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Gamma sequence

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hey_thr67 Really wants to Beat The GMAT!
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Gamma sequence Tue Jun 19, 2012 2:07 am
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A “Gamma Sequence” is defined as an infinite sequence of positive integers where no integer appears more than once and there is a finite number of prime numbers in that sequence. The sequence H is an infinite sequence of positive integers, where no integer appears more than once. Is H a gamma sequence?

(1)There are infinitely many multiples of 4 in H.
(2)Only the first thirty integers in the sequence H are ODD, and there is at-least one prime integer in sequence H.

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Tue Jun 19, 2012 7:20 am
hey_thr67 wrote:
A “Gamma Sequence” is defined as an infinite sequence of positive integers where no integer appears more than once and there is a finite number of prime numbers in that sequence. The sequence H is an infinite sequence of positive integers, where no integer appears more than once. Is H a gamma sequence?

(1)There are infinitely many multiples of 4 in H.
(2)Only the first thirty integers in the sequence H are ODD, and there is at-least one prime integer in sequence H.
Note that for a sequence to "Gamma Sequence", it needs to satisfy the following three properties.
1. It must be an infinite sequence of positive integers
2. There should not be any integer more than once
3. The number of prime numbers in that sequence must be finite

Now from the question stem, we know that sequence H already satisfies the first two properties. To determine whether H is a "Gamma Sequence" or not, we need to know whether H satisfies the third property or not.

Statement 1: We don't know whether there is any prime number at all in H.

Not Sufficient

Statement 2: The number of odd integers in H is finite and there is at-least one prime integer in sequence H.
As we know that all the prime numbers are odd except 2, we can conclude that H has a finite number of prime numbers.

Sufficient

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