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If ab<0 and bc>0, then which of the following expressions must be nega

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If ab<0 and bc>0, then which of the following expressions must be nega  [#permalink]

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New post 24 Apr 2017, 04:18
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

60% (01:45) correct 40% (01:39) wrong based on 261 sessions

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Re: If ab<0 and bc>0, then which of the following expressions must be nega  [#permalink]

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New post 24 Apr 2017, 04:43
1
stat III can be split as ab * bc..

given ab<0 bc>0 hence ab^2 c will be negative

ans B
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Re: If ab<0 and bc>0, then which of the following expressions must be nega  [#permalink]

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New post 04 May 2017, 04:56
1
Two scenarios exist:
Either a<0, b>0 and c>0
or a>0, b<0 and c< 0

Under these two scenarios, only statement III is negative
Hence, ans is B
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Re: If ab<0 and bc>0, then which of the following expressions must be nega  [#permalink]

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New post 20 May 2017, 22:24
ab<0 means a & b have opposite signs
bc>0 means b & c have same signs

Combining the two above, a is opposite in sign to both b and c.
So two cases: Either a >0 and b<0, c<0
Or a<0, b>0, c>0

abc is positive in first case
ab^2 is also positive in first case
But ab^2c is negative in both cases (because b^2 is always positive and a/c have opposite signs)

Hence answer is B
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Re: If ab<0 and bc>0, then which of the following expressions must be nega  [#permalink]

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New post 21 May 2017, 08:48
1
If ab<0 and bc>0, then which of the following expressions must be negative?

I. abc
II. ab*2
III. a\(b^2\)*c

Bunuel I have a doubt for the II option.
II option says [ab*2 not a\(b^2\)]
Solving option II;
ab*2 = a*b*2 or a x b x 2

From the question, a and b have opposite signs. The expression is negative in both cases.
ab*2
-a*b*2 = -2ab (when a is negative)
a*-b*2 = -2ab (when b is negative)

I got Answer D (Both II and III are negative)...
Pls Let me know if there's any mistake in my approach.

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Re: If ab<0 and bc>0, then which of the following expressions must be nega  [#permalink]

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New post 21 May 2017, 09:27
sashiim20 wrote:
If ab<0 and bc>0, then which of the following expressions must be negative?

I. abc
II. ab*2
III. a\(b^2\)*c

Bunuel I have a doubt for the II option.
II option says [ab*2 not a\(b^2\)]
Solving option II;
ab*2 = a*b*2 or a x b x 2

From the question, a and b have opposite signs. The expression is negative in both cases.
ab*2
-a*b*2 = -2ab (when a is negative)
a*-b*2 = -2ab (when b is negative)

I got Answer D (Both II and III are negative)...
Pls Let me know if there's any mistake in my approach.

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Edited the question. II should read \(ab^2\). Thank you.
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Re: If ab<0 and bc>0, then which of the following expressions must be nega  [#permalink]

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New post 21 May 2017, 09:33
Bunuel wrote:
sashiim20 wrote:
If ab<0 and bc>0, then which of the following expressions must be negative?

I. abc
II. ab*2
III. a\(b^2\)*c

Bunuel I have a doubt for the II option.
II option says [ab*2 not a\(b^2\)]
Solving option II;
ab*2 = a*b*2 or a x b x 2

From the question, a and b have opposite signs. The expression is negative in both cases.
ab*2
-a*b*2 = -2ab (when a is negative)
a*-b*2 = -2ab (when b is negative)

I got Answer D (Both II and III are negative)...
Pls Let me know if there's any mistake in my approach.

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Edited the question. II should read \(ab^2\). Thank you.


Thank you Bunuel.
Now I get Answer B (only III is negative).

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If ab<0 and bc>0, then which of the following expressions must be nega  [#permalink]

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New post 21 May 2017, 14:02
a and b is negative of each other.
c and b is positive of each other.

So c and a is negative of each other.

Answer is B
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Re: If ab<0 and bc>0, then which of the following expressions must be nega  [#permalink]

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New post 25 Sep 2018, 13:35
While this problem could be solved by considering individual scenarios for the signs of each variable, it is much easier if you simplify/”decouple” the three possibilities so that you can leverage the information provided in the question stem more easily.

Quote:
I. can be rewritten as (ab)(c)
II. can be rewritten as (ab)(b)
III. can be rewritten as (ab)(bc)


The expression in statement III is the easiest to assess in its rewritten form. ab is given as negative in the question stem and bc is given as positive in the question stem and negative times positive is always negative. This guarantees that the expression in statement III is always negative and allows you to eliminate answers (A) and (E).

For the expression in statement I you know that ab is negative but you do not know the sign of c it could be positive or negative. Therefore the expression in statement 1 does not have to be negative. In statement II you again know that ab is negative but you do not know the sign of b it could be positive or negative. The expression in statement II therefore does not have to be negative. The correct answer is (B).
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Re: If ab<0 and bc>0, then which of the following expressions must be nega  [#permalink]

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New post 25 Sep 2018, 21:10
Variables a b c ab<0 bc>0 abc ab^2 acb^2
Case1 + - - - + + + -
Case2 - + + - + - - -
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Re: If ab<0 and bc>0, then which of the following expressions must be nega  [#permalink]

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New post 27 Sep 2018, 17:38
Bunuel wrote:
If \(ab<0\) and \(bc>0\), then which of the following expressions must be negative?

I. \(abc\)

II. \(ab^2\)

III. \(ab^2*c\)


A. I only
B. III only
C. I and III only
D. II and III only
E. None of the above


Since ab is less than zero and bc is greater than zero, we have:

Case 1: If b is negative, then a is positive and c is negative.

Case 2: If b is positive, then a is negative and c is positive.

Thus, we see that abc does not have to be negative (if the values of a, b and c are from case 1) and ab^2 does not have to be negative (if the values of a and b are from case 1).

However, since the product of a and c is always negative (in either case) and since b^2 is always positive, ab^2 * c is always negative.

Answer: B
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Re: If ab<0 and bc>0, then which of the following expressions must be nega   [#permalink] 27 Sep 2018, 17:38
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