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divya23: Master | Next Rank: 500 Posts; Posts: 113; Joined: Mon Apr 26, 2010 8:58 amFollowed by: 14 members; Thanked: 2 times

by divya23 » Fri Jun 10, 2011 5:41 pm

In the xy plane ,line k passes thru the point (1,1) and m thru (1,-1) are lines k and m perpendicular to each other?
lines k and m intersect at point (1,-1)
line k intersect the x axis at point (1,0)
[spoiler]ans = e[/spoiler]

here if we take the slopes then it come sout to be 0 for both the lines then how should we proceed further??
please explain the concept

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Source: Beat The GMAT — Data Sufficiency | Fri Jun 10, 2011 5:41 pm

cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Fri Jun 10, 2011 5:52 pm

A(1,1) B(1,-1)
let slope of line K=k and slope of M=m
for them to be perpendicular, k*m=-1
also K passes through A
thus 1=k+c1 -> K: y=kx + (1-k)
M passes through B,
-1=m+c2 -> M: y=mx + (-1-m)
a)K and M intersect at (1,-1)
Thus K also passes through B or K:x=1 (slope is infinity)
no information about slope of m. insufficient
b)k passes through (1,0)
we get equation of line L:x=1 (slope=infinity)
still no information about m.
Insufficient
a&b) k=infinity and m is not given. insufficient
IMO E

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Fri Jun 10, 2011 6:41 pm

>>When two lines are perpendicular to each other (at right angles or 90Â°), their slopes have a particular relationship to each other. If the slope of one line is m then the slope of the other line is the negative reciprocal of m, or -1/m
st(1) doesn't allow for calculating two slopes and comparing them, k {(1,1)&(1,-1)} m{(1,-1)&(1,-1)} as two points' coordinates of line m are the same, Not sufficient
st(2) one more point of line k, BUT missing another point of line m for calculating and comparing the slopes, Not sufficient

combined st(1&2): still Not sufficient, as we can't calculate the slope of line m.

e

divya23 wrote:In the xy plane ,line k passes thru the point (1,1) and m thru (1,-1) are lines k and m perpendicular to each other?
lines k and m intersect at point (1,-1)
line k intersect the x axis at point (1,0)
[spoiler]ans = e[/spoiler]

here if we take the slopes then it come sout to be 0 for both the lines then how should we proceed further??
please explain the concept

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