Find all School-related info fast with the new School-Specific MBA Forum

It is currently 23 Jul 2014, 04:19

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

How many integers are there between, but not including

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 06 Jul 2011
Posts: 214
Location: Accra, Ghana
Followers: 1

Kudos [?]: 21 [0], given: 39

GMAT Tests User
How many integers are there between, but not including [#permalink] New post 20 Mar 2012, 00:19
00:00
A
B
C
D
E

Difficulty:

  25% (low)

Question Stats:

68% (01:37) correct 32% (00:51) wrong based on 168 sessions
How many integers are there between, but not including, integers r and s ?

(1) s – r = 10
(2) There are 9 integers between, but not including, r + 1 and s + 1.

I may have mistakenly chosen the wrong answer, but nevertheless some expert explanation will help me understand this better.
[Reveal] Spoiler: OA
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18693
Followers: 3233

Kudos [?]: 22243 [0], given: 2602

Re: How many integers are there between, but not including [#permalink] New post 20 Mar 2012, 00:38
Expert's post
How many integers are there between, but not including, integers r and s ?

Notice that we are told that r and s are integers.

(1) s – r = 10 --> since r and s are integers and s – r = 10 then there will be 9 integers between them. For example take s=10 and r=0, then there are following integers between them: 1, 2, 3, 4, 5, 6, 7, 8, and 9. Sufficient.

(2) There are 9 integers between, but not including, r + 1 and s + 1 --> the distance between r and s is the same as the distance between r+1 and s+1, so if there are 9 integers between, but not including, r+1 and s+1 then there will be 9 integers between, but not including, r and s too. For example consider s+1=11 and r+1=1 (9 integers between them: 2, 3, 4, 5, 6, 7, 8, 9, and 10) --> s=10 and r=0 the same as above. Sufficient.

Answer: D.

Hope it's clear.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Status: I laugh all day, and scrabble all night. I badazzle my clothes, so my outfits tight.
Joined: 29 Jan 2011
Posts: 3
Followers: 0

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

Re: How many integers are there between, but not including [#permalink] New post 21 Mar 2012, 17:42
nice explanation!
Manager
Manager
avatar
Joined: 07 Dec 2011
Posts: 174
Location: India
Followers: 1

Kudos [?]: 31 [0], given: 24

Re: How many integers are there between, but not including [#permalink] New post 23 Mar 2012, 03:12
number of integers including s and r = s-r+1. Number of integers excluding s and r = s-r+1-2 = s-r-1.

1) gives us s-r-1 = 9. Sufficient
2) The number of integers between s and r will be the same as number of integers between s+1 and r+1 = 9 .Sufficient.

Hence D
Manager
Manager
User avatar
Joined: 13 Feb 2012
Posts: 148
Location: Italy
Concentration: General Management, Entrepreneurship
GMAT 1: 560 Q36 V34
GPA: 3.1
WE: Sales (Transportation)
Followers: 4

Kudos [?]: 0 [0], given: 85

Re: How many integers are there between, but not including [#permalink] New post 05 Sep 2012, 04:41
I might be wrong, but I think the second part of statement 2) : "not including r+1 and s+1" is useless since it does not change anything to the distance the two values are apart.

At least this is how I got D.

_________________

"The Burnout" - My Debrief

Kudos if I helped you ;)


Andy

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18693
Followers: 3233

Kudos [?]: 22243 [1] , given: 2602

Re: How many integers are there between, but not including [#permalink] New post 05 Sep 2012, 05:07
1
This post received
KUDOS
Expert's post
highdiving wrote:
I might be wrong, but I think the second part of statement 2) : "not including r+1 and s+1" is useless since it does not change anything to the distance the two values are apart.

At least this is how I got D.


If we were not told that, then yes the statement would still be sufficient, but in this case the two statements would contradict each other: answer from (1) would be 9, and the answer from (2) would be 7.

Note that: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

1 KUDOS received
Manager
Manager
User avatar
Joined: 13 Feb 2012
Posts: 148
Location: Italy
Concentration: General Management, Entrepreneurship
GMAT 1: 560 Q36 V34
GPA: 3.1
WE: Sales (Transportation)
Followers: 4

Kudos [?]: 0 [1] , given: 85

Re: How many integers are there between, but not including [#permalink] New post 05 Sep 2012, 05:39
1
This post received
KUDOS
I must be missing something and I am sorry to bother you: but why would I even need to consider s+1 when I am looking for numbers between them? Maybe Im just assuming s is the upper end and so on.

Thank you for your time and patience.

