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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, 03:18
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A
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C
D
E

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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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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, 03:43
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, 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
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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, 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)

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, 07:48
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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. 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, 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.

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

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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User avatar
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Joined: 04 Dec 2015
Posts: 696
Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
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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, 08:33
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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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, 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.

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

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