XY coordinate

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danjuma: Senior | Next Rank: 100 Posts; Posts: 89; Joined: Thu Aug 26, 2010 9:29 am; Thanked: 4 times

by danjuma » Mon Nov 01, 2010 8:46 pm

In the XY coordinate plane, lines L and K intersect at the point (4,3). Is the product of their slopes negative?

a. The product of the x-intercept of lines l and k is positve

b.The product of the y-intercept of lines l and k is negative

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Source: Beat The GMAT — Data Sufficiency | Mon Nov 01, 2010 8:46 pm

Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Tue Nov 02, 2010 11:55 am

danjuma wrote:In the XY coordinate plane, lines L and K intersect at the point (4,3). Is the product of their slopes negative?

a. The product of the x-intercept of lines l and k is positive

b.The product of the y-intercept of lines l and k is negative

Looked into this problem when did GMAT Prep. It has been over-solved at the forum and comes pretty easy after finishing OG11.

Basically, you know what's the slope ... linear equation y=ax+b where a is a slope (direction, also unit change in y for every unit change in x) of the line and b is intercept.

slope is derived by using formula = change in y over change in x or (y1-y0/x1-x0)

Question asks for the sign of value of the product of slopes i.e. +, -. We need to solve for individual signs of each slope and then will decide on the product sign.

To solve this problem and to answer a question we need to assign missing x values (x0 and x1, BTW x0 is x-intercept here) and locate missing y0 value or y-intercept. We are given in the problem x1 and y1 for both lines as they cross at the point (4, 3) hence x1=4, y1=3.

Now calculate the sign of value - you would need the sign for value in nominator (y1-y0) and denominator (x1-x0) for both lines. Two lines have identical x1 and y1 since they cross at point (4,3) we need to assign signs (+, -) for their x and y intercepts or x0 and y0. Only with the statements (1) and (2) taken together this is possible. So the answer is C.

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diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Wed Nov 03, 2010 5:27 am

danjuma wrote:In the XY coordinate plane, lines L and K intersect at the point (4,3). Is the product of their slopes negative?

a. The product of the x-intercept of lines l and k is positve

b.The product of the y-intercept of lines l and k is negative

L: y=ax+b L's x intercept x=-b/a and y intercept=b
K: y=cx+d K's x intercept x= -d/c and y intercept= d
1/ -b/a*-d/c=ab/cd >0 this could happen wen ab>0 and cd>0 or ab<0 and cd<0
insufficient
2/ bd<0 while ac is unknown so insufficient
1+2: bd<0 so ca<0 sufficient
pick C

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