Set T is an infinite sequence of positive integers. A

Question

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.

Isn't the right answer A?  If the first six integers in T are multiples of three, doesn't that make T a "superset?"

According to the  PrincetonReview , where I swiped this question, the answer is E. Their reasoning:

thanks,

- kevin

stardustsparklin · Answer

If we have established that the first six integers of set T are multiples of three, then does it matter whether the other positive integers are? Are not the first six integers a finite sequence of multiples of three? For example, if we have a set of numbers: 6, 7, 8 & 9. This set of positive integers contains multiples of three. Does that not make this set a "superset?" Or do all the numbers have to be multiples of three? Taken from: https://www.gmatclub.com/phpbb/viewtopic ... t=superset Why is this insufficient? Because the other numbers in the infinite set may not be multiples of three? Confused and bitter about standardized tests, - kevin

gayathri · Answer

One thing to remember in DS questions in GMAT is that, you pick a choice if it gives you  one and only one solution  if there is two or more possibilities then you dont pick the choice.

A simple illustration:
What is the value of x?
1) x=2
2) x^2=4

Here the answer is A because in statement 2, x can either be +2 or -2.

That said, in this problem it says that T is a set with infinite infinite +ve integers. T is a superset if it has a finite number of multiples of 3.

S : The first six integers in T are multiples of three
Let's look at two examples for T.
a) T =  
This set above has no pattern but has infinite positive integers. Let's assume however that after the 1st 6 numbers which are multiples of 3 there are no other multiples of 3 in set T. i.e, T has a finite number(=6) of multiples of 3. So, T is a superset.

b) T =  
In this you can see that set T is a infinite set of multiples of 3. This set satisfies the S  in that the first 6 integers in T are multiples of 3. But this set has an infinite number of multiples of 3, so T cannot be a Superset.

Based on the two examples of T that satisfy S  you cannot state conclusively that T is a Superset or T is not a Superset. Hence it is Insufficient. 

HTH.

banerjeea_98 · Answer

"E"

Superset = finite number of multiples of 3

state 1: T={3,6,9,12,15,18......}...can go on with infinite number of multiples of 3 or can be just first 6 numbers....so ans can be NO or YES...insuff

state 2: T={4,8,12,16.....}....may have finite multiples of 3 also or may not...insuff

combine......insuff.....again we can have infinite number of multiples of 3 or may be not

ywilfred · Answer

St1:
We have no knowledge if there are other multiples of three after the first 6 integers. So T could or could not be a superset. Insufficient.

St2:
Useless information. We need to know if there are a finite number of multiples of 3 in order to determine if T is a superset. Insufficient.

Using st1 and st2:
No further useful information. Insufficient.

Ans E

IrinaOK · Answer

The OA is E, and the explanation is clear. Ywilfred, thank you once again.

But I still can not understand the question text. It says set T is infinite, and 'superset' is finite. Then how can T be ever superset....

Gmat probably doesn`t ask ambigous questions like this one.. it is from PrincetonReview.

anulfc · Answer

Bunuel 
Doesn't the word sequence mean that the order is related in some manner?
So, in statement 1, if the first 6 number are multiples of 3, then we can assume that the rest are related as well in some way(can be AP/GP/HP) and therefore statement 1 is sufficient?

Harley1980 · Answer

Hello AnubhavRao According to this article: math-sequences-progressions-101891.html "sequence is an ordered list of objects. It can be finite or infinite. The elements may repeat themselves more than once in the sequence, and their ordering is important unlike a set" So in task should be specified what kind of sequence we have: arithmetic, geometric, multiple of some number and so on. Sometimes sequences can be described by some rule and you need to calculate each element individually to find the pattern. In our case we have only information that this sequence consists from positivie integers so it can be or or (order is important but doesn't mean that it should be increasing order) So, first six element can't determine all sequence.

GMATinsight · Answer

Sequesnce : In mathematics, a sequence is an ordered collection of objects

Statement 1: The first six integers in T are multiples of three

Case 1:  But T may have first 6 numbers multiple of 3 and then next six multiple of 5 and then next six multiple of 7 etc.

i.e. There is a possibility that there are only 6 multiples of 3

Case 2:  But T may have first 6 numbers multiple of 3 and then next six multiple of 6 and then next six multiple of 9 etc.

i.e. There is a possibility that there are Infinite multiples of 3

Hence,   NOT SUFFICIENT

I hope it clears your doubt!!!

Bunuel · Answer

A sequence, by definition, is an  ordered  list of terms. While a set, is a collection of elements without any order.

Note, that it's not necessary for the terms of a sequence to form any kind of progression, or to be related by some formula. For example, {1, 2.8,  \sqrt{3} ,  \pi , -17.4} is a sequence.

As for the question: the answer is straight E. Consider the following two sequences:
{12, 12, 12, 12, 12, 12, 12, 12, 12, ...}: the sequence has infinite number of multiples of 3. 
{12, 12, 12, 12, 12, 12, 4, 4, 4, 4, ...}: the sequence has finite number of multiples of 3.

Hope it helps.

GMATinsight · Answer

Statement 1 : The first six integers in T are multiples of three. 
After the First six number in T, rest of the numbers may or may not have finite multiples of 3. Hence,
NOT SUFFICIENT

Statement 2 : An infinite number of integers in T are multiples of four.  
Multiples of 4 has nothing to do with Number of Multiples of 3 hence, nothing can be concluded about set T being a Superset
NOT SUFFICIENT

Combining the two statements 
After the First six number in T, rest of the numbers may or may not have finite multiples of 3 and Multiples of 4 has nothing to do with Number of Multiples of 3 hence, nothing can be concluded about set T being a Superset
NOT SUFFICIENT

Answer: Option E

itwarriorkarve · Answer

How come A is not the answer for this? See the question mentions that a "superset" will contain finite number of multiples of three. The first condition proves that the set indeed does contain a finite number of multiples of T. Then irrespective of what else it contains, it should be a superset according to the question right?

OptimusPrepJanielle · Answer

Hi itwarriorkarve,

The statement 1 simply says that the first 6 integers are multiple of 3, it does not tell us about
1. Are there any more integers in the set
2. If yes, are they multiples of 3 or not.

From the definition of the "superset", it should be a finite set. But we cannot tell this by statement 1.
Does this help?

Gmat860sanskar · Answer

We need to know if T has only a finite number of multiples of 3.

(1) First six are multiples of 3 → not sufficient (could be only six, or infinitely many).

(2) Infinitely many multiples of 4 → not sufficient (they may or may not overlap with multiples of 3).

(1) + (2) Together still not sufficient (could be finite multiples of 3 or infinite).

Final Answer: (E) Not sufficient.

Advait01 · Answer

Statement 1:
We have no knowledge if there are other multiples of three after the first 6 integers. So T could or could not be a superset. Insufficient.

Statement 2:
Useless information. We need to know if there are a finite number of multiples of 3 in order to determine if T is a superset. Insufficient.

Using 1 and 2:
No further useful information. Insufficient.

Ans E

Set T is an infinite sequence of positive integers. A

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GMAT Data Sufficiency (DS) Questions

Set T is an infinite sequence of positive integers. A

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