Max@Math Revolution wrote:Is x-intercept of y=ax+b greater than 0?
1) ab < 0
2) a+b<0
Target question: Is x-intercept POSITIVE?
The x-intercept is the x-value that satisfies the equation of the line when y = 0
So, we take y = ax + b and let y = 0 to get: 0 = ax + b
Subtract b from both sides to get: -b = ax
Divide both sides by a to get: -b/a = x
So, the x-intercept will be
-b/a
This means we can REPHRASE the target question as ....
REPHRASED target question: Is -b/a POSITIVE?
Aside: We have a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Statement 1: ab < 0 (in other words, ab is NEGATIVE)
This information is sufficient to answer the REPHRASED target question.
If the product ab is NEGATIVE, then we know that one value is positive and one is negative.
This tells us that b/a is also NEGATIVE,
which means -b/a is POSITIVE
Since we can answer the
REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: a+b<0
There are several values of a and b that satisfy statement 2. Here are two:
Case a: a = -1 and b = -1. In this case
-b/a = -1. In other words, -b/a is NEGATIVE
Case b: a = 1 and b = -2. In this case
-b/a = 2. In other words, -b/a is POSITIVE
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer =
A
Related Video
x- and y- intercepts:
https://www.gmatprepnow.com/module/gmat ... /video/996
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
