It is currently 20 Nov 2017, 08:47

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

For real numbers, A, B, C, and D on the number line

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

Hide Tags

Intern
Intern
avatar
Joined: 21 Mar 2013
Posts: 42

Kudos [?]: 160 [0], given: 56

GMAT Date: 03-20-2014
GMAT ToolKit User
For real numbers, A, B, C, and D on the number line [#permalink]

Show Tags

New post 04 Jan 2014, 23:57
22
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

42% (01:22) correct 58% (01:40) wrong based on 308 sessions

HideShow timer Statistics

Image

For real numbers, A, B, C, and D on the number line above, is |A| + |B| < |C| + |D| ?

(1) |B| < |C|
(2) The product of any two of the numbers A, B, C and D is between 0 and 1.
[Reveal] Spoiler: OA

Attachments

download.jpg
download.jpg [ 1.43 KiB | Viewed 4022 times ]

Kudos [?]: 160 [0], given: 56

Expert Post
4 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42264

Kudos [?]: 132782 [4], given: 12372

Re: For real numbers, A, B, C, and D on the number line [#permalink]

Show Tags

New post 05 Jan 2014, 06:27
4
This post received
KUDOS
Expert's post
6
This post was
BOOKMARKED
Image

For real numbers, A, B, C, and D on the number line above, is |A| + |B| < |C| + |D| ?

Notice that from the diagram we have that A<B<C<D.

(1) |B| < |C|. This one is clearly insufficient. Consider: A=1, B=2, C=3, and D=4 for an YES answer and A=-10, B=2, C=3, and D=4 for a NO answer. Not sufficient.

(2) The product of any two of the numbers A, B, C and D is between 0 and 1. So, we have that the product of ANY two of the numbers is positive. This implies either that all the numbers are negative or that all the numbers are positive. In the first case the answer is NO and in the second case the answer is YES. Not sufficient.

(1)+(2) If all the numbers were negative, then because we also have that B < C, then we would have that |B| > |C|, which contradicts the first statement, thus we have the second case: all the numbers are positive. Therefore since A<B<C<D, then |A| + |B| < |C| + |D|. Sufficient.

Answer: C.

Hope it's clear.
_________________

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 [?]: 132782 [4], given: 12372

Current Student
avatar
Joined: 25 Feb 2013
Posts: 7

Kudos [?]: [0], given: 3

GMAT Date: 12-22-2014
Re: For real numbers, A, B, C, and D on the number line [#permalink]

Show Tags

New post 13 Jan 2015, 10:26
Bunuel wrote:

(2) The product of any two of the numbers A, B, C and D is between 0 and 1. So, we have that the product of ANY two of the numbers is positive. This implies either that all the numbers are negative or that all the numbers are positive. In the first case the answer is NO and in the second case the answer is YES. Not sufficient.



Hi Bunuel,

I have been reading your posts quite regularly, and they are very helpful. I am really grateful to you for providing assistance to people like us.

As far as this question is concerned i have a doubt on s(2). As you have mentioned above "that all the numbers are negative or that all the numbers are positive."
I have been working on one or two examples and came across this one
Suppose B and C are -1/2 and -1/3. Their product is 1/6, which is between 0 and 1. Now the possible values can be
A<B<C<D :- -1 < -1/2 < -1/3 <1 . In this case |A| + |B| IS NOT LESS THAN |C| + |D| insufficient

Suppose A and B are -1/2 and -1/3. Again their product is 1/6, which is between 0 and 1. Now the possible values can be
A<B<C<D :- -1/2 < -1/3 < 1 < 2. In this case |A| + |B| < |C| + |D| sufficient.

So, how can we say "that all the numbers are negative or that all the numbers are positive." ? and it doesn't say that The product of every two of the numbers A, B, C and D is between 0 and 1.

Thanks

Kudos [?]: [0], given: 3

Expert Post
EMPOWERgmat Instructor
User avatar
P
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10128

Kudos [?]: 3517 [0], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: For real numbers, A, B, C, and D on the number line [#permalink]

Show Tags

New post 13 Jan 2015, 14:06
Hi pahujanavdeep,

Unfortunately, your example does NOT fit the "restriction" that is described in Fact 2:

Fact 2: The product of any two of the numbers A, B, C and D is between 0 and 1.

