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

It is currently 20 Sep 2014, 04:05

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

If a, b, and c are positive integers, with a < b < c,

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Intern
Intern
avatar
Joined: 21 Jul 2009
Posts: 11
Followers: 0

Kudos [?]: 8 [1] , given: 1

If a, b, and c are positive integers, with a < b < c, [#permalink] New post 22 Oct 2009, 22:27
1
This post received
KUDOS
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

51% (02:34) correct 49% (01:54) wrong based on 167 sessions
If a, b, and c are positive integers, with a < b < c, are a, b, and c consecutive integers?

(1) 1/a – 1/b = 1/c

(2) a + c = b^2 – 1
[Reveal] Spoiler: OA

Last edited by Bunuel on 10 Jun 2012, 22:02, edited 1 time in total.
Edited the question.
Expert Post
4 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23482
Followers: 3504

Kudos [?]: 26494 [4] , given: 2712

Re: are a, b, and c consecutive integers? [#permalink] New post 22 Oct 2009, 22:59
4
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
SMAbbas wrote:
If a, b, and c are positive integers, with a < b < c, are a, b, and c consecutive integers?

(1) 1/a – 1/b = 1/c

(2) a + c = b2 – 1


IMO D,

Please verify my answer :?: :shock:


If a, b, c are consecutive and a<b<c, then must be true that: b=a+1 and c=a+2.

(1) \frac{1}{a}-\frac{1}{b}=\frac{1}{c} --> (b-a)c=ab --> (a+1-a)(a+2)=a(a+1) --> a^2=2 --> a^2=2 as a is positive integer this equation has no positive integer roots --> a, b, c, are not consecutive positive integers. Sufficient.

(2) a+c=b^2-1 --> a+a+2=(a+1)^2-1 --> 2a+2=a^2+2a+1-1 --> a^2=2. The same here: a, b, c, are not consecutive positive integers. Sufficient.

Answer D.
_________________

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

Current Student
avatar
Joined: 21 Oct 2009
Posts: 41
Followers: 0

Kudos [?]: 4 [0], given: 4

Re: are a, b, and c consecutive integers? [#permalink] New post 27 Oct 2009, 06:01
I think I must have misunderstood the basic rule on DS

Like this question, when we find it SUFFICIENT to say "it can't be a real number," it should be good enought to choose (D).

I thought I could choose (D) as long as I could verify YES for quesitions.
1 KUDOS received
Senior Manager
Senior Manager
User avatar
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 326
Followers: 11

Kudos [?]: 268 [1] , given: 20

GMAT Tests User
Re: are a, b, and c consecutive integers? [#permalink] New post 22 May 2010, 07:19
1
This post received
KUDOS
i approached the question differently ... this may not be the best way but i'm going to share it anyway ... sharing is caring :)

a, b, c > 0 [positive integers]
b=a+1, c=a+2 [a, b, c are consecutive integers]

(1) 1/a - 1/b = 1/c
1/a - 1/a+1 = 1/a+2
1/a(a+1) = 1/(a+2)
a+2 = a(a+1)
c = a*b [c=a+2, b=a+1]

if a, b, c are consecutive ... the above equation in bold can never be true
2 ? 0*1
3 ? 1*2
4 ? 2*3

1 is sufficient to explain that a, b, c are not consecutive integers

(2) a+c = (b-1)(b+1)
a+c = a*c [a=b-1, c=b+1]

if a, b, c are consecutive ... the above equation in bold can never be true
0+2 ? 0*2
1+3 ? 1*3
2+4 ? 2*4

2 is sufficient to explain that a, b, c are not consecutive integers

ans is D

_________________

press kudos, if you like the explanation, appreciate the effort or encourage people to respond.

