AbeNeedsAnswers wrote:Line L lies in the xy-plane and does not pass through the origin. What is the slope of line L?

(1) The x-intercept of line L is twice the y-intercept of line L.
(2) The x- and y-intercepts of line L are both positive.

A

Target question: What is the slope of line l?

Statement 1: The x-intercept of line l is twice the y-intercept of line l
Let k = the y-intercept of line l
This means 2k = the x-intercept of line l
If the y-intercept is k, then line l passes through the y-axis at the point (0, k)
If the x-intercept is 2k, then line l passes through the x-axis at the point (2k, 0)
Since (0, k) and (2k, 0) are both points on line l, we can apply the slope formula to these points to find the slope of line l.
We get: slope = (k - 0)/(0 - 2k) = k/(-2k) = -1/2
So, the slope of line l = -1/2
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The x-and y-intercepts of line l are both positive
If we're able to imagine different lines (with DIFFERENT SLOPES) that satisfy this condition, we'll quickly see that statement 2 is not sufficient. However, if we don't automatically see this, we can take the following approach...
There are many different cases that satisfy statement 2 yet yield different answers to the target question. Here are two:
Case a: the x-intercept is 1 and the y-intercept is 1, which means line l passes through (1, 0) and (0, 1). Applying the slope formula, we get: slope = (0 - 1)/(1 - 0) = -1
Case b: the x-intercept is 2 and the y-intercept is 1, which means line l passes through (2, 0) and (0, 1). Applying the slope formula, we get: slope = (0 - 1)/(2 - 0) = -1/2
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

AbeNeedsAnswers wrote:Line L lies in the xy-plane and does not pass through the origin. What is the slope of line L?

(1) The x-intercept of line L is twice the y-intercept of line L.
(2) The x- and y-intercepts of line L are both positive.

We need to determine the slope of line L, given that it doesn't pass through the origin.

Statement One Alone:

The x-intercept of line L is twice the y-intercept of line L.

We can let b = the y-intercept of line L; thus, 2b = the x-intercept of line L. Thus, the two points through which line L passes are (2b, 0) and (0, b). With two points known, we can calculate the slope of line L:

(b - 0)/(0 - 2b) = b/(-2b) = -½

Statement one alone is sufficient to answer the question.

Statement Two Alone:

The x- and y-intercepts of line L are both positive.

Knowing that both the x- and y-intercepts of a line are positive does not allow us to determine the slope of the line. For example, the slope of the line with x-intercept = 1 and y-intercept = 2 will be different from the slope of the line with x-intercept = 1 and y-intercept = 3. Statement two alone is not sufficient to answer the question.

Answer: A

Hi All,

We're told that Line L lies in the xy-plane and does NOT pass through the origin. We're asked for the slope of line L. This question can be solved by TESTing VALUES (and drawing a few pictures as needed).

1) The X-intercept of line L is TWICE the Y-intercept of line L.

With the X-intercept and the Y-intercept, we can calculate the slope of the line. Now we just have to see if the answer stays the same or changes based on the values we TEST...
IF....
The X-intercept is 2 and the Y-intercept is 1, then the points (2,0) and (0,1) are on the line and the slope is (0 - 1)/(2 - 0) = -1/2.
The X-intercept is 4 and the Y-intercept is 2, then the points (4,0) and (0,2) are on the line and the slope is (0 - 2)/(4 - 0) = -2/4 = -1/2.
The X-intercept is -6 and the Y-intercept is -3, then the points (-6,0) and (0, -3) are on the line and the slope is (0 - -3)/(-6 - 0) = 3/-6 = -1/2.
The slope is ALWAYS -1/2
Fact 1 is SUFFICIENT

2) The X- and Y-intercepts of line L are both positive.

IF....
The X-intercept is 2 and the Y-intercept is 1, then the points (2,0) and (0,1) are on the line and the slope is (0 - 1)/(2 - 0) = -1/2.
The X-intercept is 2 and the Y-intercept is 2, then the points (2,0) and (0,2) are on the line and the slope is (0 - 2)/(2 - 0) = -2/2 = -1.
Fact 2 is INSUFFICIENT

Final Answer: A

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