paldrich1287 wrote:
(Note: I found two older topics for this question, but they were each over a year old and I assumed there were bump rules here..)
This is from Kaplan CAT3:
If ab < ac, which is greater, b or c?
(1) a < 0
(2) c < 0
Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
EITHER statement BY ITSELF is sufficient to answer the question.
Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.
I just have one issue with this problem: when I originally did it I tried picking numbers rather than just dividing by -a to get b > c. This is what I got:
(1) If a < 0, then perhaps a = -1. Then if b =3 and c=2, ab < ac and c > b. But if b = -2 and c = -3, ab < ac and b > c.
I'm not finding any rules I'm missing in the problem, so my answer was C.. or E... Why is the above reasoning wrong?
Thanks...
\(ab<ac\) can be rewritten as \(ab-ac<0\) or \(a(b-c)<0\), which means that \(a\) and \(b-c\) have opposite signs.
(1) \(a<0\) then necessarily \(b-c>0.\)
Sufficient.
(2) \(c<0\)
Obviously not sufficient, as we know nothing about \(b.\)
Answer A.