In the xy-coordinate plane, line A is defined by the equation j*x-y=-7

Question

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)

EMPOWERgmatRichC · Accepted Answer

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:  B

GMAT assassins aren't born, they're made, 
Rich

ENGRTOMBA2018 · Answer

Please follow the posting guidelines.

Given: A: y = jx+7, B : y = -1.5x+k/2

As A is NOT parallel to B ---> j  
eq -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  
eq -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.

anupamadw · Answer

Sorry, red part is not clear, you solved A and B , got j=-1.5 --> The only case possible is for (0,7) to be the actual point of interesection, can you please elaborate ..please
B: y = -1.5x+7
A: y = jx+7

ENGRTOMBA2018 · Answer

Sure, look below.

From statement 2, you get the equation of line B: y = -1.5x+7 and A: y= jx+7

Now,when you plot A and B such that j  
eq -1.5, you will see that

y = -1.5x+7 and
y = jx+7 (with j = anything BUT -1.5)

will intersect at (0,7) ONLY. Try with j = 2 or 5 or 10 or -4.

Case 1: j = 2 ---> A: y = 2x+7 and B: y = -1.5x+7 ---> (0,7) is the ONLY point of intersection.

Case 2: j = 10 ---> A: y = 10x+7 and B: y = -1.5x+7 ---> (0,7) is the ONLY point of intersection.

Case 3: j = -10 ---> A: y = -10x+7 and B: y = -1.5x+7 ---> (0,7) is the ONLY point of intersection.

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.

Hope this helps.

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.

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)
 
Transforming the original condition and question, jx-y=-7, 3x+2y=k and we have 2 variable (j,k), 1 equation. Since we need to match the number of variables and equations, we need 1 more equation and sine we have 1 each in 1) and 2), D is likely the answer.

In case of 1), 3j-1=-7, j=-2 but we don't know what k is, thus we can't find the point of interaction
In case of 2), 3*0+2*7=k gives us k=14 and line B: 3x+2y=14, y=-1.5x+7. Since line A cross (0,7) in jx-y=-7, line A and line B are not parallel and they meet in (0,7). Thus the condition is sufficient.Therefore the answer is B.

ENGRTOMBA2018 · Answer

IMO, your quote "Remember equal number of variables and equations ensures a solution." is a bit misleading as it should be stated as "Remember equal number of variables and DISTINCT equations ensures a solution.".

Case in point,

2a+3b =16
4a+6b=-3.5. Although you have 2 equations and 2 variables, you still can not find the solution as the 2 equations are necessarily the same.

Lucy Phuong · Answer

Good question. Just learn my own lesson that never ever overlook a single detail of information provided that is, in this case, (0,7)

General equation for any line on x-y coordinate: y=ax+b
--> Line A: y=j*x+7
Line B: y=-1.5x + 0.5k

(0,7) is definitely a turning point, which helps 0.5k=7 matched exactly with 7 in equation of line A. Remember (0,7) is the one and only point that makes statement (2) become sufficient. Otherwise, if that is another value, let's say (0,5), we cannot find intersect point with only statement (2), because j*x+7=-1.5x+5, then (j+1.5)x = -2. In this case, we cannot find out a consistent answer.

Well in the first place, I just thought we cannot work out intersect point without knowing proper equations of lines A and B. That's why I ended up with option (C) in only 20s. Oh goshhhh too fast too "dangerous":'(

AdityaHongunti · Answer

Cool Cool Cool..

First lets absorb the info and infer as much as we can >
equation of line >> y=mx+b >> m=slope >> b = y intercept (0,b)
 line A: jx-y=-7 >> y=jx+7 >> get y intercept>> put x=0 > y=7 (y intercept)> Line A intersects Y axis at (0,7). 
Line B: 3x+2y=k >> y= -1.5x+k/2 >> K is the Y intercept of line B.

Line A NOT PARALLEL to line B >> slopes of parallel lines are equal>> given- lines not parallel. Therefore slopes are not equal >> slope of B =-1.5 >> slope of A CANNOT BE -1.5.

Question- Point of intersection of lines A & B.

St 1. line A passes through the point (3,1) >> we can get the slope of line A >> m=(y1-y2/x1-x2) >> but line B can pass through anywhere .  INSUFFICIENT.

st2. Line B passes through point (0,7) >>  but (0,7) is also a point on Line A  as (0,7) is y intercept of line A >> Therefore point of intersection = (0,7) >>  SUFFICIENT.

Hero8888 · Answer

To those who struggle with questions about xy-plane: 99% of such questions can be solved drawing lines on xy plane, without messing with formulae. Just start drawing, and the answer will jump on you.

thangvietnam · Answer

this is tricky. we do not need to have 2 identified lines. we need just that the two line intersect at a specific point. mayber one line is unidentifie or mayby both lines are unidentified but both of them need to intersect at one specific point for us to find out the point.

with this thinking in mind, we anticipate that we need to find the specific point, not find 2 identified lines.

i dont think that we can do so on test day

with this thinking in mind, we anticipate that we need to find the specific point, not find 2 identified lines.

i dont think that we can do so on test day

CEdward · Answer

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

A: y = jx + 7
B: y = -3/2x + k/2

If line A and line B are not parallel, at what point do they intersect?

(1) Line A passes through the point (3,1)
y = jx + 7
1 = 3j + 7
j = -2

y = -2x + 7

Insufficient

(2) Line B passes through the point (0,7)
y = -3/2x + k/2
7= -3/2(0) + k/2
k = 14

y = -3/2x + 7

Sufficient (A and B each have the same y-intercept: 0,7)

B

bumpbot · Answer

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In the xy-coordinate plane, line A is defined by the equation j*x-y=-7

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