GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Jan 2019, 17:32

### 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

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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

January 20, 2019

January 20, 2019

07:00 AM PST

07:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.
• ### GMAT Club Tests are Free & Open for Martin Luther King Jr.'s Birthday!

January 21, 2019

January 21, 2019

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday.

# M05-13

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52296

### Show Tags

15 Sep 2014, 23:25
00:00

Difficulty:

25% (medium)

Question Stats:

72% (00:53) correct 28% (00:50) wrong based on 137 sessions

### HideShow timer Statistics

In xy plane, line K passes through the points A(6, -7) and B(4, 5). Does line K also pass through point C?

(1) Coordinates of Point C are ( 5, -1)

(2) Point C is equidistant from Point A and Point B.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 52296

### Show Tags

15 Sep 2014, 23:25
Official Solution:

Notice that since we have two distinct points of line K, then we can find its equation.

(1) Coordinates of Point C are (5, -1). We know the equation of line K, hence we can find whether it passes through some particular point. Sufficient.

(2) Point C is equidistant from point A and point B. Point C may be the midpoint of the line segment AB, so on line K. But point C can also be anywhere on the line which is perpendicular to line K and passes through that midpoint. Not sufficient.

_________________
Intern
Status: in process
Joined: 18 Jun 2017
Posts: 30
Location: Uzbekistan
Schools: Babson '21
GMAT 1: 690 Q47 V37
GPA: 4
WE: Education (Education)

### Show Tags

16 Dec 2017, 13:00
1
Bunuel
Can you please tell me if we always assume that "the line" is straight?
Math Expert
Joined: 02 Sep 2009
Posts: 52296

### Show Tags

16 Dec 2017, 13:10
1
BobsterGMAT wrote:
Bunuel
Can you please tell me if we always assume that "the line" is straight?

Yes. In Euclidean geometry, a line is a straight curve. In coordinate geometry, lines in a Cartesian plane can be described algebraically by linear equations and linear functions.
_________________
SVP
Joined: 26 Mar 2013
Posts: 2002

### Show Tags

17 Dec 2017, 07:44
Bunuel wrote:
Official Solution:

Notice that since we have two distinct points of line K, then we can find its equation.

(1) Coordinates of Point C are (5, -1). We know the equation of line K, hence we can find whether it passes through some particular point. Sufficient.

(2) Point C is equidistant from point A and point B. Point C may be the midpoint of the line segment AB, so on line K. But point C can also be anywhere on the line which is perpendicular to line K and passes through that midpoint. Not sufficient.

Bunuel

Can you expain how the highlited part can be the case?

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 52296

### Show Tags

17 Dec 2017, 08:20
1
Mo2men wrote:
Bunuel wrote:
Official Solution:

Notice that since we have two distinct points of line K, then we can find its equation.

(1) Coordinates of Point C are (5, -1). We know the equation of line K, hence we can find whether it passes through some particular point. Sufficient.

(2) Point C is equidistant from point A and point B. Point C may be the midpoint of the line segment AB, so on line K. But point C can also be anywhere on the line which is perpendicular to line K and passes through that midpoint. Not sufficient.

Bunuel

Can you expain how the highlited part can be the case?

Thanks

Check the image below:

Point (5, -1), red point, is the midpoint of (6, -7) and (4, 5). Red line is passing through that midpoint and is perpendicular to the blue line. Any point on the red line will be equidistant from (6, -7) and (4, 5).

Attachment:
Untitled.png

>> !!!

You do not have the required permissions to view the files attached to this post.

_________________
Manager
Joined: 26 Dec 2017
Posts: 158

### Show Tags

14 Jan 2018, 00:15
1
Hi Bunnel,
I might have a perpendicular line passing through C but C is on the line K right which in question we need to say whether k pass through C. In the above graph which you posted the point C is on line K. pls explain.
_________________

--If you like my post pls give kudos

Math Expert
Joined: 02 Sep 2009
Posts: 52296

### Show Tags

14 Jan 2018, 00:34
tejyr wrote:
Hi Bunnel,
I might have a perpendicular line passing through C but C is on the line K right which in question we need to say whether k pass through C. In the above graph which you posted the point C is on line K. pls explain.

Any point on red line is equidistant from point A and point B, so C could be anywhere on that red line. If it's on the intersection (red dot) then it'll be on blue line to but if it's anywhere else on red line then it won't be on blue line.
_________________
Manager
Joined: 26 Dec 2017
Posts: 158

### Show Tags

14 Jan 2018, 06:18
I was unable to understand how any point on the red line is equidistant from A and B.
For instance I took a point on the red perpendicular line (0,-11/6).
when i calculate the distance between (0,-11/6) and A
;(0,-11/6) and B are not equal.
_________________

--If you like my post pls give kudos

Math Expert
Joined: 02 Sep 2009
Posts: 52296

### Show Tags

14 Jan 2018, 06:49
tejyr wrote:
I was unable to understand how any point on the red line is equidistant from A and B.
For instance I took a point on the red perpendicular line (0,-11/6).
when i calculate the distance between (0,-11/6) and A
;(0,-11/6) and B are not equal.

The distance MUST be the same. The distance between (0, -11/6) and (4, 5) as well as the distance between (0, -11/6) and (6, -7) is $$\frac{\sqrt{2257}}{6}$$.

I'll try to explain in another way. Consider points A = (0, 1) and B = (0, -1). Perpendicular bisector of AB is x-axis. Obviously any point on x-axis is equidistant from A and B.

The same way, any point on perpendicular bisector, of segment AB in our question, will be equidistant from A and B.
_________________
Manager
Joined: 26 Dec 2017
Posts: 158

### Show Tags

15 Jan 2018, 20:43
My bad any point in red line is equidistant from A,b. Tq for explanation.
_________________

--If you like my post pls give kudos

Re: M05-13 &nbs [#permalink] 15 Jan 2018, 20:43
Display posts from previous: Sort by

# M05-13

Moderators: chetan2u, Bunuel

 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®.