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As you said Both a or c-b should be +ve or both should be -ve.

Let assume a= .1 its is a positive b = .1 c= .2

AB = .1*.1 = 0.01 AC = .1*.2 = 0.02

so ab< ac

In this case if a < 0 and a is -ve then b>c but if a<0 and +ve then C>b

So we are not pretty sure.. Again in the question it is not mentioned that a,b,c are integer

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.
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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.

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 \(b>c\).

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?

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 > bBut 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.
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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.
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PhD in Applied Mathematics Love GMAT Quant questions and running.

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...

Merging similar topics. Please refer to the solutions above.
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Re: If ab<ac , which is greater b or c ? i. a<0 2. c<0 [#permalink]

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02 Nov 2012, 15:01

the difficulty level tag assigned to this question is 600-700, but that is a wide range, can some one try to put it in a narrower band, i.e. is it a 610-630 or 670-700 type question.

Re: If ab<ac , which is greater b or c ? i. a<0 2. c<0 [#permalink]

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23 Apr 2016, 09:47

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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