Download the Ultimate SC Flashcards

Senior Manager
Senior Manager
User avatar
Joined: 19 Nov 2009
Posts: 329
Followers: 4

Kudos [?]: 60 [0], given: 44

GMAT Tests User
Re: are a, b, and c consecutive integers? [#permalink] New post 22 May 2010, 15:01
i approached the question differently ... this may not be the best way but i'm going to share it anyway ... sharing is caring


As long as you get the right answer, any approach should be fine ! :wink:
Manager
Manager
User avatar
Joined: 02 Jan 2010
Posts: 135
Followers: 3

Kudos [?]: 4 [0], given: 3

Re: are a, b, and c consecutive integers? [#permalink] New post 22 May 2010, 19:43
I got D too, used sample numbers to check. The methods given here are useful as well!!!
_________________

Regards
Ganesh
Class of 2012
Great Lakes Institute of Management
http://greatlakes.edu.in

Manager
Manager
User avatar
Joined: 29 Jun 2011
Posts: 165
WE 1: Information Technology(Retail)
Followers: 3

Kudos [?]: 13 [0], given: 29

Re: If a, b, and c are positive integers, with a < b < c, [#permalink] New post 02 Sep 2013, 23:11
I solved the questions by plugging in consecutive numbers.
Got the ans D. Would you suggest to use plugging in method to solve such questions?
1 KUDOS received
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1666
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 12

Kudos [?]: 164 [1] , given: 274

GMAT ToolKit User
Re: If a, b, and c are positive integers, with a < b < c, [#permalink] New post 24 Oct 2013, 06:05
1
This post received
KUDOS
SMAbbas wrote:
If a, b, and c are positive integers, with a < b < c, are a, b, and c consecutive integers?

(1) 1/a – 1/b = 1/c

(2) a + c = b^2 – 1


Hey guys - The way I did it was

(1) 1/a – 1/b = 1/c ---> 1/a = 1/b + 1/c

LCM of 'b' and 'c' would never be smaller than b or c because these numbers are co-prime which means that they do not share any common integer factor other than 1.

Now since c>b>a then they following the logic above they can't be consecutive integers. Sufficient

(2) a + c = b^2 – 1 ---> a+c = (b+1)(b-1)

Now if a,b,c were consecutive integers it will be true that (a+c)/2 is equal to b
So we would have that a+c = 2b

Now if we replace a+c = 2b in the first equation we would have that

2b = b^2-1

And when trying to solve this quadratic we would realize that b is not an integer, since we would have to use the formula
So it contradicts the information that a,b,c are integers. Hence a,b,c cannot be consecutive integers

Insuff

Answer (D)

Please let me know whether this makes sense.
If it does, throw me some Kudos!

Cheers
J :)

Last edited by jlgdr on 24 Oct 2013, 07:05, edited 1 time in total.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23482
Followers: 3504

Kudos [?]: 26494 [0], given: 2712

Re: If a, b, and c are positive integers, with a < b < c, [#permalink] New post 24 Oct 2013, 06:41
Expert's post
jlgdr wrote:
SMAbbas wrote:
If a, b, and c are positive integers, with a < b < c, are a, b, and c consecutive integers?

(1) 1/a – 1/b = 1/c

(2) a + c = b^2 – 1


Hey guys - The way I did it was

(1) 1/a – 1/b = 1/c ---> 1/a = 1/b + 1/c

LCM of 'b' and 'c' would never be smaller than b or c because these numbers are co-prime which means that they do not share any common integer factor other than 1.

Now since c>b>a then they following the logic above they can't be consecutive integers. Sufficient

(2) a + c = b^2 – 1 ---> a+c = (b+1)(b-1)

Now if a,b,c were consecutive integers it will be true that (a+c)/2 is equal to b
So we would have that a+c = 2b

Now if we replace a+c = 2b in the first equation we would have that

2b = b^2-1

And when trying to solve this quadratic we would realize that b is not an integer, since we would have to use the formula
So it contradicts the information that a,b,c are integers. Hence a,b,c cannot be consecutive integers

Insuff

Answer (E)


Please let me know whether this makes sense.
If it does, throw me some Kudos!

Cheers
J :)


Notice that OA is D.
_________________

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

SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1666
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 12

Kudos [?]: 164 [0], given: 274

GMAT ToolKit User
Re: If a, b, and c are positive integers, with a < b < c, [#permalink] New post 24 Oct 2013, 07:06
Bunuel wrote:
jlgdr wrote:
SMAbbas wrote:
If a, b, and c are positive integers, with a < b < c, are a, b, and c consecutive integers?

(1) 1/a – 1/b = 1/c

(2) a + c = b^2 – 1


Hey guys - The way I did it was

(1) 1/a – 1/b = 1/c ---> 1/a = 1/b + 1/c

LCM of 'b' and 'c' would never be smaller than b or c because these numbers are co-prime which means that they do not share any common integer factor other than 1.

