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15 Apr 2020, 04:06
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B
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Line M travels through three quadrants of the coordinate plane. Does Line M travel through Quadrant IV?
(1) Line M has a negative x-intercept
(2) Line M has a negative y-intercept
Are You Up For the Challenge: 700 Level Questions
Attachment:
Coordinate_Grid.png [ 1.45 KiB | Viewed 5051 times ]
15 Apr 2020, 04:48
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We are given that line M travels through 3 quadrants of the coordinate plane. We are to determine whether line M passes through the fourth quadrant, in which the x coordinates are positive and the y coordinates are negative.
Statement 1: Line M has a negative x-intercept.
This insufficient because line M could pass through the points (-3,0) and (0,2), thereby satisfying the given condition in statement 1, and this case line M does not pass through the 4th quadrant. On the other hand, line M could pass through the points (-3,0) and (0,-2), thereby satisfying the given condition in statement 1, and in this case line M passes through the 4th quadrant.
Statement 2: Line M has a negative y-intercept.
This is sufficient. This is because as long as line M has a negative y-intercept, it must definitely pass through the 4th quadrant. For instance line M could pass through the points (0,-2) and (3,0); this line has a negative y-intercept, y=-2, and passes through the 4th quadrant. Line M can pass the points (0,-4) and (-2,0); this line has a negative y-intercept, y=-4, and passes through the 4th quadrant.
The answer is B.
Statement 1: Line M has a negative x-intercept.
This insufficient because line M could pass through the points (-3,0) and (0,2), thereby satisfying the given condition in statement 1, and this case line M does not pass through the 4th quadrant. On the other hand, line M could pass through the points (-3,0) and (0,-2), thereby satisfying the given condition in statement 1, and in this case line M passes through the 4th quadrant.
Statement 2: Line M has a negative y-intercept.
This is sufficient. This is because as long as line M has a negative y-intercept, it must definitely pass through the 4th quadrant. For instance line M could pass through the points (0,-2) and (3,0); this line has a negative y-intercept, y=-2, and passes through the 4th quadrant. Line M can pass the points (0,-4) and (-2,0); this line has a negative y-intercept, y=-4, and passes through the 4th quadrant.
The answer is B.
15 Apr 2020, 04:53
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Bunuel
Refer attached figure..
Statement I is given by blue colour line ...Insuff
As the quadrant next to negative x-intercept is III and II quadrant, the line has to pass through them..but may or may not pass through IV quadrant
Statement II is given by brown lines C and D...
As the quadrant next to negative y-intercept is III and IV quadrant, the line has to pass through them..
B
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Coordinate_Grid.png [ 5.45 KiB | Viewed 4756 times ]
