Question: Intersection of Lines A and B

Comment on Intersection of Lines A and B

thas cool..

How would this approach change if the question said the two lines were parallel?

gmat-admin's picture

Parallel will never intersect.
So, the question would be unanswerable of the two lines were parallel.

I thought of an insight to answer this question without really doing any work.

Line A's formula gives us one definite point(y-intercept), but doesn't tell us the slope.

Line B's formula tells us the slope but doesn't give us a point.

Statement 1 tells us another point, so since we have two points for line A, it is fully constrained (we can plot it). We can tell that it is insufficient because we can imagine line B as a line with an arbitrary constant slope that isn't constrained in terms of vertical displacement (we can visualize a line that is able to slide up and down)

And statement 2 gives us this the same y-intercept given in the question.
gmat-admin's picture

Perfect logic for statement 1!
Nice work!


Thank you. Out of curiosity, I went further to solve for both equations. I noticed they are both y=-3/2x + 7, am I right? How can two lines not be parallel if they have the same equation?
gmat-admin's picture

You're correct to say the equation of line B is y = (-3/2)x + 7, but the equation of line A is different.

Line A: jx - y = -7
The point (3,1) lies on the line. So, we can plug in those values to get:
j(3) - 1 = -7
Add 1 to both sides: 3j = -6
Solve: j = -2
So, the equation of line A is: -2x - y = -7
Solve for y to get: y = -2x + 7


Thank you! I see it now. I must have missed a step the first time.

Hi Brent,

I understood the solution, but I am kind of confused...

I remember in one of your Data Sufficiency videos you recommended that we shall never use information from one statement when analyzing the other statement, except when examining the statements combined. However, this is not the case since we used info from statement 1 (Line A) to compare it with the info given in statement 2. Can you please explain?

gmat-admin's picture

I think you're confusing information about line A with statement 1.
The information about lines A and B is found in the given information (not in the statements).
Line A is defined by the equation jx - y = -7, and Line B is defined by the equation 3x + 2y = k.
Notice that neither equation has anything to do with statements 1 or 2.

The only thing that statement 1 tells us is that line a passes through the point (3, 1), and we never use that information when analyzing statement 2.

Does that help?

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