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

 It is currently 17 Oct 2019, 18:31 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  M05-13

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58402

Show Tags 00:00

Difficulty:   25% (medium)

Question Stats: 71% (01:21) correct 29% (01:27) wrong based on 171 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 V
Joined: 02 Sep 2009
Posts: 58402

Show Tags

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  S
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

1
Bunuel
Can you please tell me if we always assume that "the line" is straight?
Math Expert V
Joined: 02 Sep 2009
Posts: 58402

Show Tags

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  V
Joined: 26 Mar 2013
Posts: 2345

Show Tags

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 V
Joined: 02 Sep 2009
Posts: 58402

Show Tags

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  G
Joined: 26 Dec 2017
Posts: 149

Show Tags

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 V
Joined: 02 Sep 2009
Posts: 58402

Show Tags

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  G
Joined: 26 Dec 2017
Posts: 149

Show Tags

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 V
Joined: 02 Sep 2009
Posts: 58402

Show Tags

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  G
Joined: 26 Dec 2017
Posts: 149

Show Tags

My bad any point in red line is equidistant from A,b. Tq for explanation.
_________________
--If you like my post pls give kudos
Manager  S
Joined: 25 May 2019
Posts: 68

Show Tags

I was totally OK with the concept. I found that c is not on Line AB. Got the equation right, substituted Cs coordinates, and understood it doesn't pass.

But I failed to remember that it is Yes - No question and ans, in this case, is No.

Friends keep this in mind. We often forget about it
_________________
_________________
Please give kudos, if you like my post

When the going gets tough, the tough gets going... Re: M05-13   [#permalink] 18 Sep 2019, 02:53
Display posts from previous: Sort by

M05-13

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

Moderators: chetan2u, Bunuel

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  