GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Oct 2019, 15:42

### 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

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

# If a, b, and c are consecutive odd positive integers and a

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
4
25
00:00

Difficulty:

95% (hard)

Question Stats:

34% (01:38) correct 66% (01:53) wrong based on 605 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

_________________
Kudos will encourage many others, like me.
Good Questions also deserve few KUDOS.

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: 590
Re: If a, b, and c are consecutive odd positive integers and a  [#permalink]

### Show Tags

14 Jun 2013, 03:04
11
4
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 90-100 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.
_________________
##### General Discussion
SVP
Joined: 24 Jul 2011
Posts: 1882
GMAT 1: 780 Q51 V48
GRE 1: Q800 V740
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.
_________________

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: 130
Concentration: Strategy, Technology
GMAT Date: 08-01-2013
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
1
But 1 is not a prime number. Isn't it?
Math Expert
Joined: 02 Sep 2009
Posts: 58434
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: 58
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
GMAT 1: 650 Q49 V29
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: 233
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: 144
Location: United States (NY)
Schools: Cambridge"19 (A)
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: 9704
Location: Pune, India
Re: If a, b, and c are consecutive odd positive integers and a  [#permalink]

### Show Tags

31 Oct 2018, 03:33
1
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

Re: If a, b, and c are consecutive odd positive integers and a   [#permalink] 31 Oct 2018, 03:33
Display posts from previous: Sort by