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Set T is an infinite sequence of positive integers. A

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Set T is an infinite sequence of positive integers. A [#permalink] New post 07 Jan 2005, 15:41
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

38% (02:23) correct 63% (00:57) wrong based on 32 sessions
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.

[Reveal] Spoiler:
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:

Quote:
Yes. Statement (1) is not sufficient, because we don't know if there are other multiples of 3 besides the first six. Eliminate A and D. Statement (2) is not sufficient, because it says nothing about multiples of 3. Eliminate B. The two statements together are not sufficient , because they still give no information about any other multiple of 3. Eliminate C, and the answer is E.


thanks,

- kevin
[Reveal] Spoiler: OA
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 [#permalink] New post 07 Jan 2005, 17:41
E is the right answer.

You can find my explanation here
http://www.gmatclub.com/phpbb/viewtopic.php?t=11816&highlight=superset
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 [#permalink] New post 08 Jan 2005, 11:31
Quote:
A "superset" is a sequence in which there is a finite number of multiples of three.


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: http://www.gmatclub.com/phpbb/viewtopic ... t=superset
Quote:
s[1]: The first 6 integers are 3. But since we know that T is an infinite sequence of positive integers, what about the rest of the integers they can either be multiples of 3 or not. So, insufficient.


Why is this insufficient? Because the other numbers in the infinite set may not be multiples of three?

Confused and bitter about standardized tests,

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 [#permalink] New post 08 Jan 2005, 15:32
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[1]: The first six integers in T are multiples of three
Let's look at two examples for T.
a) T = [6,9,12,15,24,27,31,40,49,...]
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 = [6,9,12,15,18,21,24,27,30,33,...infinity]
In this you can see that set T is a infinite set of multiples of 3. This set satisfies the S[1] 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[1] you cannot state conclusively that T is a Superset or T is not a Superset. Hence it is Insufficient.

HTH.
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Set T is an infinite sequence of positive integers. A [#permalink] New post 19 Mar 2005, 09:18
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.
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Re: DS:sets [#permalink] New post 19 Mar 2005, 10:27
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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PrincetonR_DS_sets [#permalink] New post 23 Sep 2007, 11:16
DS
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 [#permalink] New post 24 Sep 2007, 01:15
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] New post 24 Sep 2007, 07:57
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.
  [#permalink] 24 Sep 2007, 07:57
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