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

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Math Expert
Joined: 02 Sep 2009
Posts: 43894
If ab<0 and bc>0, then which of the following expressions must be nega [#permalink]

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24 Apr 2017, 03:18
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Difficulty:

65% (hard)

Question Stats:

57% (01:06) correct 43% (01:49) wrong based on 157 sessions

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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
[Reveal] Spoiler: OA

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Director
Joined: 21 Mar 2016
Posts: 551
Re: If ab<0 and bc>0, then which of the following expressions must be nega [#permalink]

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24 Apr 2017, 03:43
stat III can be split as ab * bc..

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

ans B
Intern
Joined: 13 Dec 2016
Posts: 45
Re: If ab<0 and bc>0, then which of the following expressions must be nega [#permalink]

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04 May 2017, 03:56
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
DS Forum Moderator
Joined: 21 Aug 2013
Posts: 805
Location: India
Re: If ab<0 and bc>0, then which of the following expressions must be nega [#permalink]

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20 May 2017, 21:24
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)

Director
Joined: 04 Dec 2015
Posts: 696
Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
Re: If ab<0 and bc>0, then which of the following expressions must be nega [#permalink]

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21 May 2017, 07:48
1
KUDOS
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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Math Expert
Joined: 02 Sep 2009
Posts: 43894
Re: If ab<0 and bc>0, then which of the following expressions must be nega [#permalink]

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21 May 2017, 08:27
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.

_________________
Kindly press "+1 Kudos" to appreciate

Edited the question. II should read $$ab^2$$. Thank you.
_________________
Director
Joined: 04 Dec 2015
Posts: 696
Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
Re: If ab<0 and bc>0, then which of the following expressions must be nega [#permalink]

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21 May 2017, 08:33
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.

_________________
Kindly press "+1 Kudos" to appreciate

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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Intern
Joined: 20 May 2017
Posts: 10
If ab<0 and bc>0, then which of the following expressions must be nega [#permalink]

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21 May 2017, 13:02
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.

If ab<0 and bc>0, then which of the following expressions must be nega   [#permalink] 21 May 2017, 13:02
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