It is currently 23 Oct 2017, 12:20

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

Events & Promotions in June
Open Detailed Calendar

If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41913

Kudos [?]: 129491 [0], given: 12201

If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is [#permalink]

Show Tags

New post 31 Mar 2015, 05:43
Expert's post
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

54% (00:47) correct 46% (00:44) wrong based on 249 sessions

HideShow timer Statistics

If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is the maximum number of integers that can be negative?

A. 2
B. 3
C. 4
D. 5
E. 6


Kudos for a correct solution.
[Reveal] Spoiler: OA

_________________

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

Kudos [?]: 129491 [0], given: 12201

Senior Manager
Senior Manager
avatar
Status: On a mountain of skulls, in the castle of pain, I sit on a throne of blood.
Joined: 30 Jul 2013
Posts: 361

Kudos [?]: 207 [0], given: 133

GMAT ToolKit User Reviews Badge CAT Tests
Re: If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is [#permalink]

Show Tags

New post 31 Mar 2015, 05:48
Bunuel wrote:
If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is the maximum number of integers that can be negative?

A. 2
B. 3
C. 4
D. 5
E. 6


Kudos for a correct solution.



Minimuum should be 1

Maximum should be 4:

1 out of a or b to make the multiplication negative
3 out of c, d, e or f to make the multiplication negative.

Negative+Negative<0

Answer:C

Kudos [?]: 207 [0], given: 133

Director
Director
User avatar
Joined: 07 Aug 2011
Posts: 582

Kudos [?]: 539 [0], given: 75

Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
GMAT ToolKit User
If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is [#permalink]

Show Tags

New post 31 Mar 2015, 07:23
1
This post was
BOOKMARKED
Bunuel wrote:
If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is the maximum number of integers that can be negative?

A. 2
B. 3
C. 4
D. 5
E. 6


Kudos for a correct solution.


Case 1: |ab| > |cdef|
Then we have 1negative in ab and 3 negatives in cdef


Case 2 |ab| <|cdef|
Then we can have 2negative in ab and 3 negatives in cdef

Eg:
-3*-2 + 4*-7*-5*-6 <0

Answer 5.

Without knowing magnitudes it is hard to determine but as question asks for maximum value it should be second case . I.e. D

Good question for number properties revision .
_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the Image to appreciate my post !! :-)

Kudos [?]: 539 [0], given: 75

Expert Post
1 KUDOS received
Math Forum Moderator
avatar
P
Joined: 02 Aug 2009
Posts: 4994

Kudos [?]: 5533 [1], given: 112

If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is [#permalink]

Show Tags

New post 31 Mar 2015, 07:49
1
This post received
KUDOS
Expert's post
AmoyV wrote:
Bunuel wrote:
If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is the maximum number of integers that can be negative?

A. 2
B. 3
C. 4
D. 5
E. 6


Kudos for a correct solution.



Minimuum should be 1

Maximum should be 4:

1 out of a or b to make the multiplication negative
3 out of c, d, e or f to make the multiplication negative.

Negative+Negative<0

Answer:C


hi AmoyV,

maximum will be 5..
you dont require both the multiplicatin to be negative for entire equation to be negative...
any one a or b can be negative to make ab negative and it can still be more(away from 0) than the multiplication of 4 other -ve numbers...
actually by writing minimum required as 1 out of 6,you are actually meaning 5 out of 6 also possible as you will see 5 or 1 will give you same equation..
ans D
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5533 [1], given: 112

Senior Manager
Senior Manager
avatar
Status: On a mountain of skulls, in the castle of pain, I sit on a throne of blood.
Joined: 30 Jul 2013
Posts: 361

Kudos [?]: 207 [0], given: 133

GMAT ToolKit User Reviews Badge CAT Tests
Re: If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is [#permalink]

Show Tags

New post 31 Mar 2015, 08:54
chetan2u wrote:
AmoyV wrote:
Bunuel wrote:
If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is the maximum number of integers that can be negative?

A. 2
B. 3
C. 4
D. 5
E. 6


Kudos for a correct solution.



Minimuum should be 1

Maximum should be 4:

1 out of a or b to make the multiplication negative
3 out of c, d, e or f to make the multiplication negative.

