student22 wrote: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 .
