Brent@GMATPrepNow wrote: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
Difficulty level: 650 - 700
Source:
www.gmatprepnow.com
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
