Data Sufficiency

sachin_yadav wrote:An infinite sequence of positive integers is called an "alpha sequence" if the number of even integers in the sequence is finite. If S is an infinite sequence of positive integers, is S an alpha sequence?

(1) The first ten integers in S are even.
(2) An infinite number of integers in S are odd.

A sequence is just a list of numbers in order. We can create two sequences which satisfy both statements here, one of which will have an infinite number of even values, and one of which will have a finite number of even values. We can just make the first ten values of our sequence all equal to 8, say, just to ensure Statement 1 is true. The remaining values could just be all of the positive integers, in which case we will have an infinite number of even values and an infinite number of odd values:

8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11....

or we can make the remaining values just the odd positive integers only, in which case we will only have ten even values in our sequence:


8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 3, 5, 7, 9, 11, 13, 15, 17, ....

So even with both statements we have no way of knowing if there is an infinite number of even values in the sequence, and the answer is E.