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

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13 Feb 2012, 16:14

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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.

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.

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

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08 Feb 2014, 03:38

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, 17:53

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.

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

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09 Jun 2016, 11:18

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

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09 Jun 2016, 15:12

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.

Answer: B.

Great analysis.

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

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