Negative+Negative<0

Answer:C


hi AmoyV,

maximum will be 5..
you dont require both the multiplicatin to be negative for entire equation to be negative...
any one a or b can be negative to make ab negative and it can still be more(away from 0) than the multiplication of 4 other -ve numbers...
actually by writing minimum required as 1 out of 6,you are actually meaning 5 out of 6 also possible as you will see 5 or 1 will give you same equation..
ans D


Crap. Yeah, thanks.

Funny part is I had considered this option when I read the question but messed up the execution. Made a mental note of slowing down. :D

Kudos [?]: 207 [0], given: 133

Expert Post
1 KUDOS received
Optimus Prep Instructor
User avatar
B
Joined: 06 Nov 2014
Posts: 1905

Kudos [?]: 525 [1], given: 23

Re: If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is [#permalink]

Show Tags

New post 31 Mar 2015, 11:46
1
This post received
KUDOS
Expert's post
Bunuel wrote:
If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is the maximum number of integers that can be negative?

A. 2
B. 3
C. 4
D. 5
E. 6


Kudos for a correct solution.


The number can be negative in following conditions:
1) If ab is a bigger negative number than cdef => Both a & b cannot be negative at a time.
2) If cdef is a bigger negative number than ab => All four c, d, e & f cannot be negative at a time

Let one of a & b be negative and let all 4 of c, d, e & f be negative.
So, ab will be negative and cdef will be positive but their sum will be negative.
Hence maximum 5 can be negative.
Hence option (D).

--
Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: http://www.optimus-prep.com/gmat-on-demand-course
_________________

Janielle Williams

Customer Support

Special Offer: $80-100/hr. Online Private Tutoring
GMAT On Demand Course $299
Free Online Trial Hour

Kudos [?]: 525 [1], given: 23

1 KUDOS received
Manager
Manager
avatar
Joined: 28 Jan 2015
Posts: 131

Kudos [?]: 25 [1], given: 51

Concentration: General Management, Entrepreneurship
GMAT 1: 670 Q44 V38
Re: If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is [#permalink]

Show Tags

New post 31 Mar 2015, 19:49
1
This post received
KUDOS
Originally I chose E but now I changed my mind! I ignored that the sum of the numbers had to be under zero, and tried to make the number positive. Now I think the answer is D --

I put in values to try and make it work:

25 * (-1) + (-1 * -2 * -3 * -4) =
-25 + 24 = -1

That's 5 negative numbers that create a value under 1. one more value were to have been positive, the numbers summed up would not be less than 1. Silly mistake I made originally.

Note to self: READ THE QUESTION!!!

Kudos [?]: 25 [1], given: 51

LBS Thread Master
avatar
B
Joined: 13 Jan 2015
Posts: 114

Kudos [?]: 18 [0], given: 67

Location: United Kingdom
Concentration: Other, General Management
Schools: LBS '19 (WL)
GMAT 1: 690 Q48 V36
Re: If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is [#permalink]

Show Tags

New post 01 Apr 2015, 05:53
For maximum number of negative values, then

ab must be negative, so either a or b can be negative, we assume a is negative

cdef should also give us a negative value and we can actually have 3 integers negative here to give us an overall negative value

so my answer is 4 for the maximum number of negative integers

Kudos [?]: 18 [0], given: 67

1 KUDOS received
Manager
Manager
User avatar
Joined: 02 Nov 2014
Posts: 215

Kudos [?]: 129 [1], given: 75

GMAT Date: 08-04-2015
GMAT ToolKit User Reviews Badge
Re: If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is [#permalink]

Show Tags

New post 01 Apr 2015, 23:39
1
This post received
KUDOS
Tmoni26 wrote:
ab must be negative, so either a or b can be negative, we assume a is negative

cdef should also give us a negative value


Hi there,

As u said, ab must be negative, does cdef have to be negative? What if |ab| > |cdef| which makes the expression negative.

So, ab->negative, -> a negative, b positive. And c,d,e,f all negative. And |ab|>|cdef| makes the whole thing negative. So, 5 can be negative. D.

~Binit.

Kudos [?]: 129 [1], given: 75

1 KUDOS received
Intern
Intern
avatar
Joined: 22 Aug 2014
Posts: 42

Kudos [?]: 24 [1], given: 6

GMAT ToolKit User
Re: If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is [#permalink]

Show Tags

New post 02 Apr 2015, 02:10
1
This post received
KUDOS
Bunuel wrote:
If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is the maximum number of integers that can be negative?