This tells us that if we take ANY two of the 4 values and multiply them....then the product will be a POSITIVE fraction.

Your example:
A = -1
B = -1/2
C = -1/3
D = 1

If one of the two numbers chosen is D, then the product will be a NEGATIVE fraction. This is NOT a viable option given what Fact 2 tells us. The ONLY ways for the product of ANY two of those values to be a POSITIVE fraction is if ALL 4 values are negative OR ALL 4 are positive.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Kudos [?]: 3517 [0], given: 173

Current Student
avatar
Joined: 25 Feb 2013
Posts: 7

Kudos [?]: [0], given: 3

GMAT Date: 12-22-2014
Re: For real numbers, A, B, C, and D on the number line [#permalink]

Show Tags

New post 14 Jan 2015, 06:34
Thank you Rich :)

I got confused with the wording. But it make sense now. Appreciate it :-D

Regards
Navdeep

Kudos [?]: [0], given: 3

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15637

Kudos [?]: 283 [0], given: 0

Premium Member
Re: For real numbers, A, B, C, and D on the number line [#permalink]

Show Tags

New post 10 May 2016, 01:04
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 283 [0], given: 0

Manager
Manager
avatar
Joined: 22 Sep 2015
Posts: 111

Kudos [?]: 79 [0], given: 136

Re: For real numbers, A, B, C, and D on the number line [#permalink]

Show Tags

New post 28 Aug 2016, 13:29
Bunuel wrote:
Image

Notice that from the diagram we have that A<B<C<D.



where does the diagram tell us that?

Kudos [?]: 79 [0], given: 136

Expert Post
EMPOWERgmat Instructor
User avatar
P
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10128

Kudos [?]: 3517 [0], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: For real numbers, A, B, C, and D on the number line [#permalink]

Show Tags

New post 28 Aug 2016, 21:29
Hi nycgirl212,

The prompt specifically refers to the number line that's presented. On a number line, numbers increase from left to right. Thus, based on the given number line, A < B < C < D.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Kudos [?]: 3517 [0], given: 173

Manager
Manager
avatar
Joined: 22 Sep 2015
Posts: 111

Kudos [?]: 79 [0], given: 136

Re: For real numbers, A, B, C, and D on the number line [#permalink]

Show Tags

New post 29 Aug 2016, 08:31
EMPOWERgmatRichC wrote:
Hi nycgirl212,

The prompt specifically refers to the number line that's presented. On a number line, numbers increase from left to right. Thus, based on the given number line, A < B < C < D.

GMAT assassins aren't born, they're made,
Rich


so even though it doesn't explicitly state that the numbers increase from left to right, we are automatically supposed to assume that they do when we see a number line?

Kudos [?]: 79 [0], given: 136

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42264

Kudos [?]: 132782 [1], given: 12372

Re: For real numbers, A, B, C, and D on the number line [#permalink]

Show Tags

New post 29 Aug 2016, 09:15
1
This post received
KUDOS
Expert's post
nycgirl212 wrote:
EMPOWERgmatRichC wrote:
Hi nycgirl212,

The prompt specifically refers to the number line that's presented. On a number line, numbers increase from left to right. Thus, based on the given number line, A < B < C < D.

GMAT assassins aren't born, they're made,
Rich


so even though it doesn't explicitly state that the numbers increase from left to right, we are automatically supposed to assume that they do when we see a number line?


Please check the highlighted part below.

OFFICIAL GUIDE:

Problem Solving
Figures: All figures accompanying problem solving questions are intended to provide information useful in solving the problems. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

Data Sufficiency:
Figures:
• Figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2).
• Lines shown as straight are straight, and lines that appear jagged are also straight.
• The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero.
• All figures lie in a plane unless otherwise indicated.
_________________

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 [?]: 132782 [1], given: 12372

Manager
Manager
avatar
Joined: 22 Sep 2015
Posts: 111

Kudos [?]: 79 [0], given: 136

Re: For real numbers, A, B, C, and D on the number line [#permalink]

Show Tags

New post 29 Aug 2016, 10:06
Bunuel wrote:
nycgirl212 wrote:
EMPOWERgmatRichC wrote:
Hi nycgirl212,

The prompt specifically refers to the number line that's presented. On a number line, numbers increase from left to right. Thus, based on the given number line, A < B < C < D.

