Data Sufficiency

alishagmat wrote: ↑

Fri Oct 02, 2020 4:27 am

In the xy-plane, if line k has negative slope and passes through the point (-5,r) , is the x-intercept of line k positive?

(1) The slope of line k is -5.
(2) r > 0
[spoiler][/spoiler]

Target question: Is the x-intercept of line k positive?

When I scan the two statements, I can see that, if r is POSITIVE, then the point (-5, r) can be very close to the x-axis or the point (-5, r) can be very far from the x-axis.
Given this, let's go straight to the statements COMBINED, and see if we can find two cases that yield DIFFERENT answers to the target question.

CASE A: If r =1, then the point (-5, r) is very close to the x-axis, and we get something like this:

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


CASE B: If r =50, then the point (-5, r) is far from the x-axis, and we get something like this:

In this case, the answer to the target question is YES, the x-intercept of line k IS positive

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent