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Re: DS:sets [#permalink]
vprabhala 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.

I know that this has been discussed earlier. still not very clear..


"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
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[#permalink]
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
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[#permalink]
ywilfred wrote:
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


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.
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Re: Set T is an infinite sequence of positive integers. A [#permalink]
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?
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Set T is an infinite sequence of positive integers. A [#permalink]
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AnubhavRao wrote:
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?


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 [1, 2, 3] or [1, 1, 2, 2, 3, 3] or [3, 2, 1, 0] (order is important but doesn't mean that it should be increasing order)
So, first six element can't determine all sequence.
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Re: Set T is an infinite sequence of positive integers. A [#permalink]
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AnubhavRao wrote:
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?



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 [Limited Multiples of 6]

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 [Infinite Multiples of 6]

Hence, NOT SUFFICIENT

I hope it clears your doubt!!!
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Re: Set T is an infinite sequence of positive integers. A [#permalink]
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AnubhavRao 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.

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?


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.
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Re: Set T is an infinite sequence of positive integers. A "superset" is a [#permalink]
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draditya 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.
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.[/quote]
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
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Re: Set T is an infinite sequence of positive integers. A "superset" is a [#permalink]
draditya 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.



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?
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Re: Set T is an infinite sequence of positive integers. A [#permalink]
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itwarriorkarve wrote:
draditya 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.



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?


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?
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Re: Set T is an infinite sequence of positive integers. A [#permalink]
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Re: Set T is an infinite sequence of positive integers. A [#permalink]
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