In the rectangular coordinate system shown above, does the : Data Sufficiency (DS)

1. If the slope of line is negative, line WILL intersect quadrants II and IV. X and Y intersects of the line with negative slope have the same sign. Therefore if X and Y intersects are positives, line intersects the quadrant I too, if negative quadrant III.

2. If the slope of line is positive, line WILL intersect quadrants I and III. Y and X intersects of the line with positive slope have opposite signs. Therefor if X intersect is negative, line intersects the quadrant II too, if positive quadrant IV.

3. Every line (but the one crosses origin or parallel to X or Y axis) crosses three quadrants. Only the line which crosses origin (0,0) OR is parallel of either of axis crosses two quadrants.

4. The line with slope 0 is parallel to X-axis and crosses quadrant I and II, if the Y intersect is positive OR quadrants III and IV, if the Y intersect is negative.

If you draw the couple of lines with different slopes you'll understand this better.

BACK TO THE ORIGINAL QUESTION:
In the rectangular coordinate system shown above, does the line k (not shown) intersect quadrant II?

(1) The slope of k is -1/6
(2) The y-intercept of k is -6


Statement (1) says that slope is negative (case 1) so the line will intersect the quadrants II and IV (line goes from up to down). Sufficient.

Statement (2) provides us with y-intercept -6, now if line has positive slope then the line goes from down to up and thus won't intersect quadrant II but if the slope is negative then the line goes from up to down thus it will intersect quadrant II. Two different answers. Not sufficient.

Answer: A.

For more on this topic check Coordinate Geometry chapter of Math Book (link in my signature).

Hope it helps.

shelrod007 wrote:I am a little confused on this one ...
Here the slope will be negative and line will not pass through Y axis

Line extends in both directions without end (infinitely). What you've drawn there is a line segment.

In the rectangular coordinate system shown above, does the line k (not shown) intersect quadrant II?

(1) The slope of k is -1/6
When a slope of a line is negative that means the line is decreasing, and goes downwards from left to right.
So when we extend the line, it will definitely pass through quadrant II and IV.
Hence Statement 1 alone is sufficient.

(2) The y-intercept of k is -6

The y-intercept is the point where the line intersects the y-axis. Here the y intercept of the line is (0,-6).

Case 1:
At (0,-6), we can draw a line parallel to X axis (Slope is 0) and passing through quadrant III and IV. In this case, line doesn't intersect quadrant II

Case 2 :Also we can draw a line passing through (0,-6) with a negative slope passing through the quadrants II,III and IV.
Here, the line will pass through quadrant II

Case 3:
Similarly a line with positive slope can be drawn at the same point passing through the quadrants I,III and IV. Here the line will not intersect quadrant II

Hence we cannot confirm whether the line k intersect quadrant II or not as both cases are possible .

Statement 2 alone is insufficient.

Option A is the answer

Hope this helps,
Clifin J Francis,
GMAT SME
_________________