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

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Manager
Joined: 09 Feb 2013
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If a, b, and c are consecutive odd positive integers and a  [#permalink]

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Updated on: 14 Jun 2013, 00:41
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95% (hard)

Question Stats:

32% (01:40) correct 68% (01:55) wrong based on 334 sessions

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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

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

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14 Jun 2013, 03:04
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6
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.
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Re: If a, b, and c are consecutive odd positive integers and a  [#permalink]

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

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

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

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

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

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

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

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07 Feb 2017, 03:46
Is this a good math?!
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Re: If a, b, and c are consecutive odd positive integers and a  [#permalink]

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

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

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