In the xy coordinate plane, line L and line K intersect at the point (4,3). Is the product of their slopes negative?
1) The product of the x-intersects of lines L and K is positive.
2) The product of the y-intersects of lines L and K is negative.
The OA is C
Source: GMAT Prep
In the xy coordinate plane, line L and line K intersect at
This topic has expert replies
GMAT/MBA Expert
- Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Say the equations of line L and K areswerve wrote:In the xy coordinate plane, line L and line K intersect at the point (4, 3). Is the product of their slopes negative?
1) The product of the x-intersects of lines L and K is positive.
2) The product of the y-intersects of lines L and K is negative.
The OA is C
Source: GMAT Prep
y = m1*x + c1; eqn of line L;
y = m2*x + c2; eqn of line K
Here, m1 and m2 are slopes of line L and line K; and c1 and c2 are y-intercepts of line L and line K.
We have to determine whether m1*m2 < 0.
Let's take each statement one by one.
1) The product of the x-intersects of lines L and K is positive.
Let's transform the equations to get the x-intersects.
We have
y = m1*x + c1=> y - c1 = m1*x => y/m1 - c1/m1 = x => x-intercept of line L = -c1/m1
y = m2*x + c2=> y - c2 = m2*x => y/m2 - c2/m2 = x => x-intercept of line K = -c2/m2
Thus, (-c1/m1)*(-c2/m2) > 0
(c1*c2)/(m1*m2) > 0
Case 1: If c1*c2 > 0, we muat have m1*m2 > 0; the answer is No.
Case 2: If c1*c2 < 0, we must have m1*m2 < 0; the answer is Yes.
No unique answer. Insufficient.
2) The product of the y-intersects of lines L and K is negative.
=> c1*c2 < 0
It can't help determine whether m1*m2 < 0. Insufficient.
(1) and (2) together
Thus, Case 1 discussed in Statement 1 is invalid; or, only Case 2 is valid; thus, m1*m2 < 0. Sufficient.
The correct answer: C
Hope this helps!
-Jay
_________________
Manhattan Review GMAT Prep
Locations: GMAT Classes Boston | GMAT Tutoring NYC | GRE Prep Dallas | TOEFL Prep Classes Seattle | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Statement 1: The product of the x-intercepts of line L and K is positive.swerve wrote:In the xy coordinate plane, line L and line K intersect at the point (4,3). Is the product of their slopes negative?
1) The product of the x-intersects of lines L and K is positive.
2) The product of the y-intersects of lines L and K is negative.
K has a negative x-intercept, L has a negative x-intercept, the product of the slopes is positive:
K has a positive x-intercept, L has a positive x-intercept, the product of the slopes is negative:
INSUFFICIENT.
Statement 2: The product of the y-intercepts of line L and k is negative.
K has a negative y-intercept, L has a positive y-intercept, the product of the slopes is negative:
K has a negative y-intercept, L has a positive y-intercept, the product of the slopes is positive:
INSUFFICIENT.
Statements 1 and 2 combined:
Statement 1 requires that both x-intercepts be negative or that both x-intercepts be positive (so that their product is positive).
If both x-intercepts are negative, then both y-intercepts must be positive, violating statement 2:
Thus, both x-intercepts must be positive.
Statement 2 requires that one of the y-intercepts be positive, the other negative.
A positive x-intercept and a positive y-intercept yields a negative slope.
A positive x-intercept and a negative y-intercept yields a positive slope.
See below:
Thus, the product of the slopes must be negative.
SUFFICIENT.
The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3