BTGModeratorVI wrote: ↑

Wed Feb 03, 2021 10:32 am

In the x-y coordinate plane, does line k have a positive x-intercept?

(1) (slope of line k)(y-intercept of line k) > 0
(2) (slope of line k) - (y-intercept of line k) < 0

Answer: A
Source: GMAT prep now

Target question: Does line k have a positive x-intercept?

Statement 1: (slope of line k)(y-intercept of line k) > 0
There are two possible cases that that satisfy statement 1:
- the slope and y-intercept are both positive
- the slope and y-intercept are both negative
Let's examine each case:

Case a: the slope and y-intercept are both positive
No matter now you sketch a line that has these two features, it will look something like this:

As you can see, the answer to the target question is NO, line k does NOT have a positive x-intercept

Case b: the slope and y-intercept are both negative.
No matter now you sketch a line that has these two features, it will look something like this:

As you can see, the answer to the target question is NO, line k does NOT have a positive x-intercept

In both cases, the answer to the target question is the SAME.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: (slope of line k) - (y-intercept of line k) < 0
There are several lines that satisfy statement 2. Here are two:
Case a:The line has a slope of -2 and y-intercept of -1 .

In this case, the answer to the target question is NO, line k does NOT have a positive x-intercept

Case b: The line has a slope of -2 and y-intercept of 1 .

In this case, the answer to the target question is YES, line k DOES have a positive x-intercept

Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent