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Coordinate geomatry another concept of intersection of lines

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Source: — Data Sufficiency |
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by Pilot » Sat Feb 19, 2011 12:20 am
The answer is C.
I is not sufficient because, we don't know of two lines passing through this point which one is n line.
II is not sufficient because, it gives information about the independent terms of lines, but not about coefficient in term x.
Solving together these condition we can compare the slope of the lines. So answer is C.
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by rohu27 » Sat Feb 19, 2011 12:39 am
[spoiler]OA : C[/spoiler]

When a line rises from left to right, the slope is a positive number. Figure 1 (a) shows a line with a positive slope. When a line falls from left to right, the slope is a negative number.
this can be solved properly when u draw the lines in ur book and visualize.

st 1. n can be a line wth positive or negative slope. same wth p. insufficient.
st 2. let y-intercept 2. suppose n has negative slope and p has positive. st 2 is satisfied but slope of p is more thn that of n.
so isuff

take 1 & 2
line shud pass thru 5,1 and inrercept of > tht of p.
if we take 2 lines wth positive slopes satisfying the above condition, thn slope of n will be > tht of p
if we take 2 negative lines also same thng as above
if one the lines has postve slope and the other negative, for both 1 & 2 to satisfy the line wth negative slope shud have a negative y intercept and pass thru 5,1 and line wth positive slope shud have a positive intercept and pass thru 5,1. so obviosly it satisfies both the condiitons and we have no ambiguity here.

my explanation may confuse u even more, but this is all i cud manage. may be an expert can explain u wth graphs as i feel tht is the best way to solve this problem. infact once get ur concepts clear abt slopes, u can urself draw the graphs nd see.
alltimeacheiver wrote: Lines n and p lie in xy plane. Is slope of line n less than slope of line p?
a. Lines n and p intersect at (5, 1)
b. Y-intercept of line n is greater than y intercept of line p


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by rohu27 » Sat Feb 19, 2011 12:41 am
also one request, can u plz mention the source in the subject line itself. i read the entire question only to find out its frm gmat prep. im yet take tht one :(
alltimeacheiver wrote: Lines n and p lie in xy plane. Is slope of line n less than slope of line p?
a. Lines n and p intersect at (5, 1)
b. Y-intercept of line n is greater than y intercept of line p


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by Night reader » Sat Feb 19, 2011 3:43 am
@pilot, the answer can not be C, it should be Yes/No - Can not be Determined
Yes/No (A,B,C,D) and Can not be Determined (E)
st(1) Is not Sufficient, we may not determine the slope by having only one point. A slope is determined from i) line equation/function of y from x, ii) availability of x- or y- intercept data and point on the line. Statement 1 only tells us that two lines have one point at x=5 and y=1; the slopes can be defined in infinite ways - i.e. two lines could go straight up or down, or west or east :)
st(2) y-intercept of line n is greater than y-intercept of line p OR we have fulfilled one of the conditions mentioned earlier. Now if we plot only y-intercepts for both lines without st(1) we still have only one point at hand.

Combined st(1&2): we have two points x=5, y=1 and x=0, y(line n)>y(line p)

what's slope --> +ve change, Y unit increase OR -ve change, Y unit decrease over +ve change, X unit increase OR -ve change, X unit decrease. We are lucky here to deal with only +ve changes. Hence we know that the rise in Y for line n is greater than the rise in Y for line p. Sufficient to answer the question - Is slope of line n less than slope of line p? The slope of line n is less than the slope of line p. Choose C
alltimeacheiver wrote: Lines n and p lie in xy plane. Is slope of line n less than slope of line p?
a. Lines n and p intersect at (5, 1)
b. Y-intercept of line n is greater than y intercept of line p


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by Pilot » Sat Feb 19, 2011 6:01 am
Hi Night reader. I didn't understand your answer. At the beginning you wrote that C could not be answer. but at the end you prooved C is answer.

Can you explain this situation??
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by Night reader » Sat Feb 19, 2011 7:41 am
Pilot wrote:Hi Night reader. I didn't understand your answer. At the beginning you wrote that C could not be answer. but at the end you prooved C is answer.

Can you explain this situation??
we can state C as an answer choice, but the answer would be either value or Yes/No decision. You have not provided sufficient clues in your combined st(1&2) solution to conclude if the slope of line n <, >, = slope of line p
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by clock60 » Sat Feb 19, 2011 8:12 am
hi guys to me the answer is C and only C
n=y=k1x+b1
p=y=k2x+b2, where k1,k2 are slopes of lines n amd p, and b1,b2 are y-intersects of line n and p
we need to estimate does k2>k1
(1) insuff from here we know that x=5, and y=1, but no info about b1,b2, but for future purposes we can elaborate a little bit
1=5k1+b1- it is for line n.
1=5k2+b2- it is for line p, equate them
5k1+b1=5k2+b2,
5k2-5k1=b1-b2, if we find that b1-b2>0 then k2-k1>0 and k2>k1 but we hav no info about b1,b2
(2) also insuff here we have relation between b1,b2 as b1>b2, but nothing about x,y
both
5k2-5k1=b1-b2, from 2 st b1-b2>0 thus 5k2-5k1>0 cancel 5 and left with k2-k1>0, k2>k1 sufficient
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by samrendra4u » Sat Feb 19, 2011 9:30 am
alltimeacheiver wrote: Lines n and p lie in xy plane. Is slope of line n less than slope of line p?
a. Lines n and p intersect at (5, 1)
b. Y-intercept of line n is greater than y intercept of line p


st1: insufficient
st2:insufficient
let n is y=m1x + c1
& p is y =m2x +c2
from st 2 c1 > c2 i.e c1 -c2>0 (A)
from 1 st statement 5,1 is the point of intersection
Solving the two eqns of line we get,
5*m1 + c1 =5m2 +c2
or,5(m1 -m2) = c2 -c1<0
implies m1 -m2 <0 or m1 , m2

Hence the option is C.
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