Data Sufficiency

Hi sana.noor

In graphing questions, it usually helps to convert the given equations into y = mx + b format. In this case,

y = 3x/2 + k/2
y = jx + 7

The question asks at what point these two lines will intercept (at what point will x and y be the same for BOTH equations? Complicating things a bit are the two additional variables (k and j).

Fact 1 gives us a co-ordinate for the first line: (0,7).

Plug in those numbers for (x,y) and watch what happens:
7 = 0 + k/2
k = 14

Now, the two lines are;
y = 3x/2 + 7
y = jx + 7

Notice how the y-intercepts are the same in both equations? We now KNOW where the two lines intersect: at (0,7)
Fact 1 is SUFFICIENT

Fact 2 gives us a co-ordinate for the second line (3,1).

Plug those in and we get:
1 = j(3) + 7
-6 = 3j
-2 = j

Now our two equations are:
y = 3x/2 + k/2
y = -2x + 7

Unfortunately, we still have an unknown (k) that we can't figure out (and that keeps us from figuring out where the lines intersect).
Fact 2 is INSUFFICIENT

Final Answer: A (1 only is Sufficient)

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

sana.noor wrote:In the coordinate plane, line A is defined by the equation 3x + 2y = k, and line B is defined by the equation jx-y=-7. At what point do the two lines intersect?

(1) Line A passes through the point (0,7)
(2) Line B passes through the point (3,1)

Target question: At what point do the two lines intersect?

Given: line A is defined by the equation 3x + 2y = k, and line B is defined by the equation jx - y = -7

One strategy is to rewrite both equations in slope y-intercept form to get a better idea of how the variables k and j affect the lines.
We get line A: y = -3/2 x + k/2 (here we see that the slope of line A is -3/2, and k affects the line's y-intercept)
We also get line B: y = jx + 7 (here we see that j affects the slope of the line, and the y-intercept is 7 )

Statement 1: Line A passes through the point (0,7)
This tells us that the y-intercept of line A is 7.
Hey, the y-intercept of line B is also 7!
So, the two lines must intersect at (0,7)
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Line B passes through the point (3,1)
Remember that line B is defined by the equation y = jx + 7
So, if we plug x = 3 and y = 1 into the equation we can determine the value of j.
In fact, we get j = -2
So, line B is defined by the equation y = -2x + 7
However, this information tells us nothing about line A. All we know about line A is that it has slope of -3/2.
Since we don't know the y-intercept of line A, we have no idea where line A is located on the coordinate plane.
If we can't fix line A's position in the coordinate plane, we cannot determine its intersection with line B
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent