

Answer choice D.

Posted from my mobile device

I find some mistake in highlighted part Salsanousi

When slope is -1, Y-intercept may be +3 as well and (slope of line k) - (y-intercept of line k) = (-1) - (+3) < 0 also stays satisfied.
User avatar
G
Salsanousi
Joined: 19 Oct 2013
Posts: 407
Own Kudos [?]: 321 [1]
Given Kudos: 117
Location: Kuwait
GPA: 3.2
WE:Engineering (Real Estate)
Send PM
GMAT ToolKit User
Re: In the x-y coordinate plane, does line k have a positive x-intercept? [#permalink] In the x-y coordinate plane, does line k have a positive x-intercept?   19 Oct 2018, 09:27
GMATinsight thanks!! I missed that out :/

Posted from my mobile device
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6797
Own Kudos [?]: 31560 [2]
Given Kudos: 799
Location: Canada
Send PM
Re: In the x-y coordinate plane, does line k have a positive x-intercept? [#permalink] In the x-y coordinate plane, does line k have a positive x-intercept?   21 Oct 2018, 16:02
2
Kudos
Expert Reply
Top Contributor
GMATPrepNow
In the x-y coordinate plane, does line k have a positive x-intercept?

(1) (slope of line k)(y-intercept of line k) > 0
(2) (slope of line k) - (y-intercept of line k) < 0

*kudos for all correct solutions

Target question: Does line k have a positive x-intercept?

Statement 1: (slope of line k)(y-intercept of line k) > 0
There are two possible cases that that satisfy statement 1:
- the slope and y-intercept are both positive
- the slope and y-intercept are both negative
Let's examine each case:

Case a: the slope and y-intercept are both positive
No matter now you sketch a line that has these two features, it will look something like this:

As you can see, the answer to the target question is NO, line k does NOT have a positive x-intercept

Case b: the slope and y-intercept are both negative.
No matter now you sketch a line that has these two features, it will look something like this:

As you can see, the answer to the target question is NO, line k does NOT have a positive x-intercept

In both cases, the answer to the target question is the SAME.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: (slope of line k) - (y-intercept of line k) < 0
There are several lines that satisfy statement 2. Here are two:
Case a:The line has a slope of -2 and y-intercept of -1 .

In this case, the answer to the target question is NO, line k does NOT have a positive x-intercept

Case b: The line has a slope of -2 and y-intercept of 1 .

In this case, the answer to the target question is YES, line k DOES have a positive x-intercept

Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
User avatar
P
Rashed12
Joined: 26 Nov 2018
Posts: 189
Own Kudos [?]: 338 [0]
Given Kudos: 123
GPA: 3.3
Send PM
GMAT ToolKit User Reviews Badge
In the x-y coordinate plane, does line k have a positive x-intercept? [#permalink] In the x-y coordinate plane, does line k have a positive x-intercept?   11 Feb 2019, 01:28
GMATinsight
Salsanousi
GMATPrepNow
In the x-y coordinate plane, does line k have a positive x-intercept?

(1) (slope of line k)(y-intercept of line k) > 0
(2) (slope of line k) - (y-intercept of line k) < 0

*kudos for all correct solutions

If the slope is positive then the y-intercept is positive only way for this to be possible is when x-intercept is negative.

The same is true for the slope is negative and y-intercept is negative

The x-intercept is negative.

Sufficient.



For statement 2)

If slope is positive then y intercept must be a larger positive for the statement to hold true and be negative.

If both are positive then x-intercept is negative.

Now if slope is negative then y-intercept must be a smaller negative.


X-intercept is negative.

Sufficient.

The answer is best understood by a drawing.

Answer choice D.

Posted from my mobile device

I find some mistake in highlighted part Salsanousi

When slope is -1, Y-intercept may be +3 as well and (slope of line k) - (y-intercept of line k) = (-1) - (+3) < 0 also stays satisfied.

I am not clear the below statement that you have mentioned above. Kindly help me how it happens.

If the slope is positive then the y-intercept is positive only way for this to be possible is when x-intercept is negative.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 35131
Own Kudos [?]: 891 [0]
Given Kudos: 0
Send PM
Re: In the x-y coordinate plane, does line k have a positive x-intercept? [#permalink] In the x-y coordinate plane, does line k have a positive x-intercept?   05 Sep 2023, 03:42
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 Club Bot
gmatclubot
Re: In the x-y coordinate plane, does line k have a positive x-intercept? [#permalink]
05 Sep 2023, 03:42
Moderator:
Bunuel
Math Expert
95949 posts