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by priyank.hirani » Sun Apr 15, 2012 8:25 am
Lines n and p lie in the xy plane.Is the slope of line n less than the slpe of line p??

(1)Lines n and p intersect at (5,1)
(2)The y intercept of line n is greater than the y intercept of line p.
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Source: — Data Sufficiency |
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by shubham_k » Sun Apr 15, 2012 8:48 am
Lines n and p lie in the xy plane.Is the slope of line n less than the slpe of line p??

(1)Lines n and p intersect at (5,1)

We cannot say anuything abt slope INSUFF

(2)The y intercept of line n is greater than the y intercept of line p.

Here also we can't say coz one slope may be -ve or lines may be parallel.

INSUFF

combine

eqn of n is y=m1 * x +c1

p is y=m2*x + c2

at (5,1) we ave

5m1 +c1 = 5m2 +c2

also c1 >c2

then for this to be true m1 has to be less than m2

C
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by GMATGuruNY » Sun Apr 15, 2012 8:51 am
priyank.hirani wrote:Lines n and p lie in the xy plane.Is the slope of line n less than the slpe of line p??

(1)Lines n and p intersect at (5,1)
(2)The y intercept of line n is greater than the y intercept of line p.
Neither statement alone is sufficient to determine the relationship between the slopes.

Statements 1 and 2 combined:
Let (0,n) = the y-intercept of line n.
Let (0,p) = the y-intercept of line p.

Since (5,1) is on each line:
The slope of line n = (n-1)/(0-5) = (n-1)/(-5).
The slope of line p = (p-1)/(0-5) = (p-1)/(-5).

Since statement 2 indicates that n>p:
n-1 > p-1
(n-1)/(-5) < (p-1)/(-5). (When we divide by a negative value, we flip the inequality.)
Thus, the slope of line n < the slope of line p.
SUFFICIENT.

The correct answer is C.
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by Anurag@Gurome » Sun Apr 15, 2012 7:51 pm
priyank.hirani wrote:Lines n and p lie in the xy plane.Is the slope of line n less than the slpe of line p??

(1)Lines n and p intersect at (5,1)
(2)The y intercept of line n is greater than the y intercept of line p.
Let us assume that equation of line n is y = m1x + b1 and equations of line p is y = m2x + b2
Question is: Is m1 < m2?

(1) Lines n and p intersect at (5,1).
1 = m1 * 5 + b1 and 1 = m2 * 5 + b2
Subtracting the equations, we get, 0 = 5(m1 - m2) + (b1 - b2)
b2 - b1 = 5(m1 - m2); NOT sufficient.

(2) The y intercept of line n is greater than the y intercept of line p implies b1 > b2 or b2 - b1 < 0; NOT sufficient.

Combining (1) and (2), b2 - b1 = 5(m1 - m2) and (b2 - b1) < 0 implies 5(m1 - m2) < 0
m1 - m2 < 0
m1 < m2; SUFFICIENT.

The correct answer is C.
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