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# A line passes through (1,p), is its slope greater than 0?

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Director
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A line passes through (1,p), is its slope greater than 0?  [#permalink]

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05 Jun 2005, 17:45
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A line passes through (1,p), is its slope greater than 0?
1) The line passes through (p,13)
2) The line passes through (p,-1)
Director
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05 Jun 2005, 18:16
Vithal wrote:
A line passes through (1,p), is its slope greater than 0?
1) The line passes through (p,13)
2) The line passes through (p,-1)

1) slope = 0 when p=13, but we dont know p, insufficient
2) slope =0 when p=-1, insufficient

1+2) the only way for a line to go through these 3 point is if p =1, so slope equals infinity = > sufficient

C.
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05 Jun 2005, 18:26
sparky wrote:
Vithal wrote:
A line passes through (1,p), is its slope greater than 0?
1) The line passes through (p,13)
2) The line passes through (p,-1)

1) slope = 0 when p=13, but we dont know p, insufficient
2) slope =0 when p=-1, insufficient

1+2) the only way for a line to go through these 3 point is if p =1, so slope equals infinity = > sufficient

C.

I chose C too, but isn't something/0 undefined? A couple of questions here:
(i) is n/0 undefined or infinity(meaning a large number) for the purposes of GMAT (I know as limit x-->0 y tends to infinity and stuff )
(ii) what is the slope of a line parallel to y-axis? undefined or infinity
SVP
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05 Jun 2005, 18:29
Vithal wrote:
A line passes through (1,p), is its slope greater than 0?
1) The line passes through (p,13)
2) The line passes through (p,-1)

from i and ii each, we do not know what is slope. but from i and ii togather, slope = (13+1)/(p-p)=infinite or undefine.
Director
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05 Jun 2005, 18:37
slope = infinity means the slope is defined.

the equation for the line is x=1, there is no dividing by zero in this equation.

to make it more clear, the standard forumla for computing the slope cannot be applied in some cases, namely when denominator equals zero.
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05 Jun 2005, 18:51
quite a dodgy question this

cuz though i know that individually the data isn't sufficient...ideally, the two together should be...
however if you calculate the two slopes using the two sets of equations and equate them, after simplifying I get:
-1-p=13-p

anyway i suppose if i had to i would pick C...but it did throw me off
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05 Jun 2005, 18:56
cloudz9 wrote:
quite a dodgy question this

cuz though i know that individually the data isn't sufficient...ideally, the two together should be...
however if you calculate the two slopes using the two sets of equations and equate them, after simplifying I get:
-1-p=13-p

anyway i suppose if i had to i would pick C...but it did throw me off

I got into the same problem too - and then chose C (as either way I was sure that answer will be found by combining both the equations)
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05 Jun 2005, 21:22
Slope = tan (the angle made by the line)

When the angle is 90 the slope is infinity which is valid

So C is correct
SVP
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05 Jun 2005, 21:30
sparky wrote:
slope = infinity means the slope is defined.

could you pls make it clear? coz, it is little confusion. do you mean that the slope = infinite is defined is sufficient answer the question. if so, it is clear. if you mean something/0 = infinite is defined, then its not clear. thanx.
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05 Jun 2005, 21:50
HIMALAYA wrote:
sparky wrote:
slope = infinity means the slope is defined.

could you pls make it clear? coz, it is little confusion. do you mean that the slope = infinite is defined is sufficient answer the question. if so, it is clear. if you mean something/0 = infinite is defined, then its not clear. thanx.

Defined in the sense we know what it is - infinity, and therefore we can say that it's diffirent from zero.

I don't want to get into the metaphysics of infinity, because frankly I have no clue. hehe

like, k/0 is not defined because we have no idea what it equals, but

LIMx->0 (k/x) = infinity. (LIM means limit)
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05 Jun 2005, 22:01
1
KUDOS
[quote="Vithal"]A line passes through (1,p), is its slope greater than 0?
1) The line passes through (p,13)
slope = (13-p)/(p-1)
When 1<p<13 slope>0 otherwise not
Insufficient

2) The line passes through (p,-1)
slope = (p+1)/(1-p)
When -1<p<1 slope >0 otherwise not
Insufficient

Combined
p=1, slope<>0
Sufficient
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06 Jun 2005, 08:24
Basically we don't want to know what is the slope, but only if it is <>0, as HongHu demonstrates.
06 Jun 2005, 08:24
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