samrat chatterjee wrote:Someone sort this out please!!!!!!!!

Ques:
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.

The answer is indeed 2 but there are a few doubts

1. Choice 2 does not say that the prime no. has to be in the first thirty only.
2. It says at least on prime is there therefore it can be more than one also.. say the nos after the 31st are all primes then it is not a gamma sequence since there are infinite primes.....

so the answer should be 5(none)

samrat chatterjee wrote:The answer is indeed 2 but there are a few doubts

1. Choice 2 does not say that the prime no. has to be in the first thirty only.
2. It says at least on prime is there therefore it can be more than one also.. say the nos after the 31st are all primes then it is not a gamma sequence since there are infinite primes.....

so the answer should be 5(none)

1. Choice 2 does not say that the prime no. has to be in the first thirty only. : but prime number is always odd except even number 2. So we can have maximum of 30 prime numbers. So the limited prime number condition is true.
2. After 30th number, numbers in series are even so they can not be prime

Hope this clears your doubt.