Is the slope of N less than P?

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Dean Jones: Master | Next Rank: 500 Posts; Posts: 239; Joined: Thu Oct 28, 2010 8:40 amFollowed by: 2 members; Location: India; Thanked: 5 times; GMAT Score:690

by Dean Jones » Mon Jul 11, 2011 7:38 am

Hi friends,

I am having problems in solving the below mentioned problem. Please help.

Lines N and P lie in the x-y plane. Is the slope of the line N less than the slope of line P?
(1) Lines N and N intersect at (5, 1)
(2) The y-intercept of line N is greater than y-intercept of line

OA after some discussions.

Regards
Deano.

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Source: Beat The GMAT — Data Sufficiency | Mon Jul 11, 2011 7:38 am

Mom4MBA: Senior | Next Rank: 100 Posts; Posts: 90; Joined: Fri Jan 22, 2010 1:10 pmFollowed by: 4 members; Location: New Jersey; Thanked: 13 times; GMAT Score:640

by Mom4MBA » Mon Jul 11, 2011 9:38 am

statement 1:
alone is not sufficient, as nothing is known about the slopes. infinite lines with various slopes can pass through point (5,1)

statement 2:
alone is not sufficient. nothing can be done with intercepts alone.

taking together
plug (5,1) in the equation of both the lines

y = mx + c

5 = m1 + c1 .....equation for N
5 = m2 + c2 .....equation for P

m1 = 5 - c1
m2 = 5 - c2

if given c1 > c2 (intercept of N > intercept of P)

take all three conditions :
1) c1, c2 positive [let c1=2, c1=1]

m1 = 5 - c1 = 3
m2 = 5 - c2 = 4

m2 > m1

2) c1, c2 negative [let c1=-1, c1=-2]

m1 = 5 - c1 = 5 + 1 = 6
m2 = 5 - c2 = 5 + 2 = 7

m2 > m1

3) c1 positive, c2 negative [let c1=2, c1=-1]

m1 = 5 - c1 = 5 - 2 = 3
m2 = 5 - c2 = 5 + 1 = 6

m2 > m1

case 4 where c1 negative, c2 positive cannot be taken as that would make c1 < c2, hence not fulfilling condition in statement 2

so m2 > m1

hence both together sufficient

answer c

Last edited by Mom4MBA on Mon Jul 11, 2011 8:45 pm, edited 1 time in total.

Stay focused

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clock60: Legendary Member; Posts: 759; Joined: Mon Apr 26, 2010 10:15 amFollowed by: 3 members; Thanked: 85 times

by clock60 » Mon Jul 11, 2011 12:07 pm

Hi all,
for sure i agree that the answer on this problem is C and i solved the same way as Mom4MBA, but with very little correction that in no way change the answer
plug (5,1) in the equation of both the lines

y = mx + c

5 = m1 + c1 .....equation for N
5 = m2 + c2 .....equation for P
here coordinates of the point where two lines intersect are x=5 and y=1 (5.1)
so the resulting equations must looks like
1=m1*5+c1
1=m2*5+c2
in this problem the reversed coordinates does not matter, but in others it is still useful

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tpr-becky: GMAT Instructor; Posts: 509; Joined: Wed Apr 21, 2010 1:08 pmFollowed by: 85 members; Location: Irvine, CA; Thanked: 199 times; GMAT Score:750

by tpr-becky » Mon Jul 11, 2011 1:01 pm

Another way of thinking of the problem

1) - gives no slope info so BCE
2) y intercept is not helpful for slope without another point.

think of drawing this - if both y intercepts are positive - then n the slope is negative and the slope of n is smaller (a larger negative). If both y intercepts are negative then both slopes are positive and n has the smaller slope. if one is negative and one is positive then the slope of n is negative and the slope of P is positive. So each time slope of p is bigger. Thus it will work.

Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA

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Dean Jones: Master | Next Rank: 500 Posts; Posts: 239; Joined: Thu Oct 28, 2010 8:40 amFollowed by: 2 members; Location: India; Thanked: 5 times; GMAT Score:690

by Dean Jones » Mon Jul 11, 2011 5:50 pm

OA is C

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