Now since c>b>a then they following the logic above they can't be consecutive integers. Sufficient

(2) a + c = b^2 – 1 ---> a+c = (b+1)(b-1)

Now if a,b,c were consecutive integers it will be true that (a+c)/2 is equal to b
So we would have that a+c = 2b

Now if we replace a+c = 2b in the first equation we would have that

2b = b^2-1

And when trying to solve this quadratic we would realize that b is not an integer, since we would have to use the formula
So it contradicts the information that a,b,c are integers. Hence a,b,c cannot be consecutive integers

Insuff

Answer (E)


Please let me know whether this makes sense.
If it does, throw me some Kudos!

Cheers
J :)


Notice that OA is D.


Oops, typo. Yes, answer is (D) indeed
Senior Manager
Senior Manager
User avatar
Joined: 23 Oct 2010
Posts: 384
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Followers: 12

Kudos [?]: 136 [0], given: 73

GMAT ToolKit User
Re: If a, b, and c are positive integers, with a < b < c, [#permalink] New post 24 Oct 2013, 20:53
1) 1/a – 1/b = 1/c
let a=1 b=2 c=3

1/2-1/3 doesnt equal to 1/4

(2) a + c = b^2 – 1

let a(even) b(odd) c(even)
a + c = b^2 – 1 = even +even =odd^-1=even - ok!

let a(odd) b(even) c(odd)
a + c = b^2 – 1 = odd +odd doesnt equal to even^-1 not ok!
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

Manager
Manager
avatar
Joined: 25 Oct 2013
Posts: 173
Followers: 0

Kudos [?]: 24 [0], given: 56

Re: If a, b, and c are positive integers, with a < b < c, [#permalink] New post 04 Feb 2014, 05:24
I assumed a,b,c to be consecutive and substituted b-1,b,b+1 in each statement independently.

(1) gives b^2=2b+1 and b is not an integer hence my assumption that a,b,c are consecutive cannot be true. sufficient.
(2) also gives b^2 = 2b+1. same as (1) hence sufficient.

+1 D.

Hope it made sense. :)
_________________

Click on Kudos if you liked the post!

Practice makes Perfect.

Intern
Intern
avatar
Joined: 05 Feb 2014
Posts: 48
Followers: 0

Kudos [?]: 6 [0], given: 49

Re: are a, b, and c consecutive integers? [#permalink] New post 14 May 2014, 03:40
Bunuel wrote:
SMAbbas wrote:
If a, b, and c are positive integers, with a < b < c, are a, b, and c consecutive integers?

(1) 1/a – 1/b = 1/c

(2) a + c = b2 – 1


IMO D,

Please verify my answer :?: :shock:


If a, b, c are consecutive and a<b<c, then must be true that: b=a+1 and c=a+2.

(1) \frac{1}{a}-\frac{1}{b}=\frac{1}{c} --> (b-a)c=ab --> (a+1-a)(a+2)=a(a+1) --> a^2=2 --> a^2=2 as a is positive integer this equation has no positive integer roots --> a, b, c, are not consecutive positive integers. Sufficient.

(2) a+c=b^2-1 --> a+a+2=(a+1)^2-1 --> 2a+2=a^2+2a+1-1 --> a^2=2. The same here: a, b, c, are not consecutive positive integers. Sufficient.

Answer D.


Hi Bunuel,

Thanks for the answer. One question - what is the meaning of "this eq has no positive integer root ?". It is because the eq has A = +- 2 ?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23482
Followers: 3504

Kudos [?]: 26494 [0], given: 2712

Re: are a, b, and c consecutive integers? [#permalink] New post 14 May 2014, 05:35
Expert's post
gauravsoni wrote:
Bunuel wrote:
SMAbbas wrote:
If a, b, and c are positive integers, with a < b < c, are a, b, and c consecutive integers?

(1) 1/a – 1/b = 1/c

(2) a + c = b2 – 1


IMO D,

Please verify my answer :?: :shock:


If a, b, c are consecutive and a<b<c, then must be true that: b=a+1 and c=a+2.

(1) \frac{1}{a}-\frac{1}{b}=\frac{1}{c} --> (b-a)c=ab --> (a+1-a)(a+2)=a(a+1) --> a^2=2 --> a^2=2 as a is positive integer this equation has no positive integer roots --> a, b, c, are not consecutive positive integers. Sufficient.

