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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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55% (hard)

Question Stats:

51% (01:23) correct 49% (01:30) wrong based on 136 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
1
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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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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13 Jun 2019, 05:21
Mascarfi wrote:
If c ≠ 0 and $$\frac{(a*b)}{c}<0$$, is $$\frac{a}{c}<0$$ ?

(1) a < 0

(2) b < 0

Confusion with B,

If a =1, b=-1, and C=1, then $$\frac{(1*-1)}{1}<0$$. Therefore, for $$\frac{a}{c}<0$$ ; $$\frac{1}{1}<0$$ = Ans is No.

If a=1, b=-2, and C=2, then $$\frac{(1*-2)}{2}<0$$. Therefore, $$\frac{a}{c}<0$$ ; $$\frac{1}{2}<0$$ = Ans is Yes.

So, how is B okay for the answer.
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Re: If c≠0 and (a*b)/c < 0, is a/c < 0  [#permalink]

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13 Jun 2019, 05:50
MBA20 wrote:
Mascarfi wrote:
If c ≠ 0 and $$\frac{(a*b)}{c}<0$$, is $$\frac{a}{c}<0$$ ?

(1) a < 0

(2) b < 0

Confusion with B,

If a =1, b=-1, and C=1, then $$\frac{(1*-1)}{1}<0$$. Therefore, for $$\frac{a}{c}<0$$ ; $$\frac{1}{1}<0$$ = Ans is No.

If a=1, b=-2, and C=2, then $$\frac{(1*-2)}{2}<0$$. Therefore, $$\frac{a}{c}<0$$ ; $$\frac{1}{2}<0$$ = Ans is Yes.

So, how is B okay for the answer.

Hi,
If you have 3 variables a,b and c, the relation can be found as far as the sign is concerned..
(a*b)/c<0 means
1) all three are negative so a/c is positive.
2) only one is negative, if any of a and c are negative a/c<0, but if b<0, a/c>0.

Now statement II says that b<0, so a and c both can be positive or both can be negative .
In both cases a/c>0.
So B is sufficient
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Re: If c≠0 and (a*b)/c < 0, is a/c < 0  [#permalink]

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13 Jun 2019, 06:03
chetan2u wrote:
MBA20 wrote:
Mascarfi wrote:
If c ≠ 0 and $$\frac{(a*b)}{c}<0$$, is $$\frac{a}{c}<0$$ ?

(1) a < 0

(2) b < 0

Confusion with B,

If a =1, b=-1, and C=1, then $$\frac{(1*-1)}{1}<0$$. Therefore, for $$\frac{a}{c}<0$$ ; $$\frac{1}{1}<0$$ = Ans is No.

If a=1, b=-2, and C=2, then $$\frac{(1*-2)}{2}<0$$. Therefore, $$\frac{a}{c}<0$$ ; $$\frac{1}{2}<0$$ = Ans is Yes.

So, how is B okay for the answer.

Hi,
If you have 3 variables a,b and c, the relation can be found as far as the sign is concerned..
(a*b)/c<0 means
1) all three are negative so a/c is positive.
2) only one is negative, if any of a and c are negative a/c<0, but if b<0, a/c>0.

Now statement II says that b<0, so a and c both can be positive or both can be negative .
In both cases a/c>0.
So B is sufficient

So is it that my assumption value of a,b, and c are wrong. As as per assumption it is fulfilling the condition that "a and c both can be positive or both can be negative" .
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Re: If c≠0 and (a*b)/c < 0, is a/c < 0  [#permalink]

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13 Jun 2019, 06:07
MBA20 wrote:
Mascarfi wrote:
If c ≠ 0 and $$\frac{(a*b)}{c}<0$$, is $$\frac{a}{c}<0$$ ?

(1) a < 0

(2) b < 0

Confusion with B,

If a =1, b=-1, and C=1, then $$\frac{(1*-1)}{1}<0$$. Therefore, for $$\frac{a}{c}<0$$ ; $$\frac{1}{1}<0$$ = Ans is No.

