line L and k intersect at point 4,3. Is the product of their

Question

line L and k intersect at point 4,3. Is the product of their slopes negative?


1) The product of x-intercepts of the lines is positive

2) The product of the y-intercepts of the lines is negative.




I'm stumped why the correct answer is not  E

Fistail · Answer

E.
1. x of lines could be both -ves or both +ves. similarly the slopes could be both -ves and +ves. nsf.
2. if y intercept of one line is -ve, the the same of the other line is +ve and vice versa. again the slops could be both -ves, and +ves. so nsf.
togather also not sufficient.

Vlad77 · Answer

Yes it is C. Look inside!!!

Fistail · Answer

if the coordinates of Lines L and K are (-2, 1) and (-1, -15) respectively, their slopes are:
L = (1-3)/(-2-4) = -2/-6 = 1/3
K = (-15-3)/(-1-4) = -18/-5 = 18/5
so the product of their slopes is +ve.

again, if the coordinates of Lines L and K are (-2, 15) and (-1, -15) respectively, their slopes are:
L = (15-3)/(-2-4) = 12/-6 = -2
K = (-15-3)/(-1-4) = -18/-5 = 18/5
so the product of their slopes is -ve.


again, if the coordinates of Lines L and K are (2, 1) and (1, -15) respectively, their slopes are:
L = (1-3)/(2-4) = -2/-2 = 1
K = (-15-3)/(1-4) = -18/-3 = 6
their product is +ve.

again, if the coordinates of Lines L and K are (2, 15) and (1, -15) respectively, their slopes are:
L = (15-3)/(2-4) = 12/-2 = -6
K = (-15-3)/(1-4) = -18/-3 = 6
their product is -ve.

you have -ve and +ve as the product of the slopes. So how it is C?

bkk145 · Answer

C Say we have: Y1 = M1*X1 + B1 Y2 = M2*X2 + B2 (1) We have (-B1/M1) * (-B2/M2) > 0 We don't know the values of B, so INSUFFICIENT (2) B1*B2<0 Don't know anything about M, so INSUFFICIENT Together, we know that B1*B2 < 0 It must be the case that either B1 or B2 are negative. Now, using what we have from (1): (-B1/M1) * (-B2/M2) > 0 Take out negative sign: (B1*B2)/(M1*M2) > 0 Knowing that B1*B2 is negative This means that M1*M2 must also be negative. SUFFICIENT.

trivikram · Answer

Perfect <img src="{SMILIES_PATH}/icon_smile.gif" alt=":)" title="Smile" />

bkk145 · Answer

Bud, if I understand you correctly, I think you are misinterpreting the stem here. (1) says that the product of the  x-intercepts  are positive. (2) says that the product of the  y-intercepts  are negative. 
x-intercepts & y-intercepts aren't the slope.

Correct me if I am wrong. Otherwise, please show the multiplication of each x-y intercepts so I can understand this better.

Fistail · Answer

I believe i have not misunderstood the terms and used them as under:

Since (1) the product of x-intercepts of the lines is positive and (2) the product of the y-intercepts of the lines is negative, x intercepts of lines L and K are either both -ves, or both +ves. Similarly, y intercepts of lines L and K are opposite to each other. if so, then we have 4 scenarios as under: 

1. if the coordinates of Lines L and K are (-2, 1) and (-1, -15) respectively, their slopes are:
L = (1-3)/(-2-4) = -2/-6 = 1/3
K = (-15-3)/(-1-4) = -18/-5 = 18/5
so the product of their slopes is +ve.

2. if the coordinates of Lines L and K are (-2, 15) and (-1, -15) respectively, their slopes are:
L = (15-3)/(-2-4) = 12/-6 = -2
K = (-15-3)/(-1-4) = -18/-5 = 18/5
so the product of their slopes is -ve.

3. if the coordinates of Lines L and K are (2, 1) and (1, -15) respectively, their slopes are:
L = (1-3)/(2-4) = -2/-2 = 1
K = (-15-3)/(1-4) = -18/-3 = 6
their product is +ve.

4. if the coordinates of Lines L and K are (2, 15) and (1, -15) respectively, their slopes are:
L = (15-3)/(2-4) = 12/-2 = -6
K = (-15-3)/(1-4) = -18/-3 = 6
their product is -ve.

where i am missing??????????????????

bkk145 · Answer

Okay, let's take a look at this more carefully. To satisfy (1) and (2) 
x-intercept must be both negative or both positive <=basically the same sign
y-intercept must be one positive, one negative <=basically different sign

 1. if the coordinates of Lines L and K are (-2, 1) and (-1, -15) respectively, their slopes are:
L = (1-3)/(-2-4) = -2/-6 = 1/3
K = (-15-3)/(-1-4) = -18/-5 = 18/5
so the product of their slopes is +ve. 

In this case, 
L intersect (4,3) and (-2,1) then
x-intercept is negative, y-intercept is positive
K intersect (4,3) and (-1,-15), then 
x-intercept is positive, y-intercept is negative
Since x-intercepts have different sign,  this doesn't satisfy the stems .

 2. if the coordinates of Lines L and K are (-2, 15) and (-1, -15) respectively, their slopes are:
L = (15-3)/(-2-4) = 12/-6 = -2
K = (-15-3)/(-1-4) = -18/-5 = 18/5
so the product of their slopes is -ve. 

In this case, 
L intersect (4,3) and (-2,15) then
x-intercept is positive, y-intercept is positive
K intersect (4,3) and (-1,-15), then 
x-intercept is positive, y-intercept is negative
 This satisfy the stem. 

 
3. if the coordinates of Lines L and K are (2, 1) and (1, -15) respectively, their slopes are:
L = (1-3)/(2-4) = -2/-2 = 1
K = (-15-3)/(1-4) = -18/-3 = 6
their product is +ve.
 

In this case, 
L intersect (4,3) and (2,1) then
x-intercept is positive, y-intercept is negative
K intersect (4,3) and (1,-15), then 
x-intercept is positive, y-intercept is negative
Since y-intercepts have the same sign,  this doesn't satisfy the stems. 


 4. if the coordinates of Lines L and K are (2, 15) and (1, -15) respectively, their slopes are:
L = (15-3)/(2-4) = 12/-2 = -6
K = (-15-3)/(1-4) = -18/-3 = 6
their product is -ve. 

In this case, 
L intersect (4,3) and (2, 15) then
x-intercept is positive, y-intercept is positive
K intersect (4,3) and (1,-15), then 
x-intercept is positive, y-intercept is negative
 This satisfy the stems. 


The only valid comparison that you made are case 2 & 4 and they both produces negative multiplication of the slopes.
Clear?

line L and k intersect at point 4,3. Is the product of their

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards