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# If c≠0 and (a*b)/c < 0, is a/c < 0

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Manager
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If c≠0 and (a*b)/c < 0, is a/c < 0  [#permalink]

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Updated on: 11 Aug 2015, 02:26
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Difficulty:

55% (hard)

Question Stats:

55% (01:17) correct 45% (01:28) wrong based on 122 sessions

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If c ≠ 0 and $$\frac{(a*b)}{c}<0$$, is $$\frac{a}{c}<0$$ ?

(1) a < 0

(2) b < 0

Originally posted by Mascarfi on 10 Aug 2015, 17:58.
Last edited by Bunuel on 11 Aug 2015, 02:26, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If c≠0 and (a*b)/c < 0, is a/c < 0  [#permalink]

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10 Aug 2015, 18:15
1
Mascarfi wrote:
If c≠0 and $$\frac{(a*b)}{c}$$<0, is $$\frac{a}{c}$$<0 ?

(1) a<0

(2) b<0

$$\frac{ab}{c} < 0$$ ---> 2 cases possible:

1. Either a/c < 0 and b>0 or

Per statement 1, a<0 ---> clearly not sufficient.

Per statement 2, b<0---> this eliminates case (1) mentioned above leaving just 1 possible case and is thus sufficient.

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Re: If c≠0 and (a*b)/c < 0, is a/c < 0  [#permalink]

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11 Aug 2015, 03:03
1
Mascarfi wrote:
If c ≠ 0 and $$\frac{(a*b)}{c}<0$$, is $$\frac{a}{c}<0$$ ?

(1) a < 0

(2) b < 0

Given: $$\frac{(a*b)}{c}<0$$

Is $$\frac{a}{c}<0$$, to rephrase the qn, is b>0?

St 1: a < 0. No info about b. Not Sufficient.

St 2: b < 0, which implies that $$\frac{a}{c}>0$$. The answer is No. Sufficient.

Option B

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Re: If c≠0 and (a*b)/c < 0, is a/c < 0  [#permalink]

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11 Aug 2015, 23:37
Mascarfi wrote:
If c ≠ 0 and $$\frac{(a*b)}{c}<0$$, is $$\frac{a}{c}<0$$ ?

(1) a < 0

(2) b < 0

Ans: B

solution: we have (a*b)/c < 0 ; is a/c<0 means we need to find that a and c have different signs.
from the given statement we know that either one or all of them are<0 only then (a*b)/c < 0 will be true.

1) a<0, but it does not say anything about b and c,
so what if b and c both <0 ; (a*b)/c < 0 true and a/c>0
what if b and c both >0 ; (a*b)/c < 0 true, and a/c<0
[Insufficient]

2) b<0, no information is given about a and c.
so (a*b)/c < 0 to be true either a and c must have the same sign.
and in both the cases a/c>0
[Sufficient]
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Manager
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Re: If c≠0 and (a*b)/c < 0, is a/c < 0  [#permalink]

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04 Dec 2016, 00:09
Not taken much time to solve this question,
Option 1: If a<0, No information about b and c values. Hence, a/c value can not be determined. Insufficient.
Option 2: If b<0,
To comply the original question, (a∗b)/c<0. The ratio a/c must have to be positive. Hence sufficient.
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Re: If c≠0 and (a*b)/c < 0, is a/c < 0  [#permalink]

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22 Apr 2018, 18:13
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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Re: If c≠0 and (a*b)/c < 0, is a/c < 0 &nbs [#permalink] 22 Apr 2018, 18:13
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