Slope of LIne

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tttrn333: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Thu Sep 08, 2011 8:06 am; Followed by:1 members

Slope of LIne

by tttrn333 » Mon Sep 19, 2011 3:21 am

Line m and n lie in the xy-plane and intersect at the point (-2,-4). Is the slope of line m less than the slope of n?

1) X-intercept of m is greater than n

2) y-intercept of line n is greater than m

OA: D

I don't see how 1 is sufficient. Suppose line M has intercept of 10 and positive slope. Now suppose slope of N is negative with x-intercept at negative 3. Slope of N is less than Slope of M. The case for Slope of N is greater than Slope of M if x-intercept of N is greater than zero and less than N.

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Source: Beat The GMAT — Data Sufficiency | Mon Sep 19, 2011 3:21 am

cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 am; Location: India; Thanked: 310 times; Followed by:123 members; GMAT Score:750

by cans » Mon Sep 19, 2011 3:55 am

B) y=mx+p and y=nx+q. q>p
(-2,4)
4=-2m+p = -2n+q
2(m-n) = p-q.
p-q<0
thus m<n. Sufficient

i think it hsould be B. As A is not sufficient

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knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pm; Thanked: 114 times; Followed by:11 members

by knight247 » Mon Sep 19, 2011 4:17 am

(1) X-intercept of m is greater than n
Both lines pass thru (-2,-4). We can use that as the point for calculation of the slope for both lines.
At the x-intercept of each line y=0 so it will be of the form (a,0) for both lines. Since x intercept of m is greater than n lets plug in values,

Let x intercept of m be (4,0) and since it passes thru (-2,-4) slope m=[0-(-4)]/[4-(-2)]=4/6

Let x intercept of n be (2,0) since it passes thru (-2,-4) slope m=[0-(-4)]/[2-(-2)]=1

Let x intercept of m be (3,0) so slope will be 4/5
Let x intercept of n be (-6,0) so slope will be -1 here the slope of m is greater than n. Since we get conflicting values. Hence INSUFFICIENT.

You can try plugging in other values by urself to verify this as long you keep in mind that x intercept of m has to be greater than x intercept of n

(2) y-intercept of line n is greater than m

Just like above y intercept of each line is going to be of the form (0,a). Take (-2,-4) as the point for calculating slope of each line. Take values of y intercept of m as (0,6) and values of y intercept of n as (0,8) and calculate the slope. U'll see that that slope of n is always greater than that of m. SUFFICIENT Hence B

Last edited by knight247 on Tue Sep 20, 2011 5:09 am, edited 1 time in total.

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knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pm; Thanked: 114 times; Followed by:11 members

by knight247 » Mon Sep 19, 2011 4:19 am

tttrn333 wrote: I don't see how 1 is sufficient. Suppose line M has intercept of 10 and positive slope. Now suppose slope of N is negative with x-intercept at negative 3. Slope of N is less than Slope of M. The case for Slope of N is greater than Slope of M if x-intercept of N is greater than zero and less than N.

Also Bro, when your making assumptions you can't directly assume the slopes to be negative or positive. You have to consider values of x and y intercept for lines m and n as per the conditions in statements 1 and 2 and then calculate the slope. Cheers.

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 am; Location: India; Thanked: 310 times; Followed by:123 members; GMAT Score:750

by cans » Mon Sep 19, 2011 9:41 am

x-intercept of m>n.
m: my = x-p and n: ny=x-q.
p>q (x-intercept)
also (-2,4)
4m=-2-p and 4n=-2-q.
4(n-m)=p-q
or (n-m)>0. or n>m...
Slope: 1/m and 1/n...
if n>m, how can we say that 1/m < 1/n??????
maybe they are positive or negative........

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dhonu121: Master | Next Rank: 500 Posts; Posts: 316; Joined: Sun Aug 21, 2011 6:18 am; Thanked: 16 times; Followed by:6 members

by dhonu121 » Mon Sep 19, 2011 11:47 am

knight247 wrote:@tttrn333 . The answer IS D

(1) X-intercept of m is greater than n
Both lines pass thru (-2,-4). We can use that as the point for calculation of the slope for both lines.
At the x-intercept of each line y=0 so it will be of the form (a,0) for both lines. Since x intercept of m is greater than n lets plug in values,

Let x intercept of m be (4,0) and since it passes thru (-2,-4) slope m=[0-(-4)]/[4-(-2)]=4/6

Let x intercept of n be (2,0) since it passes thru (-2,-4) slope m=[0-(-4)]/[2-(-2)]=1

Slope of n is greater than m. SUFFICIENT

You can try plugging in other values by urself to verify this as long you keep in mind that x intercept of m has to be greater than x intercept of n

(2) y-intercept of line n is greater than m

Just like above y intercept of each line is going to be of the form (0,a). Take (-2,-4) as the point for calculating slope of each line. Take values of y intercept of m as (0,6) and values of y intercept of n as (0,8) and calculate the slope. U'll see that that slope of n is always greater than that of m. SUFFICIENT Hence D