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.
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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

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.

Thanks Karishma....You have discovered my other problem....I tend to read super fast and miss things in the process....my biggest weakness...

Great analysis.

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

Thanks

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