If a, b, and c are consecutive positive integers and a < b < : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

It is currently 07 Dec 2016, 23:58
GMAT Club Tests

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

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

Hide Tags

1 KUDOS received
Manager
Manager
avatar
Joined: 02 Dec 2012
Posts: 178
Followers: 5

Kudos [?]: 2206 [1] , given: 0

If a, b, and c are consecutive positive integers and a < b < [#permalink]

Show Tags

New post 29 Dec 2012, 05:44
1
This post received
KUDOS
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

84% (01:51) correct 16% (00:51) wrong based on 738 sessions

HideShow timer Statistics

If a, b, and c are consecutive positive integers and a < b < c, which of the following must be true?

I. c - a = 2
II. abc is an even integer.
III. (a + b + c)/3 is an integer.

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III
[Reveal] Spoiler: OA
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35912
Followers: 6852

Kudos [?]: 90037 [0], given: 10402

Re: If a, b, and c are consecutive positive integers and a < b < [#permalink]

Show Tags

New post 29 Dec 2012, 05:49
Expert's post
6
This post was
BOOKMARKED
If a, b, and c are consecutive positive integers and a < b < c, which of the following must be true?

I. c - a = 2
II. abc is an even integer.
III. (a + b + c)/3 is an integer.


(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III

Since a, b, and c are consecutive positive integers and a < b < c, then c = a + 2, from which it follows that c - a = 2. So, I is true.

Next, out of 3 consecutive integers at least 1 must be even, thus abc=even. II is true.

Finally, since b = a + 1, and c = a + 2, then (a + b + c)/3 = (a + a + 1 + a + 2)/3 = a + 1 = integer. III is true as well.

Answer: E.
_________________

New to the Math Forum?
Please read this: 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

1 KUDOS received
Intern
Intern
avatar
Joined: 16 Sep 2010
Posts: 12
Followers: 0

Kudos [?]: 18 [1] , given: 0

Re: If a, b, and c are consecutive positive integers and a < b < [#permalink]

Show Tags

New post 22 Jun 2013, 10:32
1
This post received
KUDOS
Hey Bunuel, I know I'm a few years late to this but I have a general question about consecutive integers.
According to your explanation, consecutive integers are always 1 apart. However in Sackmann's Total GMAT Math, he defines 'consecutive integers' as any set of integers that are EVENLY SPACED. I'm a little confused here. What's the correct way to think about them?
Thanks!
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35912
Followers: 6852

Kudos [?]: 90037 [0], given: 10402

Re: If a, b, and c are consecutive positive integers and a < b < [#permalink]

Show Tags

New post 22 Jun 2013, 10:37
tricialin wrote:
Hey Bunuel, I know I'm a few years late to this but I have a general question about consecutive integers.
According to your explanation, consecutive integers are always 1 apart. However in Sackmann's Total GMAT Math, he defines 'consecutive integers' as any set of integers that are EVENLY SPACED. I'm a little confused here. What's the correct way to think about them?
Thanks!


When we see "consecutive integers" it ALWAYS means integers that follow each other in order with common difference of 1: ... x-3, x-2, x-1, x, x+1, x+2, ....

For example:

-7, -6, -5 are consecutive integers.

2, 4, 6 ARE NOT consecutive integers, they are consecutive even integers.

3, 5, 7 ARE NOT consecutive integers, they are consecutive odd integers.

So, not all evenly spaced sets represent consecutive integers.
_________________

New to the Math Forum?
Please read this: 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

Intern
Intern
avatar
Joined: 16 Sep 2010
Posts: 12
Followers: 0

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

Re: If a, b, and c are consecutive positive integers and a < b < [#permalink]

Show Tags

New post 22 Jun 2013, 10:44
awesome. Thanks a lot.
1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 29 Oct 2013
Posts: 297
Concentration: Finance
GMAT 1: 750 Q V46
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Followers: 14

Kudos [?]: 365 [1] , given: 197

GMAT ToolKit User
Re: If a, b, and c are consecutive positive integers and a < b < [#permalink]

Show Tags

New post 28 May 2014, 08:54
1
This post received
KUDOS
1
This post was
BOOKMARKED
If a, b, and c are consecutive positive integers and a < b < c, which of the following must be true?

