In the rectangular coordinate system, if line l is parallel to one of

Question

In the rectangular coordinate system, if line l is parallel to one of the axes, does line contain the point (4, 5) ?

(1) Line l contains the point (4, -5).
(2) Line l crosses the x-axis.

globaldesi · Answer

1 ) says line passes through any axis but point 4,-5 doesn't x axis or y axis.
insufficient

2) line x cross x axis but then x can be 4, 5,

combine both
that means lien apsses though x and parallel to y axis
and cut x at 4
so it will definitely pass through all values of y 
thus it passes through 4,5 and 4,-5

C IMO
Thanks

madgmat2019 · Answer

(1) Line l contains the point (4, -5).

then there are 2 possibilities
i) line is parallel to y-axis
ii) line is parallel to x-axis

So Insufficient.

(2) Line l crosses the x-axis.

that means line is parallel to y-axis, but we cannot say if the line l contain point(4,5) 
So insufficient.

by combining both we can say line l contain point(4,5). 
OA:C

AndrewN · Answer

I am uploading a graph for anyone who needs clarification on why the answer is (C) . Screen Shot 2021-02-12 at 10.36.09.png Statement (1) tells us that (4, -5) is on the graph of the line, but looking at the image above, we cannot tell whether that point exists on the red line , in which case the answer to the question would be yes, or on the green line , which would make the answer to the question no. Since both lines conform to the given information about line l being parallel to one of the axes, we cannot say that statement (1) is sufficient on its own. Statement (2) is even more open-ended, with an infinite number of vertical lines possible in the image above. Of course, one of these, the red line , would lead to a yes answer, but any other line would lead to a no answer. Hence, statement (2) is not sufficient on its own. Taken together, there is no way the line can be parallel to the x-axis, as the blue line shows, since it would not contain the point (4, -5) from statement (1) and would not cross the x-axis, per statement (2). The only valid line, the one that conforms to both statements, is the red line , and the answer to the question is yes, but only if both statements are taken together: (C). I hope that helps if anyone was confused. Good luck with your studies. - Andrew

CEdward · Answer

In the rectangular coordinate system, if line l is parallel to one of the axes, does line contain the point (4, 5) ?

(1) Line l contains the point (4, -5).
Insufficient.
Line l can be a vertical line that contains (4,-5) and (4,5) OR 
Line l can be horizontal and contain (4,-5) only

(2) Line l crosses the x-axis.
Clearly insufficient.

C: Sufficient (must be a vertical line that contains both).

gmatpro15 · Answer

Combine both the options
that means line apsses though x and parallel to y axis
and cut x at 4
so it will definitely pass through all values of y
thus it passes through 4,5 and 4,-5

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In the rectangular coordinate system, if line l is parallel to one of

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In the rectangular coordinate system, if line l is parallel to one of

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