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# An infinite sequence of positive integers is called a coprime sequence

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General Discussion
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alchemist009 wrote:
An infinite 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 infinite
sequence of distinct positive integers, is S a coprime sequence?
(1) An infinite number of integers in S are prime.
(2) Each term in S has exactly two factors.

does the statement 1 mean that all numbers in sequence S are prime???

we have to determine if all the integers in series are prime or not

stm 1: it says number of integers is prime so the series can contain prime numbers or not hence : NOT SUFFICIENT

Stm 2: Each number is a prime number : Hence SUFFICIENT
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Re: An infinite sequence of positive integers is called a coprime sequence [#permalink]
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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 infinite sequence of positive integers is called a coprime sequence [#permalink]
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 infinite sequence of positive integers is called a coprime sequence [#permalink]
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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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Re: An infinite sequence of positive integers is called a coprime sequence [#permalink]
Thanks Karishma....You have discovered my other problem....I tend to read super fast and miss things in the process....my biggest weakness...
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Re: An infinite sequence of positive integers is called a coprime sequence [#permalink]
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.
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Re: An infinite sequence of positive integers is called a coprime sequence [#permalink]
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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Re: An infinite sequence of positive integers is called a coprime sequence [#permalink]
A) An infinite number of integers in S are prime.
^ would mean; what about the other integers? there maybe infinite PRIME integers in S but what about non prime?So NS
B)Each term in S has exactly two factors.
Only a prime has ITSELF and one as their factors.

B is Sufficient
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Re: An infinite sequence of positive integers is called a coprime sequence [#permalink]
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Re: An infinite sequence of positive integers is called a coprime sequence [#permalink]
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