I. c - a = 2 #True: Since a,b,c are consecutive integers a and c must be 2 integers apart
II. abc is an even integer. #True: For any 3 consecutive integers a,b,c the product has to be divisible by 3! i.e. 6 --> it is even
III. (a + b + c)/3 is an integer. #True: This is a mean of the series. That is this has to be the middle no. b which as per the question stem is an integer

Answer: E
_________________

Please contact me for super inexpensive quality private tutoring

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 12891
Followers: 561

Kudos [?]: 158 [0], given: 0

Premium Member
Re: If a, b, and c are consecutive positive integers and a < b < [#permalink]

Show Tags

New post 23 Sep 2015, 19:21
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

Expert Post
Senior Manager
Senior Manager
User avatar
Joined: 20 Aug 2015
Posts: 398
Location: India
GMAT 1: 760 Q50 V44
Followers: 23

Kudos [?]: 202 [0], given: 10

Re: If a, b, and c are consecutive positive integers and a < b < [#permalink]

Show Tags

New post 24 Sep 2015, 00:00
Assume the following variables to make the calculations simpler:
3 consecutive integers: x-1, x, x+1
3 consecutive even/odd integers: x-2, x, x+2


Although, this question can be solved without the information, still you should keep it in mind if you encounter questions involving consecutive integers/even integers/odd integers etc.

If a, b, and c are consecutive positive integers and a < b < c, which of the following must be true?

I. c - a = 2. By our assumption, (a, b, c) are x-1, 1, x+1.
c - a = (x+1) - (x-1) = 2
Correct

II. abc is an even integer.
2 or more consecutive integers will always be even as every alternate number is even
Correct

III. (a + b + c)/3 is an integer.
((x+1) + x + (x-1))/3 = 3x/3 =x
And x is an integer.
Correct.

Hence option E: I, II, and III
_________________

Reach out to us at bondwithus@gmatify.com

Image

Senior Manager
Senior Manager
User avatar
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 392
Followers: 21

Kudos [?]: 138 [0], given: 2

Re: If a, b, and c are consecutive positive integers and a < b < [#permalink]

Show Tags

New post 15 Jul 2016, 03:49
Walkabout wrote:
If a, b, and c are consecutive positive integers and a < b < c, which of the following must be true?

I. c - a = 2
II. abc is an even integer.
III. (a + b + c)/3 is an integer.

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III


The easiest way to solve the problem is to plug in some real numbers for a, b, and c. Since we know they are consecutive and we know that a < b < c, we can say:

a = 1

b = 2

c = 3

or

a = 2

b = 3

c = 4

It is good to test two cases because in our first case we start with an odd integer and in the second case we start with an even integer.

Let’s use these values in each Roman numeral answer choice. Remember we need to determine which answer must be true, meaning in all circumstances.

I. c – a = 2

Case #1

3 – 1 = 2

Case #2

4 - 2 = 2

I must be true.

II. abc is an even integer.

Case #1

1 x 2 x 3 = 6

Case #2

2 x 3 x 4 = 24

II must be true.

III. (a + b + c)/3 is an integer.

Case #1

(1 + 2 + 3)/3 = 6/3 = 2

Case #2

(2 + 3 + 4)/3 = 9/3 = 3

III must be true.

I, II, and III are all true.

The answer is E.
_________________

Image
Jeffrey Miller
Jeffrey Miller
Head of GMAT Instruction

Re: If a, b, and c are consecutive positive integers and a < b <   [#permalink] 15 Jul 2016, 03:49
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic If a, b, and c are consecutive integers such that a < b < c and a is Bunuel 2 13 Apr 2016, 04:31
5 a, b, c, and d are positive consecutive integers and a < b < Stiv 4 17 Aug 2013, 09:34
1 Experts publish their posts in the topic If a, b, c are consecutive positive integers and a<b<c, whic Lolaergasheva 3 07 Feb 2011, 22:23
31 Experts publish their posts in the topic Positive integers a, b, c, d and e are such that a<b<c<d<e shrive555 13 18 Oct 2010, 09:57
23 Experts publish their posts in the topic a, b, and c are integers and a < b < c. S is the set of all KocharRohit 13 27 Oct 2009, 22:18
Display posts from previous: Sort by

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

  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 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®.