A. 2
B. 3
C. 4
D. 5
E. 6


Kudos for a correct solution.


looking at the eqn: (ab + cdef) < 0

In order for the sum of two terms to be -ve, one term has to be -ve for sure. With this mind, we can build mutliple scenarios. To restrict time take to solve this problem assume the same small integers for all unkowns.

a = -2, b= -2, c= -2, d=-2, e=-2, f= 2

-2*-2 + -2*-2*-2*2 = -12 < 0

It can have a max of 5 -ve integers. Option D

Kudos [?]: 24 [1], given: 6

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41913

Kudos [?]: 129491 [0], given: 12201

Re: If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is [#permalink]

Show Tags

New post 06 Apr 2015, 05:46
Bunuel wrote:
If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is the maximum number of integers that can be negative?

A. 2
B. 3
C. 4
D. 5
E. 6


Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:
Attachment:
abcdef_text.PNG
abcdef_text.PNG [ 17.26 KiB | Viewed 2688 times ]

_________________

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

Kudos [?]: 129491 [0], given: 12201

Intern
Intern
avatar
B
Joined: 09 Apr 2017
Posts: 10

Kudos [?]: 0 [0], given: 48

Premium Member CAT Tests
Re: If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is [#permalink]

Show Tags

New post 23 Aug 2017, 03:02
Apologies, i'm getting confused with total integers, why do you multiply the numbers? Shouldn't each of this be treated as individual numbers?

Kudos [?]: 0 [0], given: 48

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41913

Kudos [?]: 129491 [0], given: 12201

Re: If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is [#permalink]

Show Tags

New post 23 Aug 2017, 03:09

Kudos [?]: 129491 [0], given: 12201

Intern
Intern
avatar
B
Joined: 09 Apr 2017
Posts: 10

Kudos [?]: 0 [0], given: 48

Premium Member CAT Tests
Re: If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is [#permalink]

Show Tags

New post 23 Aug 2017, 03:22
So should the question rephrased as the products of the integers ... .

Or we can make the assumption that when we find similiar questions during the GMAT exam, we should just treat it as multiple of products?

Kudos [?]: 0 [0], given: 48

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41913

Kudos [?]: 129491 [0], given: 12201

Re: If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is [#permalink]

Show Tags

New post 23 Aug 2017, 03:25
bae wrote:
So should the question rephrased as the products of the integers ... .

Or we can make the assumption that when we find similiar questions during the GMAT exam, we should just treat it as multiple of products?


If cdef were a 4-digit number if would have been mentioned explicitly. Without that, cdef can only be c*d*e*f since only multiplication sign (*) is usually omitted.
_________________

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

Kudos [?]: 129491 [0], given: 12201

Director
Director
avatar
P
Joined: 22 May 2016
Posts: 837

Kudos [?]: 273 [0], given: 559

If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is [#permalink]

Show Tags

New post 23 Aug 2017, 15:18
Bunuel wrote:
If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is the maximum number of integers that can be negative?

A. 2
B. 3
C. 4
D. 5
E. 6


Kudos for a correct solution.

To achieve negative result here with maximum number of negative integers, we can't use six. An even number of negative factors yields positive. Six negative factors "eat up" all the individual terms.

Five negative factors, however, will work.

Maximize and minimize

1. Maximize the number of negative factors in (cdef): there can be three. Odd number of negative factors = negative product.

2. Maximize negative factors by two more. Make both a and b negative, but minimize their positive product's absolute value.

Make c, d, and e negative, and for ease, keep them small. Let f be the one positive number. Make it large so that |(cdef)| is > (ab).

Result is a small positive number plus a larger negative number, which yields a negative.

3. Let a, b, c, d, and e = -1
Let f = 20

(-1)(-1) + (-1)(-1)(-1)(20) =

1 + (-20) =
1 - 20 =
-19

4. Alternatively, make all but a or b negative, and one number large because:
-- if one term in (ab) is negative, and
-- the absolute value of (ab) is greater than (cdef)
-- the result is a very small negative number (far to the right on the number line) plus a smaller positive number, such that
-- sum of terms with those properties is less than 0.

Let b, c, d, e, and f = -1
Let a = 20

(20)(-1) + (-1)(-1)(-1)(-1) =
-20 + 1 = -19

The maximum number of negative factors possible for this expression is 5

Answer D

Kudos [?]: 273 [0], given: 559

If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is   [#permalink] 23 Aug 2017, 15:18
Display posts from previous: Sort by

If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.