XY Plane GMAT Prep question

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Baldini: Senior | Next Rank: 100 Posts; Posts: 90; Joined: Mon Mar 02, 2009 6:06 am; Thanked: 3 times

by Baldini » Tue Mar 10, 2009 1:19 am

In the XY Plane, line K passes through the point (1,1) and line M passes through the point (1, -1). Are lines K and M perpendicular to each other?

(1) Lines k and m intersect at the point (1, -1)
(2) Line k intersects the x-axis at the point (1, 0)

OA is E. Can someone please explain?

Thanks

GMAX

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Source: Beat The GMAT — Data Sufficiency | Tue Mar 10, 2009 1:19 am

cubicle_bound_misfit: Master | Next Rank: 500 Posts; Posts: 246; Joined: Mon May 19, 2008 7:34 am; Location: Texaco Gas Station; Thanked: 7 times

by cubicle_bound_misfit » Tue Mar 10, 2009 2:43 am

two lines are perpendicular only if product of thier slopes = -1

to find out slopes you need at least another point for each line

from stmt 1 only slope for line k can be determined (insuf)

from stmt 2 only slope for like k can be determined

together , if we plot these points you will see there can be infinite line m going thru point (1,-1) which may or may not be perpendicular to line k.
hence E.

Cubicle Bound Misfit

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perfectstranger: Master | Next Rank: 500 Posts; Posts: 177; Joined: Wed Jul 16, 2008 11:06 amFollowed by: 1 member; Thanked: 2 times

by perfectstranger » Mon Mar 16, 2009 12:58 am

can someone give a detailed explain. I do not know anything about analytical geometry. I do think many of us don't know as well.

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m&m: Master | Next Rank: 500 Posts; Posts: 134; Joined: Sun Feb 15, 2009 7:44 pm; Thanked: 14 times

by m&m » Mon Mar 16, 2009 7:35 am

If you tried to do this visually you would need to draw the 2 lines above on an x-y graph. Since the question stem gives us a point for each line k and m we need either another distinct-point (for each) or the slope (for each). So rewording the question "can we draw the 2 lines on an x-y plot"

1) gives us another point but notice that this point same point given for m. This allows us to draw line k but not m. --> Insuff

2) This gives us a point for line k. SO again we can draw k but not m. --> insuff

Combined - for both we can draw k but not m --> insuff

E

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rs2010: Master | Next Rank: 500 Posts; Posts: 232; Joined: Fri Jul 04, 2008 4:14 pmFollowed by: 1 member; Thanked: 14 times; GMAT Score:760

by rs2010 » Tue Mar 17, 2009 11:20 am

perfectstranger wrote:can someone give a detailed explain. I do not know anything about analytical geometry. I do think many of us don't know as well.

remember basic thing that 2 lines will be perpendicular if the product of slopes of both lines is -1.

Since we 2 points for line k we can find out its slope but we do not have any information about line m except that its passes thru point(1,-1).

We can determine its and hence unable to answer with the give choices.
So, answer is 'E'

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