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

Redeem

Is the product of the slopes negative?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 239
Joined: Thu Oct 28, 2010 8:40 am
Location: India
Thanked: 5 times
Followed by:2 members
GMAT Score:690

Is the product of the slopes negative?

by Dean Jones » Mon Jul 11, 2011 7:41 am
Hi Freinds,

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

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-intercepts of line L and K is positive.
(2) The product of the y-intercepts of line L and k is negative.

OA after some discussion.

Regards
Deano.
Top
Source: — Data Sufficiency |
Legendary Member
Posts: 759
Joined: Mon Apr 26, 2010 10:15 am
Thanked: 85 times
Followed by:3 members

by clock60 » Mon Jul 11, 2011 11:31 am
hi, i saw this problem, earlier and try to say something
line L=y=kx+b, and
line K=y=k1*x+b1,
we need to estimate does k*k1<0
(1)if y=0, then for line L. kx=-b,x=-b/k and for line K k1*x=-b1. x=-b1/k1 and the product of x interceps is +ve
(-b/k)*(-b1/k1)>0
(b*b1)/(k*k1)<0 it possible in two cases
b*b1>0 and k*k1<0 or
b*b1<0 and k*k1>0 as we don`t know for sure the sign st 1 is insuff
(2)if x=0 then for line L y=b and for line K y=b1
and given that b*b1<0, but nothing is said about k and k1 also insuff
both
as b*b1>0 from 1 st it follows that k*k1<0
so suff my answer is C
P,S don`t know for what purpose we need point (4,3)
Top
Legendary Member
Posts: 1084
Joined: Fri Apr 15, 2011 2:33 pm
Thanked: 158 times
Followed by:21 members

by pemdas » Mon Jul 11, 2011 11:47 am
the easiest way to solve this q. is to start from the question itself and to fix x,y coordinates for L and K to prove the product of their slopes can be negative, positive or both.
st(1) is not Sufficient alone as it fixes only x coordinate for the intercepts (y=0) and can be positive for their products on the LHS from the origin too;
st(2) is not Sufficient alone as well, it can be below y=3 but still negative with another coordinate of y below 0;
combined st(1&2) we get the fixed ceilings for x and y coordinates crossing the point (4,3) and exclude x on the LHS (only RHS may exist) Sufficient;

c
Dean Jones wrote:Hi Freinds,

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

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-intercepts of line L and K is positive.
(2) The product of the y-intercepts of line L and k is negative.

OA after some discussion.

Regards
Deano.
Success doesn't come overnight!
Top
Master | Next Rank: 500 Posts
Posts: 239
Joined: Thu Oct 28, 2010 8:40 am
Location: India
Thanked: 5 times
Followed by:2 members
GMAT Score:690

by Dean Jones » Mon Jul 11, 2011 5:56 pm
OA is C
Top
User avatar
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

by GMATGuruNY » Mon Jul 11, 2011 7:48 pm
I
Dean Jones wrote:Hi Freinds,

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

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-intercepts of line L and K is positive.
(2) The product of the y-intercepts of line L and k is negative.

OA after some discussion.

Regards
Deano.
Don't solve. Draw.

Statement 1: The product of the x-intercepts of line L and K is positive.
K has a negative x-intercept, L has a negative x-intercept, the product of the slopes is positive:
Image

K has a positive x-intercept, L has a positive x-intercept, the product of the slopes is negative:
Image
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:
Image

K has a negative y-intercept, L has a positive y-intercept, the product of the slopes is positive:
Image
Insufficient.

Statements 1 and 2 combined:
Statement 1 requires that both x-intercepts be negative or that both be positive (so that their product is positive).
If both x-intercepts are negative, then both y-intercepts must be positive, which does not satisfy statement 2:
Image

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:
Image
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
Top
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Thu Dec 16, 2010 8:59 am

by mohank80 » Sun Jul 24, 2011 8:06 am
Dean Jones wrote:Hi Freinds,

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

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-intercepts of line L and K is positive.
(2) The product of the y-intercepts of line L and k is negative.

OA after some discussion.

Regards
Deano.
Is this true for all lines. If
(1) The product of the x-intercepts of line L and K is positive.
(2) The product of the y-intercepts of line L and k is negative.
Then: the product of their slopes negative?
Top
Post new topic Post Reply
• Page 1 of 1