BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

lines r & s

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 265
Joined: Tue Jul 03, 2012 11:04 pm
Followed by:6 members

lines r & s

by grandh01 » Thu Sep 27, 2012 11:06 am
Lines r and s lie in the xy-plane. Is the y-intercept of line r less
than the y-intercept of line s ?
(1) At the intersection point of r and s, the x-coordinate
and y-coordinate are both negative.
(2) The slope of line r is greater than the slope of line s.

oa is c
Top
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 am
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

by Ian Stewart » Thu Sep 27, 2012 1:19 pm
You can see the answer here just by drawing scenarios on a coordinate plane, but in words:

Neither statement alone tells you anything about where the lines cross the y-axis.

Together, we know they share a point with a negative x coordinate. If the slope of R is greater than the slope of S, then R rises more quickly as it moves to the right than S does (or it falls more slowly, if they have negative slopes). So as we move right from their intersection point to the y-axis, R will be higher than S, and thus has a greater y-intercept, and the answer is C.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Thu Sep 27, 2012 8:35 pm
grandh01 wrote:Lines r and s lie in the xy-plane. Is the y-intercept of line r less
than the y-intercept of line s ?
(1) At the intersection point of r and s, the x-coordinate
and y-coordinate are both negative.
(2) The slope of line r is greater than the slope of line s.

oa is c
Let the equation of line r be y = m1x+c1, where m1 is the slope and c1 is the y intercept.
Let the equation of line s be y = m2x+c2, where m2 is the slope and c2 is the y intercept.
We need to know whether c1 < c2 or not.

Statement 1:
At the intersection point x = (c2 - c1)/(m1-m2), y = (m1c2 - m2c1)/(m1-m2).
Now, x < 0 and y < 0.
Or (c2 - c1)/(m1-m2) < 0 and (m1c2 - m2c1)/(m1-m2) < 0.
But this is not enough to tell us whether c1 < c2 or not.
We need to know about m1 and m2 as well; NOT sufficient.

Statement 2:
It says m1 > m2.
But this does not tell us whether c1 < c2 or not; NOT sufficient.

Combine (1) and (2):
Since m1 > m2, (m1 - m2) > 0.
Also, since (c2 - c1)/(m1-m2) < 0 from (1), c2 - c1 < 0.
Or c1 > c2.
So, the answer to the main question is NO; SUFFICIENT.

The correct answer is C.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
Post new topic Post Reply
• Page 1 of 1