If a=1, b=-2, and C=2, then $$\frac{(1*-2)}{2}<0$$. Therefore, $$\frac{a}{c}<0$$ ; $$\frac{1}{2}<0$$ = Ans is Yes.

So, how is B okay for the answer.

1/1<0...NO
1/2<0...NO
Both times you get a NO...
It seems you are reading 1/2 <0 as 1/2<1..
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Re: If c≠0 and (a*b)/c < 0, is a/c < 0  [#permalink]

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13 Jun 2019, 21:37
Mascarfi wrote:
If c ≠ 0 and $$\frac{(a*b)}{c}<0$$, is $$\frac{a}{c}<0$$ ?

(1) a < 0

(2) b < 0

#1
a<0
so either b& c are both -ve or both +ve
so
a/c not sufficient to say is <0
#2
b<0 , a & c can be both +ve or -ve
and a/b >0 sufficient
IMO B
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Re: If c≠0 and (a*b)/c < 0, is a/c < 0  [#permalink]

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13 Jun 2019, 22:01
Hi chetan2u what if in S2 a=0, the S2 is not sufficient as we do not have any info on the nature of a,b

chetan2u wrote:
MBA20 wrote:
Mascarfi wrote:
If c ≠ 0 and $$\frac{(a*b)}{c}<0$$, is $$\frac{a}{c}<0$$ ?

(1) a < 0

(2) b < 0

Confusion with B,

If a =1, b=-1, and C=1, then $$\frac{(1*-1)}{1}<0$$. Therefore, for $$\frac{a}{c}<0$$ ; $$\frac{1}{1}<0$$ = Ans is No.

If a=1, b=-2, and C=2, then $$\frac{(1*-2)}{2}<0$$. Therefore, $$\frac{a}{c}<0$$ ; $$\frac{1}{2}<0$$ = Ans is Yes.

So, how is B okay for the answer.

Hi,
If you have 3 variables a,b and c, the relation can be found as far as the sign is concerned..
(a*b)/c<0 means
1) all three are negative so a/c is positive.
2) only one is negative, if any of a and c are negative a/c<0, but if b<0, a/c>0.

Now statement II says that b<0, so a and c both can be positive or both can be negative .
In both cases a/c>0.
So B is sufficient
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Re: If c≠0 and (a*b)/c < 0, is a/c < 0  [#permalink]

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13 Jun 2019, 22:30
Mascarfi wrote:
If c ≠ 0 and $$\frac{(a*b)}{c}<0$$, is $$\frac{a}{c}<0$$ ?

(1) a < 0

(2) b < 0

Given $$\frac{(a*b)}{c}<0$$
--> 2 cases are possible
Case 1) 1 -ve and 2 +ve or
Case 2) all 3 -ve

$$\frac{a}{c}<0$$ ?

(1) a < 0
If a < 0 -->
Case 1) b > 0 & c > 0 --> a/c < 0 - YES or
Case 2) b < 0 & c < 0 --> a/c > 0 - NO

(2) b < 0
If b < 0 -->
Case 1) a > 0 & c > 0 --> a/c > 0 - NO
Case 2) a < 0 & c < 0 --> a/c > 0 - NO

IMO Option B

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

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14 Jun 2019, 00:08
LoneSurvivor wrote:
Hi chetan2u what if in S2 a=0, the S2 is not sufficient as we do not have any info on the nature of a,b

chetan2u wrote:
Mascarfi wrote:
If c ≠ 0 and $$\frac{(a*b)}{c}<0$$, is $$\frac{a}{c}<0$$ ?

(1) a < 0

(2) b < 0

Confusion with B,

Hi,
If you have 3 variables a,b and c, the relation can be found as far as the sign is concerned..
(a*b)/c<0 means
1) all three are negative so a/c is positive.
2) only one is negative, if any of a and c are negative a/c<0, but if b<0, a/c>0.

Now statement II says that b<0, so a and c both can be positive or both can be negative .
In both cases a/c>0.
So B is sufficient

it is given $$\frac{(a*b)}{c}<0$$, so none of the three a, b and c will be 0...
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Re: If c≠0 and (a*b)/c < 0, is a/c < 0   [#permalink] 14 Jun 2019, 00:08
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