Posted from my mobile device Image

_________________

"The Burnout" - My Debrief

Kudos if I helped you ;)


Andy

Senior Manager
Senior Manager
avatar
Joined: 08 Jun 2010
Posts: 454
Followers: 0

Kudos [?]: 28 [0], given: 39

GMAT Tests User
Re: How many integers are there between, but not including [#permalink] New post 27 Feb 2013, 23:16
THERE ARE og question which ask about the number of even interger between 2 numbers. This is more cheating.
Manager
Manager
avatar
Joined: 07 Apr 2012
Posts: 127
Location: United States
Concentration: Entrepreneurship, Operations
Schools: ISB '15
GMAT 1: 590 Q48 V23
GPA: 3.9
WE: Operations (Manufacturing)
Followers: 0

Kudos [?]: 7 [0], given: 45

Re: How many integers are there between, but not including [#permalink] New post 27 Feb 2013, 23:36
In general number of integeres when extreme numbers are omiitted is s-r-1 .

A. Since s-r=10, so answer is 9, hence A is fine
B. Again difference b/w r+1 & s+1 is s-r-1, so B is also is fiine.

so D .
SVP
SVP
User avatar
Joined: 05 Jul 2006
Posts: 1542
Followers: 5

Kudos [?]: 65 [0], given: 39

Re: How many integers are there between, but not including [#permalink] New post 31 Mar 2013, 05:40
Bunuel wrote:
How many integers are there between, but not including, integers r and s ?

Notice that we are told that r and s are integers.

(1) s – r = 10 --> since r and s are integers and s – r = 10 then there will be 9 integers between them. For example take s=10 and r=0, then there are following integers between them: 1, 2, 3, 4, 5, 6, 7, 8, and 9. Sufficient.

(2) There are 9 integers between, but not including, r + 1 and s + 1 --> the distance between r and s is the same as the distance between r+1 and s+1, so if there are 9 integers between, but not including, r+1 and s+1 then there will be 9 integers between, but not including, r and s too. For example consider s+1=11 and r+1=1 (9 integers between them: 2, 3, 4, 5, 6, 7, 8, 9, and 10) --> s=10 and r=0 the same as above. Sufficient.

Answer: D.

Hope it's clear.


Hi Bunuel , if i am not mistaken , why are we assuming that r and s belongs to an evenly spaced set of integers ??
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18693
Followers: 3233

Kudos [?]: 22243 [0], given: 2602

Re: How many integers are there between, but not including [#permalink] New post 31 Mar 2013, 07:21
Expert's post
yezz wrote:
Bunuel wrote:
How many integers are there between, but not including, integers r and s ?

Notice that we are told that r and s are integers.

(1) s – r = 10 --> since r and s are integers and s – r = 10 then there will be 9 integers between them. For example take s=10 and r=0, then there are following integers between them: 1, 2, 3, 4, 5, 6, 7, 8, and 9. Sufficient.

(2) There are 9 integers between, but not including, r + 1 and s + 1 --> the distance between r and s is the same as the distance between r+1 and s+1, so if there are 9 integers between, but not including, r+1 and s+1 then there will be 9 integers between, but not including, r and s too. For example consider s+1=11 and r+1=1 (9 integers between them: 2, 3, 4, 5, 6, 7, 8, 9, and 10) --> s=10 and r=0 the same as above. Sufficient.

Answer: D.

Hope it's clear.


Hi Bunuel , if i am not mistaken , why are we assuming that r and s belongs to an evenly spaced set of integers ??


Not sure I understand what you mean.

s and r are just two integers. The question asks: how many integers are there between, but not including r and s.

Ask yourself, how many integers are there between, but not including, 0 and 10? The answer is 9: 1, 2, 3, 4, 5, 6, 7, 8, and 9.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 15 May 2012
Posts: 44
Followers: 0

Kudos [?]: 5 [0], given: 94

Re: How many integers are there between, but not including [#permalink] New post 22 May 2013, 03:51
Bunuel wrote:
How many integers are there between, but not including, integers r and s ?

Notice that we are told that r and s are integers.

(1) s – r = 10 --> since r and s are integers and s – r = 10 then there will be 9 integers between them. For example take s=10 and r=0, then there are following integers between them: 1, 2, 3, 4, 5, 6, 7, 8, and 9. Sufficient.

(2) There are 9 integers between, but not including, r + 1 and s + 1 --> the distance between r and s is the same as the distance between r+1 and s+1, so if there are 9 integers between, but not including, r+1 and s+1 then there will be 9 integers between, but not including, r and s too. For example consider s+1=11 and r+1=1 (9 integers between them: 2, 3, 4, 5, 6, 7, 8, 9, and 10) --> s=10 and r=0 the same as above. Sufficient.

Answer: D.

Hope it's clear.

