What is the probability of selecting a clean number from a set of integers containing all multiples of 3 between 1 and 99, inclusive?
1. A clean number is an integer divisible by only 2 factors, one of which is greater than 2.
2. A clean number must be odd.
Source : Veritas
I am not sure why the OA is
. Knowing that there are a finite number of odd integers between 1 and 99, B should be sufficient...
I don't like this question. The prompt is clear --- at least the set from which we are choosing is perfectly clear. It's a least a clever idea in theory, introducing a brand new term, "clean numbers", in a DS questions, but I think the requirement of a definition and the structure of the DS conflict in ways the question's authors didn't anticipate.
A number with only two factors --- that's a prime number, numbers with a factor of only 1 and the number. By specifying one factor has to be greater than 2, we are specifying a prime number greater than 2. My question: is this sufficient for the definition of a clean number? is this necessary for the definition of a clean number?
Yes, I recognize the irony, Voodoo
, my friend. Having recently persuaded you of the superfluity of these two words in CR, here I am using them in DS. To be fair, I am only using them in what I consider a poorly written DS --- a well-written DS wouldn't raise these questions.
Statement #1 says, essentially, clean number is a prime number greater than 3.
Is this a necessary statement --- only prime numbers greater than three are in the set of clean numbers?
Or, we equating clean numbers with the set of all prime numbers greater than 3? In other words, are we justified in assuming that statement #1 is a full definition of a clean number? That's somewhat unclear.
The second statement is even worse: "A clean number must be odd."
Is that saying ---- (necessary) ---- if I number is clean, it is odd?
Or, is it saying -----(sufficient) ---- if I number is odd, then its clean?
I gather, from your selection of (B) as the answer, that you interpreted the second statement as sufficient. The problem with that is: it's always the case that the two statements of a DS question have to be mathematically consistent. Since statement #1 restricts us to primes, it can't be every odd number --- that would be inconsistent. We have to take the "necessary" interpretation of statement #2.
Then, given the OA, it appears that we decide on either the "necessary" or "sufficient" interpretation of statement #1, then it would be sufficient to answer the question,and the answer would be (A). BUT, if that decision itself is something left to the reader, and no further information is given, then the answer would be (E).
My guess is that the authors of this question were not even thinking about "necessary" and "sufficient" --- they were way too naive in trying to write a "definition of a new term" question in DS form, and did not consider all the ramifications. Voodoo
, I assure you, on no legitimately constructed GMAT Quant question will you ever have even to think for a moment about the ideas of "necessary" and "sufficient" --- we only have to have recourse to them to discuss the inadequacies of questions such as this.
Does all this make sense?
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