maya2008 wrote:This is a Data sufficiency question. I know I shouldn't solve those but I really hoped someone would help me solve it so I can understand how to deal with these kinds of questions
In a rectangular coordinate system shown above (I didn't attach since it is just a regular coordinate system), does the line k (not shown) intersect quadrant 2?
Statement 1: the slope of the line is -1/6
Statement 2: the y intercept of k is -6
(the answer btw is A)
Thank's a lot...Maya
First thing to note: quadrant II is the top left quadrant.
So, the question is, does the line pass through the top left section of the co-ordinate system?
Let's start with the easier statement:
(2) the y-int is -6
This tells us that the line passes through (0,-6). We could draw a horizontal line through that point which never touches quadrant 2. We can also draw a diagonal line that does go through quadrant 2. Since the answer is "maybe", (2) is insufficient.
(1) The slope of the line is -(1/6)
You could use trial and error to see that a line with this slope will, eventually, go through sector 2.
Alternatively, you could know this rule:
If a line has a positive slope, it definitely goes through sectors 1 and 3.
If a line has a negative slope, it definitely goes through sectors 2 and 4.
As an aside:
If a line is parallel to the x or y axis, it will go through exactly 2 different sectors.
(Except, of course, for the lines x=0 and y=0, which are the axes.)
If a line is not parallel to the x or y axis it will:
go through exactly 2 sectors if it passes through the origin; or
go through exactly 3 sectors if it does not pass through the origin.