But, Bunuel - Considering your example in the first case in which r=0 and s=10, the number of integers between them could be maximum 9 or it could be any number less than that. Because, there is no mention of the word "consecutive" in the question. But, the second one clearly states that there are 9 integers. Hence B is sufficient, but A is not! Can you please explain where I am going wrong? Since this is an official problem and also you had solved it, I am 100% confident that D is the answer, but, I want to know where I am going wrong.
Thanks!
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18693
Followers: 3233

Kudos [?]: 22243 [0], given: 2602

Re: How many integers are there between, but not including [#permalink] New post 22 May 2013, 03:57
Expert's post
sharmila79 wrote:
Bunuel wrote:
How many integers are there between, but not including, integers r and s ?

Notice that we are told that r and s are integers.

(1) s – r = 10 --> since r and s are integers and s – r = 10 then there will be 9 integers between them. For example take s=10 and r=0, then there are following integers between them: 1, 2, 3, 4, 5, 6, 7, 8, and 9. Sufficient.

(2) There are 9 integers between, but not including, r + 1 and s + 1 --> the distance between r and s is the same as the distance between r+1 and s+1, so if there are 9 integers between, but not including, r+1 and s+1 then there will be 9 integers between, but not including, r and s too. For example consider s+1=11 and r+1=1 (9 integers between them: 2, 3, 4, 5, 6, 7, 8, 9, and 10) --> s=10 and r=0 the same as above. Sufficient.

Answer: D.

Hope it's clear.

But, Bunuel - Considering your example in the first case in which r=0 and s=10, the number of integers between them could be maximum 9 or it could be any number less than that. Because, there is no mention of the word "consecutive" in the question. But, the second one clearly states that there are 9 integers. Hence B is sufficient, but A is not! Can you please explain where I am going wrong? Since this is an official problem and also you had solved it, I am 100% confident that D is the answer, but, I want to know where I am going wrong.
Thanks!


You don't need the word "consecutive".

How many integers are there between, but not including 1 and 3? Only one integer: 2.
How many integers are there between, but not including 1 and 5? Three: 2, 3, and 4.

Similarly: how many integers are there between, but not including, 0 and 10? The answer is 9: 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Hope it's clear.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 15 May 2012
Posts: 44
Followers: 0

Kudos [?]: 5 [0], given: 94

Re: How many integers are there between, but not including [#permalink] New post 22 May 2013, 09:39
Bunuel wrote:
sharmila79 wrote:
Bunuel wrote:
How many integers are there between, but not including, integers r and s ?

Notice that we are told that r and s are integers.

(1) s – r = 10 --> since r and s are integers and s – r = 10 then there will be 9 integers between them. For example take s=10 and r=0, then there are following integers between them: 1, 2, 3, 4, 5, 6, 7, 8, and 9. Sufficient.

(2) There are 9 integers between, but not including, r + 1 and s + 1 --> the distance between r and s is the same as the distance between r+1 and s+1, so if there are 9 integers between, but not including, r+1 and s+1 then there will be 9 integers between, but not including, r and s too. For example consider s+1=11 and r+1=1 (9 integers between them: 2, 3, 4, 5, 6, 7, 8, 9, and 10) --> s=10 and r=0 the same as above. Sufficient.

Answer: D.

Hope it's clear.

But, Bunuel - Considering your example in the first case in which r=0 and s=10, the number of integers between them could be maximum 9 or it could be any number less than that. Because, there is no mention of the word "consecutive" in the question. But, the second one clearly states that there are 9 integers. Hence B is sufficient, but A is not! Can you please explain where I am going wrong? Since this is an official problem and also you had solved it, I am 100% confident that D is the answer, but, I want to know where I am going wrong.
Thanks!


You don't need the word "consecutive".

How many integers are there between, but not including 1 and 3? Only one integer: 2.
How many integers are there between, but not including 1 and 5? Three: 2, 3, and 4.

Similarly: how many integers are there between, but not including, 0 and 10? The answer is 9: 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Hope it's clear.

GMAT questions are tricky and they demand over- cautiousness! This is one such occasion...
Re: How many integers are there between, but not including   [#permalink] 22 May 2013, 09:39
    Similar topics Author Replies Last post
Similar
Topics:
5 Experts publish their posts in the topic How many integers are there between, but not including Bunuel 10 15 Oct 2012, 03:51
1 How many integers are there between, but not including, shashankp27 4 09 Sep 2011, 05:32
9 Experts publish their posts in the topic How many integers are there between, but not including chrisahn112 15 30 Jun 2009, 13:00
How many integers are there between, but not including yhc25 2 13 Nov 2008, 02:01
Display posts from previous: Sort by

How many integers are there between, but not including

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.