Last Updated on May 12, 2023
GMAT OFFICIAL GUIDE DS
Solution:
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
