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by jainrahul1985 » Mon Oct 17, 2011 4:17 am
In the rectangular coordinate system, lines m and n cross at the origin. Is line m perpendicular to line n?

(1) m has a slope of -1 and n passes through the point (-a, -a).

(2) If the slope of m is x and the slope of n is y, then -xy = 1.

OA D
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by shankar.ashwin » Mon Oct 17, 2011 4:20 am
For lines to be perpendicular, the product of their slopes should be -1.

(1) m=-1 and y=x(which is slope '1')
Product of slopes = -1 (Sufficient)

(2) GIven product of slopes = -1 (Sufficient) D
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by Anurag@Gurome » Mon Oct 17, 2011 4:22 am
jainrahul1985 wrote:In the rectangular coordinate system, lines m and n cross at the origin. Is line m perpendicular to line n?

(1) m has a slope of -1 and n passes through the point (-a, -a).

(2) If the slope of m is x and the slope of n is y, then -xy = 1.

OA D
(1) m has a slope of -1 and n passes through the point (-a, -a).
Line n passes through the points (-a, -a) and (0, 0). So, its slope = (0 + a)/(0 + a) = 1
Now, slope of m * slope of n = -1 * 1 = -1, which clearly implies that lines m and n are perpendicular; SUFFICIENT.

(2) If the slope of m is x and the slope of n is y, then -xy = 1 implies slope of m * slope of n = -1, which again implies that lines m and n are perpendicular; SUFFICIENT.

The correct answer is D.
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by saketk » Tue Oct 18, 2011 7:53 am
jainrahul1985 wrote:In the rectangular coordinate system, lines m and n cross at the origin. Is line m perpendicular to line n?

(1) m has a slope of -1 and n passes through the point (-a, -a).

(2) If the slope of m is x and the slope of n is y, then -xy = 1.

OA D
A request -- please hide the answer using the Spoiler [ https://www.beatthegmat.com/new-spoilers ... tml#417411 ]

Solution --

From the question we already have one co-ordinate [0,0]

The condition for perpendicular lines is -- product of slopes of the lines = -1

Stmt 2 says exactly the same. Hence sufficient

Also from stmt 1 we can deduce the slope of line Y because we know the co-ordinates

(0,0) and other (-a,-a)
slope is = (0 + a)/(0 + a) = 1

Hence, correct answer OPTION D
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