If ab < ac, which is greater b or c ? (1) a < 0 (2) c < 0

I think you are confused with notation: statement (1) says that \(a<0\), which means that \(a\) is negative, so it can not equal to 0.1 or any other non-negative value.

hi guys .... i am a beginner in prep for GMAT. I left mathematics a very very long ago ... i have a question regarding the problem...


the question itself says

ab < ac ............can't we subtract a from either side straight away which will yield ...

b < c directly from the stem itself. We have answer without any further condition. a could be anything but if ab<ac it has to as per my understanding b<c.

anyone can throw light on it ...?

I think you mean divide instead of subtract.

Never multiply or reduce (divide) inequality by an unknown (a variable) unless you are sure of its sign since you do not know whether you must flip the sign of the inequality.

So you can not divided (reduce) \(ab<ac\) by \(a\) and write \(b<c\) because you don't know whether \(a\) is positive or negative: if it's positive then you should write \(b<c\) but if its negative then you should flip the sign and write \(b>c\). Statement (1) says \(a<0\), so when reducing by \(a\) we should flip the sign and write \(b>c\).

Hope it's clear.

Thanks. Yes its clear.

Posted from my mobile device

(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...

Above c>b in yellow is incorrect. It is c<b becasue b =3 and c=2. Hence answer is A.

\(ab<ac\) 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.

D'oh! I figured it was something very obvious.. thanks..

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