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jainrahul1985: Master | Next Rank: 500 Posts; Posts: 228; Joined: Sun Aug 17, 2008 8:08 am; Thanked: 4 times

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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Source: Beat The GMAT — Data Sufficiency | Mon Oct 17, 2011 4:17 am

shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

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

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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saketk: Legendary Member; Posts: 608; Joined: Sun Jun 19, 2011 11:16 amFollowed by: 8 members; Thanked: 37 times

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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