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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:

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.

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 [#permalink]
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.

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