Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 09 Feb 2013
Posts: 111

If a, b, and c are consecutive odd positive integers and a
[#permalink]
Show Tags
Updated on: 14 Jun 2013, 00:41
Question Stats:
32% (01:40) correct 68% (01:55) wrong based on 334 sessions
HideShow timer Statistics
If a, b, and c are consecutive odd positive integers and a<b<c, which of the following must be true? I. at least one of the three numbers is prime II. ab>c III. a + b + c = 3b A. III only B. I and II only C. I and III only D. II and III only E. I, II, and III
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by emmak on 13 Jun 2013, 23:30.
Last edited by Bunuel on 14 Jun 2013, 00:41, edited 1 time in total.
Edited the question.




Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 583

Re: If a, b, and c are consecutive odd positive integers and a
[#permalink]
Show Tags
14 Jun 2013, 03:04
emmak wrote: If a, b, and c are consecutive odd positive integers and a<b<c, which of the following must be true? I. at least one of the three numbers is prime II. ab>c III. a + b + c = 3b
A)III only B)I and II only C)I and III only D)II and III only E)I, II, and III It is worth remembering that there exists only ONE prime number from 90100 and that is 97. Thus, 91,93 and 95 are not prime.Statement I is definitely not always true. For a=1,b=3,c=5, Statement II is not true. As a,b,c are in Arithmetic Progression, the average of the integers\([\frac{(a+b+c)}{3}]\) is equal to the median(b). This is always true. A.
_________________




SVP
Status: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 1916

Re: If a, b, and c are consecutive odd positive integers and a
[#permalink]
Show Tags
13 Jun 2013, 23:49
I cannot be true in all cases (e.g. 91,93,95 are consecutive odd positive integers but none is a prime). For II, the case for 1,3,5 does not hold (i.e. for this case, ab<c, whereas ab>c for all other cases) III must be true since a+b+c= 3b => b = (1/2)*(a+c), which must be true since b, being a consecutive odd integer between a and c, must always be the average of a and c. A it is.
_________________
GyanOne [www.gyanone.com] Premium MBA and MiM Admissions Consulting
Awesome Work  Honest Advise  Outstanding Results Reach Out, Lets chat!Email: info at gyanone dot com  +91 98998 31738  Skype: gyanone.services



Manager
Joined: 14 Jan 2013
Posts: 128
Concentration: Strategy, Technology
GMAT Date: 08012013
GPA: 3.7
WE: Consulting (Consulting)

Re: If a, b, and c are consecutive odd positive integers and a
[#permalink]
Show Tags
08 Apr 2014, 15:52
Do we have to remember such things or is there any way to know that after 90 , there are number not prime.
I wrote till 50 and realized that either of the number was prime and selected "1 " as option.



Manager
Joined: 04 Jan 2014
Posts: 94

Re: If a, b, and c are consecutive odd positive integers and a
[#permalink]
Show Tags
18 Apr 2014, 01:56
But 1 is not a prime number. Isn't it?



Math Expert
Joined: 02 Sep 2009
Posts: 59628

Re: If a, b, and c are consecutive odd positive integers and a
[#permalink]
Show Tags
18 Apr 2014, 02:35
pretzel wrote: But 1 is not a prime number. Isn't it? Yes, 1 is not a prime number. But what this has to do with the question?
_________________



Manager
Joined: 04 Jan 2014
Posts: 94

Re: If a, b, and c are consecutive odd positive integers and a
[#permalink]
Show Tags
20 Apr 2014, 17:47
Oh I got it. I used 1, 3, 5 as a test for I and II. That's an error on my part.



Manager
Joined: 30 Oct 2012
Posts: 59
Location: India
WE: Marketing (Manufacturing)

Re: If a, b, and c are consecutive odd positive integers and a
[#permalink]
Show Tags
29 Aug 2016, 04:51
emmak wrote: If a, b, and c are consecutive odd positive integers and a<b<c, which of the following must be true?
I. at least one of the three numbers is prime II. ab>c III. a + b + c = 3b
A. III only B. I and II only C. I and III only D. II and III only E. I, II, and III The Case 91,93,95 where there are no prime nos. is tested here. as their is only one prime number between 90 to 99 ie 97. And hence option A
_________________
i am the master of my fate, I am the captain of my soul



Manager
Joined: 17 Aug 2015
Posts: 100

Re: If a, b, and c are consecutive odd positive integers and a
[#permalink]
Show Tags
02 Nov 2016, 07:58
115, 117(13*9), 119(17*7) are not prime numbers



Manager
Joined: 12 Mar 2013
Posts: 231

Re: If a, b, and c are consecutive odd positive integers and a
[#permalink]
Show Tags
07 Feb 2017, 03:46
Is this a good math?!
_________________
We Shall Overcome... One day...



Manager
Joined: 13 Dec 2013
Posts: 142
Location: United States (NY)
Concentration: General Management, International Business
GMAT 1: 710 Q46 V41 GMAT 2: 720 Q48 V40
GPA: 4
WE: Consulting (Consulting)

Re: If a, b, and c are consecutive odd positive integers and a
[#permalink]
Show Tags
29 Apr 2017, 20:39
Seems like a question testing obscure knowledge that won't be asked for on the GMAT.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9866
Location: Pune, India

Re: If a, b, and c are consecutive odd positive integers and a
[#permalink]
Show Tags
31 Oct 2018, 03:33
emmak wrote: If a, b, and c are consecutive odd positive integers and a<b<c, which of the following must be true?
I. at least one of the three numbers is prime II. ab>c III. a + b + c = 3b
A. III only B. I and II only C. I and III only D. II and III only E. I, II, and III Actually this question does not test any obscure knowledge. The moment you read statement I, you should know that this is not necessarily true. You don't have to test any numbers. This is because you should know a very basic thing about prime numbers  you cannot find a pattern to them i.e. they appear randomly. You cannot say when exactly the next prime number will appear. If it were necessary that out of three consecutive odd numbers, one needs to be prime then there is a pattern to finding them. Hence (I) has to be false. II. ab>c This seems would be true often since 5*7 will be greater than 9 etc but what if a is a very small number. So then let's say a = 1. 1*3 < 5 So (II) is not necessarily true. Then looking at the options III must be true and answer must be (A). If you want to confirm, III. a + b + c = 3b (2X  1) + (2X + 1) + (2X + 3) = 6X + 3 = 3*(2X + 1)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



NonHuman User
Joined: 09 Sep 2013
Posts: 13739

Re: If a, b, and c are consecutive odd positive integers and a
[#permalink]
Show Tags
26 Nov 2019, 06:06
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.
_________________




Re: If a, b, and c are consecutive odd positive integers and a
[#permalink]
26 Nov 2019, 06:06






