Data Sufficiency

gmat_basher wrote: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.


The official answer as "E", but "B" alone should be sufficient to answer this "Yes/No" question..

Statement says "Superset" should have "finite numbers" and since (2) state the series is "infinite" , the answer should be "No"

A ''superset" is defined as having finite multiples of three. This also means that a ''superset" will have finite number of multiples of 3, but may have infinite number of other type of numbers.

(2) says that there are infinite number of multiples of 4 in T but does not say whether it has finite number of multiples of 3 or not.
Hence (2) alone is not sufficient.

gmat_basher wrote: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.

Statement 1: The first six integers in T are multiples of three.
There may be more integers in T which are multiples of three and the number of such integers may or may not be finite.

Not Sufficient

Statement 2: An infinite number of integers in T are multiples of four.
This does not tell us anything about the integers which are multiples of three. The number of such integers in T may or may not be finite.

Not Sufficient

1 & 2 Together: Now new information which can allow us to conclude whether the number of integer multiples of three in T are finite or infinite.

Not Sufficient

The correct answer is E.

gmat_basher wrote:The official answer as "E", but "B" alone should be sufficient to answer this "Yes/No" question..

Statement says "Superset" should have "finite numbers" and since (2) state the series is "infinite" , the answer should be "No"

The question stem also says the series is infinite. But that does not allow us to conclude whether the number of integer multiples of three in T are finite or infinite. There may be a infinite series of integers where there is finite number of integer multiples of three.

maths_for_fun wrote:Question 1 to Anurag: Should the terms in a sequence be equally spaced?

No such property is mentioned.
Thus we cannot assume they are equally spaced.

maths_for_fun wrote:Question 2 to Anurag: We know from B that multiples of 4 are infinite. There are certain numbers that are divisible by 3 &4. So, we know it for sure that multiples of 3 are infinite as well.

Where am I going wrong?

Multiples of 4 in the set are infinite. But as it is nowhere mentioned that the integers are equally spaced, it may be possible that there is a finite number of integers which are divisible by 3. For example consider a set {3, 4, 8, 12, ... rest are divisible by 4 but not by 3}. In this set number of multiples of three is 2, but the set contains infinite numbers of multiples of 4.