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# An infinite sequence of positive integers is called a

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An infinite sequence of positive integers is called a [#permalink]

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13 Feb 2012, 17:14
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46% (01:49) correct 54% (00:47) wrong based on 381 sessions

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An infinite sequence of positive integers is called a coprime sequence if no term in the sequence shares a common divisor (except 1) with any other term in the sequence. If S is an infinite sequence of distinct positive integers, is S a coprime sequence?

(1) An infinite number of integers in S are prime.
(2) Each term in S has exactly two factors.

[Reveal] Spoiler:
Struggling to understand the answer as B.

Considering statement 1

If integers in S are prime they have exactly two factors and therefore this statement is same as B and therefore should be sufficient.

Where I am not getting this right guys?
[Reveal] Spoiler: OA

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Re: An infinite sequence of positive integers is called a [#permalink]

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13 Feb 2012, 19:07
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An infinite sequence of positive integers is called a coprime sequence if no term in the sequence shares a common divisor (except 1) with any other term in the sequence. If S is an infinite sequence of distinct positive integers, is S a coprime sequence?

Notice that S is an infinite sequence of distinct positive integers.

(1) An infinite number of integers in S are prime --> obviously these primes will be coprime to each other. But we don't know whether the sequence contains some numbers other than primes, and if it does then the sequence won't be coprime (for example the sequence can contain 4 and 6 in addition to these primes). Not Sufficient.

(2) Each term in S has exactly two factors --> each term in S is a prime, so S contains only distinct primes, which will be coprime. Sufficient.

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Re: An infinite sequence of positive integers is called a [#permalink]

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05 Sep 2013, 06:39
Bumping for review and further discussion.
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Re: An infinite sequence of positive integers is called a [#permalink]

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08 Feb 2014, 04:38
Nice, nice nice. Fell into trap and chose wrong answer. Statement 1 seems like each number in s is prime but it is not! Statement 2 makes it look like the numbers are not prime but indeed they are!
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Re: An infinite sequence of positive integers is called a [#permalink]

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16 Apr 2015, 18:53
Bunuel: if two terms are 2 in the sequence S....(2,2,3,4,5..............) here the two terms have 2 as a common divisor. The question says that a coprime sequence will not have any other factor common to any other number except 1.
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Re: An infinite sequence of positive integers is called a [#permalink]

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17 Apr 2015, 01:49
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sayansarkar wrote:
Bunuel: if two terms are 2 in the sequence S....(2,2,3,4,5..............) here the two terms have 2 as a common divisor. The question says that a coprime sequence will not have any other factor common to any other number except 1.

You are given that S has distinct integers. So two terms cannot be 2 each.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 28 Jul 2013 Posts: 86 Location: India Concentration: Marketing, Strategy GPA: 3.62 WE: Engineering (Manufacturing) Re: An infi nite sequence of positive integers is called a [#permalink] ### Show Tags 17 Apr 2015, 01:57 Thanks Karishma....You have discovered my other problem....I tend to read super fast and miss things in the process....my biggest weakness... Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7440 Location: Pune, India Re: An infi nite sequence of positive integers is called a [#permalink] ### Show Tags 17 Apr 2015, 02:03 sayansarkar wrote: Thanks Karishma....You have discovered my other problem....I tend to read super fast and miss things in the process....my biggest weakness... Reading super fast is great for RC. For all others, it is not advisable. You have enough time so slow down a bit. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: An infinite sequence of positive integers is called a [#permalink]

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09 Jun 2016, 12:18
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).

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An infinite sequence of positive integers is called a [#permalink]

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09 Jun 2016, 16:12
Bunuel wrote:
An infinite sequence of positive integers is called a coprime sequence if no term in the sequence shares a common divisor (except 1) with any other term in the sequence. If S is an infinite sequence of distinct positive integers, is S a coprime sequence?

Notice that S is an infinite sequence of distinct positive integers.

(1) An infinite number of integers in S are prime --> obviously these primes will be coprime to each other. But we don't know whether the sequence contains some numbers other than primes, and if it does then the sequence won't be coprime (for example the sequence can contain 4 and 6 in addition to these primes). Not Sufficient.

(2) Each term in S has exactly two factors --> each term in S is a prime, so S contains only distinct primes, which will be coprime. Sufficient.

Great analysis.

Can you just provide similar tricky(referred to Statement 1 type trap) question to practice?

Thanks
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An infinite sequence of positive integers is called a   [#permalink] 09 Jun 2016, 16:12
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