GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 16 Dec 2018, 06:04

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • FREE Quant Workshop by e-GMAT!

     December 16, 2018

     December 16, 2018

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.
  • Free GMAT Prep Hour

     December 16, 2018

     December 16, 2018

     03:00 PM EST

     04:00 PM EST

    Strategies and techniques for approaching featured GMAT topics

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51223
If ab<0 and bc>0, then which of the following expressions must be nega  [#permalink]

Show Tags

New post 24 Apr 2017, 03:18
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

61% (01:18) correct 39% (01:38) wrong based on 248 sessions

HideShow timer Statistics

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

_________________

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

Director
Director
avatar
S
Joined: 21 Mar 2016
Posts: 521
Reviews Badge
Re: If ab<0 and bc>0, then which of the following expressions must be nega  [#permalink]

Show Tags

New post 24 Apr 2017, 03:43
1
stat III can be split as ab * bc..

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

ans B
Intern
Intern
avatar
S
Joined: 13 Dec 2016
Posts: 42
Re: If ab<0 and bc>0, then which of the following expressions must be nega  [#permalink]

Show Tags

New post 04 May 2017, 03:56
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
DS Forum Moderator
avatar
P
Joined: 21 Aug 2013
Posts: 1412
Location: India
Premium Member
Re: If ab<0 and bc>0, then which of the following expressions must be nega  [#permalink]

Show Tags

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
Director
Director
User avatar
D
Joined: 04 Dec 2015
Posts: 731
Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
GMAT ToolKit User
Re: If ab<0 and bc>0, then which of the following expressions must be nega  [#permalink]

Show Tags

New post 21 May 2017, 07:48
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.

_________________
Kindly press "+1 Kudos" to appreciate :)
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51223
Re: If ab<0 and bc>0, then which of the following expressions must be nega  [#permalink]

Show Tags

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.

_________________
Kindly press "+1 Kudos" to appreciate :)


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

Director
Director
User avatar
D
Joined: 04 Dec 2015
Posts: 731
Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
GMAT ToolKit User
Re: If ab<0 and bc>0, then which of the following expressions must be nega  [#permalink]

Show Tags

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).

_________________
Kindly press "+1 Kudos" to appreciate :)
Intern
Intern
avatar
B
Joined: 20 May 2017
Posts: 10
If ab<0 and bc>0, then which of the following expressions must be nega  [#permalink]

Show Tags

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
Manager
Manager
avatar
S
Joined: 24 Sep 2018
Posts: 138
Premium Member CAT Tests
Re: If ab<0 and bc>0, then which of the following expressions must be nega  [#permalink]

Show Tags

New post 25 Sep 2018, 12:35
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).
_________________

Please award :thumbup: kudos, If this post helped you in someway. :student_man:

Intern
Intern
avatar
B
Joined: 11 Jun 2015
Posts: 19
Location: Iran (Islamic Republic of)
Concentration: Accounting, Finance
WE: Education (Education)
GMAT ToolKit User
Re: If ab<0 and bc>0, then which of the following expressions must be nega  [#permalink]

Show Tags

New post 25 Sep 2018, 20:10
Variables a b c ab<0 bc>0 abc ab^2 acb^2
Case1 + - - - + + + -
Case2 - + + - + - - -
Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4295
Location: United States (CA)
Re: If ab<0 and bc>0, then which of the following expressions must be nega  [#permalink]

Show Tags

New post 27 Sep 2018, 16:38
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
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

GMAT Club Bot
Re: If ab<0 and bc>0, then which of the following expressions must be nega &nbs [#permalink] 27 Sep 2018, 16:38
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.