Manhatten - data sufficiency

[nickhar130]

If Z is an infinite subset of real numbers, is there a number in Z that is greater than every other number in Z?

1) Every number in Z is divisible by 5

2) Every number in Z is a negative multiple of a prime number.

[Geva@EconomistGMAT]

I think the question is problematic - either the question is transcribed wrongly, or Manhattan didn't think this through.

The problem is the phrasing of the question: there's no way that a statement will be insufficient here.
The question is asking "is there a number that is greater than every other number in an infinite set?". The possible answers here are "yes, there is such a number" or "no, there's no such number". In DS yes/no questions, a definite "no" is still considered sufficient - the answer to the question stem is "no", but it's still a definite answer. If a statement limits the answer to a "no", then that statement is sufficient - it allows only a single answer.
The only way a statement will be insufficient is if it allows both a "yes" and a "no" answer. For example, if the question asks "is x positive?", and stat. (1) says x^2=4, the x can be either 2 or -2, resulting in both a "yes" and a "no" answer, or insufficient. If stat. (2) then said "x<-1", then the answer to the question "is x positive" will be a definite "no" - but that still means that stat. (2) will be sufficient.

the problem with a phrasing of "is there a number" is that such a number either exists or doesn't exist - you can't create a statement that will allow the number to both exist and not exist. The answer to this question will be D, always - either the statement shows that there is such a number ("yes"), or the statement shows that there is no such number ("no"). Since a DS question should not be answerable without even looking at the statements, I believe the question itself is wrong.
for example, here:
(1) if z is an infinite number of terms divisible by 5, then z has no upper limit - there will always be multiple of 5 greater than the previous one in an infinite set. Answer is "no", but still sufficient.
(2) If every number in z is negative, then there is an upper limit - z can have infinite negative members, but no member of z will be greater than zero, since they're all negative. We may no know what is the value of the upper limit of z, but we know that there is one. answer is "yes', which is sufficient.

Thus, the answer for the question as is seems to be D. But I, at least, can't think of a phrasing to a statement that will not be sufficient.

[selango]

If Z is an infinite subset of real numbers, is there a number in Z that is greater than every other number in Z?

1) Every number in Z is divisible by 5

2) Every number in Z is a negative multiple of a prime number.

Are you sure this question is from the Manhattan CATs?

[nickhar130]

It is a incorrectly worded problem. Thank you for addressing that.

[Ian Stewart]

I think the question is problematic - either the question is transcribed wrongly, or Manhattan didn't think this through.

[...]

the problem with a phrasing of "is there a number" is that such a number either exists or doesn't exist - you can't create a statement that will allow the number to both exist and not exist. The answer to this question will be D, always - either the statement shows that there is such a number ("yes"), or the statement shows that there is no such number ("no"). Since a DS question should not be answerable without even looking at the statements, I believe the question itself is wrong.

There are certainly many problems with the wording of the question (if a question is going to talk about multiples, it needs to make clear the quantities concerned are integers, the GMAT never tests multiples or divisibility using negative numbers, and the question should probably make more clear that repetition of elements is not allowed), but the question doesn't suffer from the logical problem you describe. I can design a question with a similar stem to illustrate:

Z is an infinite sequence of distinct positive real numbers. Is there a number in sequence Z that is greater than every other number in Z?

1) No number in sequence Z is greater than 1.

2) 1 is in sequence Z.

Statement 1 here is not sufficient. Our sequence might be defined, for all positive integers n, by:

a_n = 1/n

in which case the sequence would be 1, 1/2, 1/3, 1/4, 1/5... In this sequence there is indeed a number, 1, which is greater than every other number. On the other hand, our sequence might be defined, for all positive integers n, by:

a_n = n/(n+1)

in which case the sequence would be 1/2, 2/3, 3/4, 4/5, 5/6, ... In this sequence, every number is greater than the number before it, and no number is ever greater than 1, but there is no number in this sequence which is greater than every other number (and that's what the question asks: is there a number which is actually in the sequence which is larger than any other number in the sequence); it just keeps getting closer and closer to 1 the further you go.

Statement 2 alone is clearly insufficient (our sequence could again be the first example I gave above, or it could be 1, 2, 3, 4, 5, ... in which case there is no number larger than every other). Combined, certainly 1 needs to be the largest element in the sequence, and the answer is C.