GMAT assassins aren't born, they're made,
Rich


so even though it doesn't explicitly state that the numbers increase from left to right, we are automatically supposed to assume that they do when we see a number line?


Please check the highlighted part below.

OFFICIAL GUIDE:

Problem Solving
Figures: All figures accompanying problem solving questions are intended to provide information useful in solving the problems. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

Data Sufficiency:
Figures:
• Figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2).
• Lines shown as straight are straight, and lines that appear jagged are also straight.
• The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero.
• All figures lie in a plane unless otherwise indicated.


thanks, but where does it say that all numbers in a number line increase from left to right? I'm just trying to understand

Kudos [?]: 79 [0], given: 136

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42264

Kudos [?]: 132782 [0], given: 12372

Re: For real numbers, A, B, C, and D on the number line [#permalink]

Show Tags

New post 29 Aug 2016, 10:55

Kudos [?]: 132782 [0], given: 12372

Manager
Manager
avatar
Joined: 22 Sep 2015
Posts: 111

Kudos [?]: 79 [0], given: 136

Re: For real numbers, A, B, C, and D on the number line [#permalink]

Show Tags

New post 29 Aug 2016, 11:12
Bunuel wrote:
nycgirl212 wrote:

thanks, but where does it say that all numbers in a number line increase from left to right? I'm just trying to understand


That's a common knowledge.


Obviously, the question was more of can i assume that a line shows in a diagram will always reflect those properties

Kudos [?]: 79 [0], given: 136

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42264

Kudos [?]: 132782 [0], given: 12372

Re: For real numbers, A, B, C, and D on the number line [#permalink]

Show Tags

New post 29 Aug 2016, 11:19
nycgirl212 wrote:
Bunuel wrote:
nycgirl212 wrote:

thanks, but where does it say that all numbers in a number line increase from left to right? I'm just trying to understand


That's a common knowledge.


Obviously, the question was more of can i assume that a line shows in a diagram will always reflect those properties


I don't understand what you mean...

1. On a number line, numbers increase from left to right - that's a common knowledge;
2. The positions of points, on a diagram exist in the order shown - that's according to the GMAC.

Hence, A < B < C < D.

What is unclear 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

Kudos [?]: 132782 [0], given: 12372

Manager
Manager
avatar
Joined: 22 Sep 2015
Posts: 111

Kudos [?]: 79 [0], given: 136

For real numbers, A, B, C, and D on the number line [#permalink]

Show Tags

New post 29 Aug 2016, 11:49
Bunuel wrote:
I don't understand what you mean...

1. On a number line, numbers increase from left to right - that's a common knowledge;
2. The positions of points, on a diagram exist in the order shown - that's according to the GMAC.

Hence, A < B < C < D.

What is unclear above?


the question is when I see a diagram like this on a GMAT question, can i automatically assume the numbers increase from left to right and are not just randomly assigned (i.e. A is 10, B is -5, C is 20, D is 4)? Yes or no?

Image

Kudos [?]: 79 [0], given: 136

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42264

Kudos [?]: 132782 [0], given: 12372

Re: For real numbers, A, B, C, and D on the number line [#permalink]

Show Tags

New post 29 Aug 2016, 11:52
nycgirl212 wrote:
Bunuel wrote:
I don't understand what you mean...

1. On a number line, numbers increase from left to right - that's a common knowledge;
2. The positions of points, on a diagram exist in the order shown - that's according to the GMAC.

Hence, A < B < C < D.

What is unclear above?


the question is when I see a diagram like this on a GMAT question, can i automatically assume the numbers increase from left to right and are not just randomly assigned (i.e. A is 10, B is -5, C is 20, D is 4)? Yes or no?

Image

________________________
Yes...
_________________

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 [?]: 132782 [0], given: 12372

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15637

Kudos [?]: 283 [0], given: 0

Premium Member
Re: For real numbers, A, B, C, and D on the number line [#permalink]

Show Tags

New post 02 Sep 2017, 03:20
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 283 [0], given: 0

Re: For real numbers, A, B, C, and D on the number line   [#permalink] 02 Sep 2017, 03:20
Display posts from previous: Sort by

For real numbers, A, B, C, and D on the number line

  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®.