PlanetZ forums - scopeusers.com

hey, I'm preparing for the GMAT and found a strange math data sufficiency problem:

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.

a. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d. EACH statement ALONE is sufficient.
e. Statements (1) and (2) TOGETHER are NOT SUFFICIENT

The correct answer is supposed to be "e".. But I think "b" is correct.
A superset needs to have a FINITE number of multiples of 3.
With statement 2, we know that T has an INFINITE number of multiples of four.
Multiples of four includes common multiples of 3, like 12 and all multiples of 12.
Since T contains an INFINITE number of multiples of four, then T also contains an infinite number of common multiples of 3.
Therefore, I concluded that 2 proves that the number of multiples of 3 in T is definitely not FINITE, and so the answer is NO.

This logic seems pretty sound to me.. are there any math specialists who can explain to me why "e" is more correct? In the answer explanation, it merely says "because statement 2 does not mention anything about multiples of 3".

Hi Ken,
the way I see the problem is that since a superset is a FINITE sequence of multiples of three, then T cannot be a superset because it's an INFINITE sequence of integers, so i'd rather say answer "b", because with the second statement alone, I can conclude that T is not a superset (infinite sequence), whereas with the first statement alone, I could make the wrong assumption, because I only have information about the first six integers, but not about the rest of the sequence..

Im not sure why you have a problem with the answer 'E'?!?!

Statement 1 : You only have information about the first 6 entries in the sequence and you can therefore not conclude anything.
Statement 2 : You only have information related to multiplies of 4 - nothing about multiplies of 3. It's correct there are common factors between 3 and 4, but you don't have that information available to you with statement 2 - they could have excluded every third multiply of 4 (12, 24, 36 etc) except 120 - you don't know. The statement 2 sequence could be : 4 8 16 20 28 32 etc. as you can see 12, 24, 36 etc are missing - or it could be : 4 8 12 20 28 32 etc (notice 12). You simply don't have enough information with those 2 statements.

The only possible answer is 'E' or am I missing something here?

Warp69 wrote:Im not sure why you have a problem with the answer 'E'?!?!

Statement 1 : You only have information about the first 6 entries in the sequence and you can therefore not conclude anything.
Statement 2 : You only have information related to multiplies of 4 - nothing about multiplies of 3. It's correct there are common factors between 3 and 4, but you don't have that information available to you with statement 2 - they could have excluded every third multiply of 4 (12, 24, 36 etc) except 120 - you don't know. The statement 2 sequence could be : 4 8 16 20 28 32 etc. as you can see 12, 24, 36 etc are missing - or it could be : 4 8 12 20 28 32 etc (notice 12). You simply don't have enough information with those 2 statements.

The only possible answer is 'E' or am I missing something here?

Thinking it twice, you are right..
I was interpretating a sequence as having increasing integers, but it's not necessarily true.. (thinking of a "sequence" in database terms )

A sequence could be 3-6-9-12-12-12-(infinite 12's). 12 is a multiple of 3 and a multiple of 4. The first six integers are multiples of 3 and there is an infinite number of multiples of 4; and also there is an infinite number of multiples of 3, meaning T is not a superset.

Or the sequence could be 3-6-9-12-15-18-8-8-8-(infinite number of 8's), where there is a finite number of multiples of 3 and an infinite number of multiples of 4, meaning T is a superset.

so, Warp is right the only possible answer is e.

If ever I take the GMAT, I'll try to have PZ somewhere near

aha! thanks for the clarification. You're right, it does not state that ALL multiples of 4 are included. Wow, how am I supposed to see these things in less that 2 minutes... arggghh.

lol.. how else can you use planetz? just works for anything! song writing woes, mid life crisis, and gmat math problems..