Is line l parallel to the y-axis?

The equation of the y-axis is x = 0

(1) The equation of line l is x = 4.
Both x = 0 and x = 4 are parallel.
Sufficient

(2) The points (4, 2) and (4, - 5) are on line l.
By joining the points (4, 2) and (4, - 5), we get a line x = 4
Both x = 0 and x = 4 are parallel.
Sufficient

Choice D is the answer.

Alternatively

As long as we get one unique line, there is no need to check whether it is parallel.
By nature, it will be either parallel or not.

(1) The equation of line l is x = 4.
So, we have a unique line.

Is line l parallel to the y-axis?
Either yes or no
Even if the answer is no, the statement is sufficient

So, Sufficient

(2) The points (4, 2) and (4, - 5) are on line l.
Joining two different points always gives a unique line.

So, we have a unique line.

Is line l parallel to the y-axis?
Either yes or no

Sufficient

Asked: Is line l parallel to the y-axis?

(1) The equation of line l is x = 4.
The line l is parallel to y-axis (x=0)
SUFFICIENT

(2) The points (4. 2) and (4, - 5) are on line l.
The equation of line l is x=4
The line l is parallel to y-axis (x=0)
SUFFICIENT

IMO D
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Question: Is line l parallel to the y-axis?

Choice A
The equation of line l is x = 4.
SUFFICIENT

Choice B
The points (4, 2) and (4, - 5) are on line l
Both points of line have x values same. i.e. parallel to y axis.
SUFFICIENT

Ans D
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