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slope

by hitmewithgmat » Sun Feb 15, 2009 5:03 pm
Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p?
1) Lines n and p intersect at the point (5,1)
2)The y-intercept of line n is greater than the y-interpcet of line p.

OA after discussion.
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by Bidisha_800 » Sun Feb 15, 2009 7:40 pm
I need the IA of this question. This was posted before and owner of the question said she/he doesn't have OA .... This was my response :


Equation of line 1

x/a1+y/b1=1 (a1 and b1 are intercepts of X and Y axis and can be negative)

slope1=-b1/a1
splope 2 = -b2/a2

since both line 1 and line 2 pass thru (5,1) so

a1(1-b1)=-5b1

so slope of line 1 = -b1/a1 = (1-b1)/5

slope of line 2 = -b2/a2 = (1-b2)/5


now unless b1 and b2 are both positive intercepts (b1, b2 >0) of Y axis, I think we can not determine whether slope1 > slope 2

(E)
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by radhaswami » Sun Feb 15, 2009 7:57 pm
I think the answer should be C and can be best explaned by drawing the lines which if you consider both the conditions will have an X shape in the xyplane

X SHAPE MEANS ONE SLOPE IS POSITIVE AND ONE IS NEGATIVE SO SUFFICIENT
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by mrsmarthi » Sun Feb 15, 2009 9:19 pm
Let line n be represented as y = m1x + b1 where m1 is the slope and b1 - y intercept.

Let line p be represented as y = m2x + b2 where m2 is the slope and b2 - y intercept.

From clue 1 it is give, that point (5,1) is the intersection ==> which means (5,1) lies on both the lines. Substitute (5,1) in the above two eq, we get

1 = 5m1 + b1 ==> m1 = 1-b1/5
1 = 5m2 + b2 ==> m2 = 1-b2/5

Slopes are dependent on the Y intercepts and this info is not provided. Hence clue is insufficient.

From clue 2, it is given b1 > b2. Now be careful here, don't think that (5,1) passes thru the lines. this from Clue 1 but not avaible in clue in 2. We need to know which of the points are passing thru these two lines. And this is crucial to decide which of the two slopes are greater. Hence clue alone is insifficient.

Now combine both the clues, We know the points which passes thru both the lines and also know which y intercept is greater.

m1 = 1-b1/5
m2 = 1-b2/5

Since b1 > b2, obviously m1 < m2. (the bigger the number in the numerator is deducted, the smaller the value becomes).

Hence with both the clues, we know which of the slopes is greater. Hence sufficent.

IMO C.
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by Bidisha_800 » Sun Feb 15, 2009 9:32 pm
Sorry, I need a better explanation. Anybody ?
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by ontopofit » Sun Feb 15, 2009 10:00 pm
its E.
i did it by drawing on a sheet of paper the possible outcomes taking both statements.
1) there can be infinite number lines with diff slopes passing from (5,1).so insuff.

2) always remember slope of a line is tan(angle).
I can draw lines with -ve slope with smaller or larger y-intercept.so 2) is insuff.

taking both I can still draw lines with greater or smaller slopes passing thru (5,1) with y-intercept,smaller or greater. so insuff.

hence E.

PS - trig concepts are are not testd on gmat but come in very handy for a few questions.
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by Maratha1 » Mon Feb 16, 2009 5:43 am
I would go for C.

Try drawing the lines on paper. Slope is nothing but the inclination of the line relative to the x axis. For example if the line is parallel to x axis then the slope of the line is 0 and if it is parallel to Y axis the slope of the line is 1.

In this case try drawing lines with the given conditions on a rough page and you will realize that line which has the smaller intercept to y axis is more inclined than the other one.

HTH!
carpe diem!
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Re: slope

by hypik21 » Mon Feb 16, 2009 8:36 am
hitmewithgmat wrote:Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p?
1) Lines n and p intersect at the point (5,1)
2)The y-intercept of line n is greater than the y-interpcet of line p.

OA after discussion.
IMO C..

1..not suff..2 not suff..if u combine

Equation for line n = AX+B=y
equation for line P= CX+D=y

sub values..LINE N= 5A+B=y
LINE P=5C+D=1
b>d..(statement 2)...therefore A is less than C..C is suff.
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C

by hitmewithgmat » Mon Feb 16, 2009 4:13 pm
OA says C
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