Data Sufficiency

Set T is an infinite sequence of positive integers. A "superset" is a sequence in which there is a finite number of multiples of three. Is T a superset?

(1) The first six integers in T are multiples of three.

(2) An infinite number of integers in T are multiples of four.

How do I approach such problems?

The only info we get from the question stem is that Set T is an infinite supersequence; we don't know whether it is arithmetic or geometric sequence (or something else). We are asked whether there are a finite number of multiples of 3.

(1) The first six integers in T are multiples of three.

The first six are integers are multiples of 3, so from (1), we know there are some multiples of 3 in the set. But we don't know whether or not multiples of 3 continuously recur in Set T. Insufficient.

(2) An infinite number of integers in T are multiples of four.

This statement tells us that there are an infinite number of multiples of four. Some multiples of four are multiples of three; namely, every third multiple of 4 is also a multiple of 3 (ie, 4, 8, 12, 16, 20, 24...). However, knowing that Set T contains an infinite number of multiples of 4 does not tell us EVERY multiple of 4 is in the set. (We can't just assume that the multiples of 4 are consecutive). Thus, we don't know whether every third (positive) multiple of 4 is included in the set. Insufficient.

(1) + (2)
Combined, you still don't know whether every third multiple of 4 is included in the set.

The statements are insufficient even when combined.

Choose E.

Thanks Testluv for the great explanation as always .

OA is E.

Regards.
Shobha