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Co-ordinate Geomatry

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Source: — Data Sufficiency |
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by kvcpk » Wed Aug 04, 2010 10:53 am
akpareek wrote:in the xy plane, line L passes through point (1,p). Does L have a positive slope ?

1. L passes through point (-p,13)
2. L passes through point (0,1)
(1,p)

Slope = (13-p)/(-p-1)
(p-13)/p+1
NO info about p. Hence INSUFF

Slope = (p-1)/1-0 = p-1
No info about p. Hence INSUFF

Combining:
Slope = -12/p
-12/p = p-1
p^2-p+12 = 0
(p-4)(p+3)=0
p = 4 or -3
one is positive and the other is negative.
Hence INSUFF

pick E
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by clock60 » Wed Aug 04, 2010 11:21 am
hi kvcpk
you solving is smart as usual.
only one point can you show how you manage to solve equation

p^2-p+12=0

can you elaborate a little bit more?
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by kvcpk » Wed Aug 04, 2010 1:09 pm
clock60 wrote:hi kvcpk
you solving is smart as usual.
only one point can you show how you manage to solve equation

p^2-p+12=0

can you elaborate a little bit more?
I am sorry.. p^2-p+12=0 will not have real roots.
becuse b^2-4ac = 1-48 =-47 is negative.
So no real roots exist.

Answer still holds to be E I believe. I wonder what is the source, because I have not seen an official problem touching outside real numbers.
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by clock60 » Wed Aug 04, 2010 1:15 pm
friend
no need to be sorry, i think it is simple error in original typing...
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by tomada » Wed Aug 04, 2010 5:44 pm
Whoa, a polynomial with complex numbers for roots. Bizarre. I agree that the answer is still 'E'.
I'm really old, but I'll never be too old to become more educated.
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by odod » Thu Aug 05, 2010 7:32 am
in the xy plane, line L passes through point (1,p). Does L have a positive slope ?

1. L passes through point (-p,13)
2. L passes through point (0,1)


I'm getting a different answer. Expert please!!!! I agree that statement 2 is not suff. since if a negative or positive value for p is chosen, then the answer differs. Howeer I believe statement 1 is suff.

1) I just plugged in a positive and negative value for p

if p = 3,
(13-3)/(-3-1) = 10/-4 =negative slope

if p = -3 then:
(13+3)/-3-1 = 16/-4 = negative slope

Wouldn't this make statement one suf?

I
ODOD
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by odod » Thu Aug 05, 2010 7:34 am
in the xy plane, line L passes through point (1,p). Does L have a positive slope ?

1. L passes through point (-p,13)
2. L passes through point (0,1)


I'm getting a different answer. Expert please!!!! I agree that statement 2 is not suff. since if a negative or positive value for p is chosen, then the answer differs. Howeer I believe statement 1 is suff.

1) I just plugged in a positive and negative value for p

if p = 3,
(13-3)/(-3-1) = 10/-4 =negative slope

if p = -3 then:
(13+3)/-3-1 = 16/-4 = negative slope

Wouldn't this make statement one suf?

I
ODOD
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by kvcpk » Thu Aug 05, 2010 7:34 am
odod wrote:in the xy plane, line L passes through point (1,p). Does L have a positive slope ?

1. L passes through point (-p,13)
2. L passes through point (0,1)


I'm getting a different answer. Expert please!!!! I agree that statement 2 is not suff. since if a negative or positive value for p is chosen, then the answer differs. Howeer I believe statement 1 is suff.

1) I just plugged in a positive and negative value for p

if p = 3,
(13-3)/(-3-1) = 10/-4 =negative slope

if p = -3 then:
(13+3)/-3-1 = 16/-4 = negative slope

Wouldn't this make statement one suf?

I
Try with p=14. you will get positive slope
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by lunarpower » Fri Aug 06, 2010 3:55 am
odod wrote: if p = 3,
(13-3)/(-3-1) = 10/-4 =negative slope

if p = -3 then:
(13+3)/-3-1 = 16/-4 = negative slope
the second of these is wrong. if p = -3, then "-p" is actually +3. therefore, the denominator of the second of these expressions should be 3 - 1 = 2. that will give an overall positive slope, then, since the sign switches.

weren't you a bit suspicious when you plugged two different numbers into (-p - 1) -- an expression that is different for any two values that are plugged into it -- and got the same value (-4) twice?
Ron has been teaching various standardized tests for 20 years.

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by lunarpower » Fri Aug 06, 2010 4:01 am
akpareek wrote:in the xy plane, line L passes through point (1,p). Does L have a positive slope ?

1. L passes through point (-p,13)
2. L passes through point (0,1)
yep, this one is wacky.

what's the source of this problem?

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as proved by other posters, each of the individual statements is insufficient.

if you take the statements together, then you now have three slopes, ALL of which must be equal to each other.
let's call the points A(1, p), B(-p, 13), and C(0, 1).

... then you've got three slopes:
slope AB = (p - 13)/(1 + p)
slope BC = (13 - 12)/(-p - 0) = -12/p
slope AC = (p - 1)/(1 - 0) = p - 1

you can set any two of these three equal to give an equation, so you may as well go with the easiest ones, i.e., the last two.
this gives -12/p = p - 1.
multiply out to -12 = p^2 - p.
this gives p^2 - p + 12 = 0, which is the same weird equation (no real solutions) that other posters got above.

therefore, you get no such points at all, meaning that the combination of the two statements is actually a mathematical impossibility.
the gmat won't do that to you, so this problem is a bad, bad problem.
Ron has been teaching various standardized tests for 20 years.

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