Max@Math Revolution wrote:
In the coordinate plane, is the x-intercept of the line ax + by + c = 0 less than 0?
1) ac > 0
2) bc > 0
Target question: Is the x-intercept less than 0?
This is a good candidate for
rephrasing the target question.
Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
The x-intercept is the point where a line crosses the x-axis. At this point, the
y-coordinate is ZERO
So, the x-intercept is the value of the x-coordinate when y =
0
Now take the equation of the line and replace y with
0 to get: ax + b(
0) + c = 0
Solve for x
Simplify: ax + c = 0
So: ax = -c
So: x = -c/a
This means the
x-intercept = -c/a
We can now REPHRASE the target question....
REPHRASED target question: Is -c/a less than 0?
Statement 1: ac > 0
If the product ac is positive, then EITHER a and c are both positive OR a and c are both negative
In both cases, c/a is positive, which means -c/a must be NEGATIVE
So, the answer to the REPHRASED target question is
YES, -c/a IS less than 0
Since we can answer the
REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: bc > 0
Since we aren't given any information about a, there's no way to determine whether
-c/a is less than 0 or greater than 0
Since we cannot answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