(2) a+c=b^2-1 --> a+a+2=(a+1)^2-1 --> 2a+2=a^2+2a+1-1 --> a^2=2. The same here: a, b, c, are not consecutive positive integers. Sufficient.

Answer D.


Hi Bunuel,

Thanks for the answer. One question - what is the meaning of "this eq has no positive integer root ?". It is because the eq has A = +- 2 ?


We are given that a is a positive integer, while from a^2=2, a=-\sqrt{2} or a=\sqrt{2}. Hence our assumption that a, b, and c were consecutive integers was wrong.
_________________

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: 05 Feb 2014
Posts: 48
Followers: 0

Kudos [?]: 6 [0], given: 49

Re: are a, b, and c consecutive integers? [#permalink] New post 14 May 2014, 06:29
gauravsoni wrote:
Bunuel wrote:
SMAbbas wrote:
If a, b, and c are positive integers, with a < b < c, are a, b, and c consecutive integers?

(1) 1/a – 1/b = 1/c

(2) a + c = b2 – 1


IMO D,

Please verify my answer :?: :shock:


If a, b, c are consecutive and a<b<c, then must be true that: b=a+1 and c=a+2.

(1) \frac{1}{a}-\frac{1}{b}=\frac{1}{c} --> (b-a)c=ab --> (a+1-a)(a+2)=a(a+1) --> a^2=2 --> a^2=2 as a is positive integer this equation has no positive integer roots --> a, b, c, are not consecutive positive integers. Sufficient.

(2) a+c=b^2-1 --> a+a+2=(a+1)^2-1 --> 2a+2=a^2+2a+1-1 --> a^2=2. The same here: a, b, c, are not consecutive positive integers. Sufficient.

Answer D.


Hi Bunuel,

Thanks for the answer. One question - what is the meaning of "this eq has no positive integer root ?". It is because the eq has A = +- 2 ?


We are given that a is a positive integer, while from a^2=2, a=-\sqrt{2} or a=\sqrt{2}. Hence our assumption that a, b, and c were consecutive integers was wrong.[/quote]


Got it , thanks...
Intern
Intern
avatar
Joined: 25 Jan 2014
Posts: 42
Concentration: Strategy, International Business
GMAT 1: 600 Q44 V29
GMAT 2: 710 Q48 V38
GPA: 3.35
WE: Analyst (Computer Software)
Followers: 1

Kudos [?]: 14 [0], given: 4

Re: If a, b, and c are positive integers, with a < b < c, [#permalink] New post 15 May 2014, 02:32
Bunuel,

We can also do it by taking a, b and c as (x-1), x, (x+1) right? It looks the same to me as taking b = a+1 and c = a+2
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23482
Followers: 3504

Kudos [?]: 26494 [0], given: 2712

Re: If a, b, and c are positive integers, with a < b < c, [#permalink] New post 15 May 2014, 02:42
Expert's post
Intern
Intern
avatar
Joined: 25 Jan 2014
Posts: 42
Concentration: Strategy, International Business
GMAT 1: 600 Q44 V29
GMAT 2: 710 Q48 V38
GPA: 3.35
WE: Analyst (Computer Software)
Followers: 1

Kudos [?]: 14 [0], given: 4

Re: If a, b, and c are positive integers, with a < b < c, [#permalink] New post 15 May 2014, 02:46
Thanks a lot Bunuel
Re: If a, b, and c are positive integers, with a < b < c,   [#permalink] 15 May 2014, 02:46
    Similar topics Author Replies Last post
Similar
Topics:
A, B, C and D are positive integers, and A < B < C < D. If A honchos 2 25 Aug 2014, 01:36
1 a, b, c, and d are positive consecutive integers and a < b < Stiv 2 17 Aug 2013, 09:34
1 Experts publish their posts in the topic If a, b, and c are consecutive positive integers and a < b < Walkabout 5 29 Dec 2012, 05:44
10 Experts publish their posts in the topic Positive integers a, b, c, d and e are such that a<b<c<d<e shrive555 11 18 Oct 2010, 09:57
If a, b, and c are positive integers, with a < b < c, abhi758 1 23 Oct 2009, 08:24
Display posts from previous: Sort by

If a, b, and c are positive integers, with a < b < c,

  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®.