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Set T is an infinite sequence of positive integers. A [#permalink]
07 Jan 2005, 15:41

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

47% (02:12) correct
53% (01:09) wrong based on 146 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.

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.

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?

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?

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.

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

Re: Set T is an infinite sequence of positive integers. A [#permalink]
11 Jun 2015, 04:44

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?

Set T is an infinite sequence of positive integers. A [#permalink]
11 Jun 2015, 05:00

1

This post received KUDOS

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?

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. _________________

Re: Set T is an infinite sequence of positive integers. A [#permalink]
11 Jun 2015, 05:02

1

This post received KUDOS

Expert's post

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]

Re: Set T is an infinite sequence of positive integers. A [#permalink]
11 Jun 2015, 05:54

1

This post received KUDOS

Expert's post

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.

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