rectangular co-ordinate system

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nikhilsrl: Master | Next Rank: 500 Posts; Posts: 109; Joined: Mon Jan 10, 2011 3:05 am; Thanked: 8 times; Followed by:7 members; GMAT Score:760

rectangular co-ordinate system

by nikhilsrl » Sun Mar 20, 2011 3:10 am

In the rectangular co-ordinate system does the line k intersect quadrant II?

1) slope of line k is -1/6
2) the y-intercept of line k is -6

OA is A. I am not sure how the slope alone can help solve this.

Please help solve this.

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Source: Beat The GMAT — Data Sufficiency | Sun Mar 20, 2011 3:10 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Sun Mar 20, 2011 3:51 am

nikhilsrl wrote:In the rectangular co-ordinate system does the line k intersect quadrant II?

1) slope of line k is -1/6
2) the y-intercept of line k is -6

While solving coordinate geometry problems, try to visualize the scenario. In this case for statement 1, try visualizing different straight lines with negative slope. And then you'll see their is no way you can draw a straight line with negative slope without intersecting the quadrant II.

This is because the slope is measured with respect to the angle made by the straight line with the positive x-axis. And if the angle is less than 90 degrees, slope is positive and if it is greater than 90 degrees, slope is negative.

Refer to figure below,

Hence, statement 1 is sufficient to answer the question in YES.

But for statement 2, slope may be negative or positive and accordingly the line may or may not intersect quadrant II.

The correct answer is A.

Anurag Mairal, Ph.D., MBA
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Gurome, Inc.
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