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Updated on: 01 Sep 2015, 08:30
Originally posted by Tornikea on 01 Sep 2015, 08:21.
Last edited by ENGRTOMBA2018 on 01 Sep 2015, 08:30, edited 1 time in total.
Last edited by ENGRTOMBA2018 on 01 Sep 2015, 08:30, edited 1 time in total.
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In the XY-coordinate plane, line A is defined by the equation j*x-y=-7 and line B is defined by the equation 3*x+2*y=k
If line A and line B are not parallel, at what point do they intersect?
(1) Line A passes through the point (3,1)
(2) Line B passes through the point (0,7)
If line A and line B are not parallel, at what point do they intersect?
(1) Line A passes through the point (3,1)
(2) Line B passes through the point (0,7)
25 Jun 2018, 21:00
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Hi All,
We're told that In the XY-coordinate plane, line A is defined by the equation (J)(X) - Y = -7 and line B is defined by the equation 3X + 2Y = K and that the two lines are NOT parallel. We're asked at what point they intersect. to start, with graphing questions, it usually helps to convert the given equations into slope-intercept format (re: Y = MX + B). In this case, the lines would be:
Y = (J)(X) + 7
Y = 3x/2 + K/2
We have to figure out at what point will X and Y be the same for BOTH equations.
1) Line A passes through the point (3,1)
With the co-ordinate in Fact 1, we can plug in and get....
1 = J(3) + 7
-6 = 3J
-2 = J
Now our two equations are:
Y = -2X + 7
Y = 3X/2 + K/2
Unfortunately, we still have an unknown (K) and that keeps us from figuring out where the lines intersect.
Fact 1 is INSUFFICIENT
2) Line B passes through the point (0,7)
With the co-ordinate in Fact 2, we can plug in and get....
7 = 0 + K/2
K = 14
Now, the two lines are;
Y = 3X/2 + 7
Y = (J)(X) + 7
Notice how the y-intercepts are the same in both equations? We now KNOW where the two lines intersect: at (0,7)
Fact 2 is SUFFICIENT
Final Answer:
GMAT assassins aren't born, they're made,
Rich
We're told that In the XY-coordinate plane, line A is defined by the equation (J)(X) - Y = -7 and line B is defined by the equation 3X + 2Y = K and that the two lines are NOT parallel. We're asked at what point they intersect. to start, with graphing questions, it usually helps to convert the given equations into slope-intercept format (re: Y = MX + B). In this case, the lines would be:
Y = (J)(X) + 7
Y = 3x/2 + K/2
We have to figure out at what point will X and Y be the same for BOTH equations.
1) Line A passes through the point (3,1)
With the co-ordinate in Fact 1, we can plug in and get....
1 = J(3) + 7
-6 = 3J
-2 = J
Now our two equations are:
Y = -2X + 7
Y = 3X/2 + K/2
Unfortunately, we still have an unknown (K) and that keeps us from figuring out where the lines intersect.
Fact 1 is INSUFFICIENT
2) Line B passes through the point (0,7)
With the co-ordinate in Fact 2, we can plug in and get....
7 = 0 + K/2
K = 14
Now, the two lines are;
Y = 3X/2 + 7
Y = (J)(X) + 7
Notice how the y-intercepts are the same in both equations? We now KNOW where the two lines intersect: at (0,7)
Fact 2 is SUFFICIENT
Final Answer:
GMAT assassins aren't born, they're made,
Rich
ENGRTOMBA2018
Joined: 20 Mar 2014
Last visit: 01 Dec 2021
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Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
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Updated on: 03 Sep 2015, 04:23
Originally posted by ENGRTOMBA2018 on 01 Sep 2015, 08:44.
Last edited by ENGRTOMBA2018 on 03 Sep 2015, 04:23, edited 1 time in total.
Last edited by ENGRTOMBA2018 on 03 Sep 2015, 04:23, edited 1 time in total.
Edited the wording to make it clearer.
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Tornikea
In the XY-coordinate plane, line A is defined by the equation j*x-y=-7 and line B is defined by the equation 3*x+2*y=k
If line A and line B are not parallel, at what point do they intersect?
(1) Line A passes through the point (3,1)
(2) Line B passes through the point (0,7)
If line A and line B are not parallel, at what point do they intersect?
(1) Line A passes through the point (3,1)
(2) Line B passes through the point (0,7)
Please follow the posting guidelines.
Given: A: y = jx+7, B : y = -1.5x+k/2
As A is NOT parallel to B ---> j \(\neq\)-1.5 ....(a)
Per statement 1, A passes through (3,1), without complete equation of B, we will not be able to solve this question. Not sufficient.
Check: solving the 2 equations y = -2x+7 and y = -1.5x+k/2, we get x = 14-k and y = 2k-21. Thus without the value 'k' we dont know the exact point of intersection.
Per statement 2, B passes through (0,7), thus 7 = 0+k/2 ---> k = 14. Thus, equation of B is y = -1.5x+7.
Solving for x, we get -1.5x+7=jx+7 ----> x(j+1.5) =0 ---> either x =0 or j=-1.5 but as per (a) above, j \(\neq\)-1.5
The only case possible is for x=0 ---> y =7 to be the actual point of intersection.
B is the correct answer.
Alternately, you can see that once you get the equations of A and B as
B: y = -1.5x+7
A: y = jx+7,
X-coordinate of intersection ----> -1.5x+7=jx+7 ---> x = 0. Put this value of x back into any 1 of the 2 equations, you will get y = 7 . Finally, note that the point of intersection is a constant/unique value without 'j' or 'k'
Hence B is sufficient to arrive at a unique answer.
