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samrat chatterjee
- Junior | Next Rank: 30 Posts
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- Joined: Wed Oct 14, 2009 11:04 am
Ques:samrat chatterjee wrote:Someone sort this out please!!!!!!!!
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.
Choices
(1) 1
(2) 2
(3) Together 1&2
(4) Either 1 or 2
(5) Neither 1 nor 2
Answer is option 2.
Let us start with option 1. As there are infinite many multiples of 4 in sequence H, we need to determine whether sequence H is having finite number of prime integers or not.
Along with infinite multiples of 4, there are other terms for which there is no information available. So we can not determine the number of prime numbers in this sequence. So this option is out.
Now move on to option 2.
it says first 30 are odd number with at least one prime. So other number in this sequence will have only even integers. 2 may be one of them.
But we know for sure that it can have maximum of 30 + 1 =31 prime numbers. So this sequence has finite number of primes and thus this option determines that H is a Gamma Sequence.
