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09 Oct 2009, 20:43
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
69% (00:59) correct
31%
(01:18)
wrong
based on 2747
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Not Attempted Yet
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
Attachment:
DS Geometery.JPG [ 13.99 KiB | Viewed 22698 times ]
Attachment:
GMAT_DS_PREP_100.png [ 2.97 KiB | Viewed 107944 times ]
09 Oct 2009, 21:30
Kudos
Bookmarks
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.
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.
21 Feb 2010, 05:01
Kudos
Bookmarks
Quote:
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
IMO A...
S1: Gives the slope to be -ve and hence it would be as shown in the diagram attached.
S2: Not necessary. without the slope...it is not possible to determine the direction and hence the intersection with the Quandrant.
Attachments
Prep1.png [ 45.79 KiB | Viewed 152733 times ]
