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# An infinite sequence of positive integers is called a

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An infinite sequence of positive integers is called a [#permalink]  06 Jun 2012, 19:33
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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 infinite 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???
[Reveal] Spoiler: OA

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Re: coprime [#permalink]  06 Jun 2012, 20:22
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???

IMO answer is "B"
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: coprime [#permalink]  06 Jun 2012, 20:30
Looks like B to me.

1)

Infinite number of integers in S are prime. This doesn't exclude the possibility that there are also integers in S that are not prime.

BCE

2)

Each term in S has exactly two factors. As we know, a term that has two factors has 1 as a factor and itself, which makes that term prime. This is sufficient.

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Re: coprime [#permalink]  06 Jun 2012, 21:08
yes guys OA is B. now its clear to me. i thought the answer was D. but its wrong. i thought that all the numbers were prime in the sequence of S. thanks guys
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Re: coprime   [#permalink] 06 Jun 2012, 21:08
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