Very interesting geometry question

[student22]

Code: Select all

In a coordinate system, line l is parallel to line k, does line l intersect the x-axis?

(1) Line k has slope zero.

(2) Point (0, 4) is on line k.

I found this question on a gmat blog and it didn't include the official answer, but had several possible solutions.

One solution was A, for obvious reasons.

Another solution was E stating that it's possible that line L is a coincident line, in that it's possible that it intersects the X-axis at all points.

1. Tell us that line K is a horizontal line, but it could be coincident.
2. Doesn't tell us anything.

Together: It tells us that line K is not coincident, but line L, which is parallel to K could be coincident.

I'm posting this question, since I want to hear from the gmat experts how the gmat would treat this concept on the test. Especially since I've never heard of this concept before (or at least don't remember it) nor have I seen it mentioned in any gmat book.

[rockeyb]

Code: Select all

In a coordinate system, line l is parallel to line k, does line l intersect the x-axis?

(1) Line k has slope zero.

(2) Point (0, 4) is on line k.

I found this question on a gmat blog and it didn't include the official answer, but had several possible solutions.

One solution was A, for obvious reasons.

Another solution was E stating that it's possible that line L is a coincident line, in that it's possible that it intersects the X-axis at all points.

1. Tell us that line K is a horizontal line, but it could be coincident.
2. Doesn't tell us anything.

Together: It tells us that line K is not coincident, but line L, which is parallel to K could be coincident.

I'm posting this question, since I want to hear from the gmat experts how the gmat would treat this concept on the test. Especially since I've never heard of this concept before (or at least don't remember it) nor have I seen it mentioned in any gmat book.

I am no expert and my reasoning may be flawed , but here is my opinion .


First of all the concept being tested in not new there are question on slope of line and lines that are parallel to each other .

Now coming back to the question we are asked to find out if line L intersects X - axis .

We know slope of line L = slope of line K .

Statement (1) : Line K has slope = 0 .

That means line K is horizontal line or its parallel to X - axis .

Now line L is parallel to K . So line L may not intersect X - axis or it may run all along the X - axis and thus intersect the X - axis at all the points (coincident line).

So we can not be sure . Not Sufficient .

Statement (2):

Point (0, 4) is on line k .

Now Point (0,4) can lie on line K in 2 cases .

Case (1) Line K is parallel to Y axis and passes through point (0,4)

OR

Case (2) Line K is running all along X - axis (coincident line).

So not sure if which one of the above cases are true .

Also we know nothing about line L .

Not Sufficient .

Combine (1) and (2).

(1) Says line K has 0 slope . So case 1 is ruled out and only case 2 is the possible case.

We know line L is parallel to line K .

And since parallel lines never intersect at any point we can say line K and L will never meet at single point .

More over from Case (2) we have established that line K is touching x -axis at all the points .

Hence we can definitely say line L will never touch X - axis .

So my pick is C .

[student22]

By unfamiliar concept, I meant coincident lines.

I think you missed something in case 2 for statement 2. K is not running at the x-axis. It is either an undetermined line going through point (0, 4) or it is a parallel line to the x-axis going through point (0, 4).

[rockeyb]

By unfamiliar concept, I meant coincident lines.

Coincident Lines : Coincident lines are essentially two linear functions whose graphs are the same; therefore, the two lines will have the same slope and the same y-intercept. When graphed, the lines will be one on top of the other.

But I am not sure if this concept is tested in GMAT or its out of the syllabus range . So I would need some GMAT Instructor to comment on this issue.

I think you missed something in case 2 for statement 2. K is not running at the x-axis. It is either an undetermined line going through point (0, 4) or it is a parallel line to the x-axis going through point (0, 4).

Point (0,4) means y = 0 and x = 4

when y = 0 then the line either is perpendicular to X - axis or run along X - axis that passes through origin (0,0) the only other place that has y= 0 .

Also I am not clear what do you mean by "undetermined line" ?

[student22]

I uploaded a picture of what I think statement 2 is trying to say. Please correct me if I misunderstood it.


By undetermined line, I meant that it could have a diagonal slope (the second graph in the picture).


That point on both graphs is (0, 4)

[rockeyb]

I uploaded a picture of what I think statement 2 is trying to say. Please correct me if I misunderstood it.


By undetermined line, I meant that it could have a diagonal slope (the second graph in the picture).


That point on both graphs is (0, 4)

Ahhh !!!! my mistake .

I do such silly mistakes some times . I was considering y - coordinate to be x - co ordinate.

yes the answer should be E .

[[email protected]]

I really do not understand that why the questions are not posted properly on such a wonderful site...

I would insist to have the questions posted properly...