Author 
Message 
TAGS:

Hide Tags

Current Student
Joined: 29 Jan 2005
Posts: 5201

What is the probability of selecting a clean number from a [#permalink]
Show Tags
26 Oct 2005, 06:52
1
This post received KUDOS
3
This post was BOOKMARKED
Question Stats:
54% (00:46) correct 46% (01:16) wrong based on 352 sessions
HideShow timer Statistics
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.
Official Answer and Stats are available only to registered users. Register/ Login.



Manager
Joined: 01 Aug 2005
Posts: 68

Re: What is the probability of selecting a clean number from a [#permalink]
Show Tags
26 Oct 2005, 07:46
1
This post received KUDOS
A? Because statement one is pretty much telling us that the number is a prime. You dont need statement 2 because all primes are odd.



Manager
Joined: 14 Apr 2003
Posts: 84

Re: What is the probability of selecting a clean number from a [#permalink]
Show Tags
26 Oct 2005, 15:27
GMATT73 wrote: 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.
D.
Too simple to be true I know kaplan will have a catch for me.



Manager
Joined: 17 Sep 2005
Posts: 72
Location: California

Re: What is the probability of selecting a clean number from a [#permalink]
Show Tags
26 Oct 2005, 16:02
A for me!
set = {3,6,9,12,...96,99}
1) We know only prime #'s have just two factors  1 and the number itself.
We also know from the set that 3 is the only prime in it and of course 3 is > 2
SUFF => AD
2) every other number in the set is odd.
NOT SUFF => A



Manager
Joined: 14 Apr 2003
Posts: 84

Re: What is the probability of selecting a clean number from a [#permalink]
Show Tags
26 Oct 2005, 18:57
mbaqst wrote: A for me!
set = {3,6,9,12,...96,99}
1) We know only prime #'s have just two factors  1 and the number itself. We also know from the set that 3 is the only prime in it and of course 3 is > 2 SUFF => AD
2) every other number in the set is odd. NOT SUFF => A
In case wont be the probability of selecting a clean number be 1/2.



Senior Manager
Joined: 05 Oct 2005
Posts: 485

Re: What is the probability of selecting a clean number from a [#permalink]
Show Tags
26 Oct 2005, 19:02
In case 2 u mean?
If that's what your asking, case
2. A clean number must be odd.
This says it will be odd, but in this case does not fully define a "clean number"
I guess the question is a little vague and confusing



VP
Joined: 06 Jun 2004
Posts: 1049
Location: CA

Re: What is the probability of selecting a clean number from a [#permalink]
Show Tags
26 Oct 2005, 20:04
GMATT73 wrote: 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.
My answer is D.
1. Clean number is defined as a prime number here. Sufficient.
2. Clean number is defined as an odd number here. Sufficient.



Senior Manager
Joined: 05 Oct 2005
Posts: 485

Re: What is the probability of selecting a clean number from a [#permalink]
Show Tags
26 Oct 2005, 20:08
As far as I know, if the answer to a DS question is D, both 1) and 2) must yield the same value...
TeHCM, technically, you are right, but i doubt ETS would ever create such a question...
Do correct me if i'm wrong



Current Student
Joined: 29 Jan 2005
Posts: 5201

Re: What is the probability of selecting a clean number from a [#permalink]
Show Tags
27 Oct 2005, 07:39
OA is A. I am just tooo exhausted to type in the OE after a 14 hr workday. Will post it wordforword ver batem after gaining some sanity over the weekend.



Manager
Joined: 01 Aug 2005
Posts: 68

Re: What is the probability of selecting a clean number from a [#permalink]
Show Tags
27 Oct 2005, 08:19
Quote: 1. Clean number is defined as a prime number here. Sufficient. 2. Clean number is defined as an odd number here. Sufficient.
You are right about statement 1, it defines what a clean number is. Please look carefully at statement 2 though, it doesnt define a clean number as odd, it says a clean number must be odd. That =/= clean numbers are all odd numbers.
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.
Think of it this way:
"A clean number is an integer divisible by 4"
"A clean number must be even"
^^
The latter doesnt mean that all even numbers are clean, and we already know that all of the numbers are even thanks to statement one.



Manager
Joined: 16 Feb 2011
Posts: 195
Schools: ABCD

What is the probability of selecting a clean number from a s [#permalink]
Show Tags
26 Sep 2012, 10:35
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...



Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4680

Re: What is the probability of selecting a clean number from a s [#permalink]
Show Tags
26 Sep 2012, 12:35
voodoochild wrote: 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 wellwritten 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? Mike
_________________
Mike McGarry Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)



Manager
Joined: 16 Feb 2011
Posts: 195
Schools: ABCD

Re: What is the probability of selecting a clean number from a s [#permalink]
Show Tags
27 Sep 2012, 17:57
mikemcgarry wrote: 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.
Mike, Thanks for your help. I think that Veritas guys are testing CR skills in this question. (I have seen some official GMAT Quant questions that actually do that. I don't blame them). However, I am a bit confused. In my opinion, both the statements are necessary conditions. How? (one uses 'must be' and the other one states a fact about any general integer). None of the conditions are sufficient. Secondly, let's assume, for our analysis, that the two conditions are sufficient. Still, a sufficient condition guarantees a specific outcome. It is not "THE sufficient condition." For instance, I could say that a 'troublesome' number is a square of 5, or a 'troublesome' number is any integer greater than 20 but less than 30 that has an integer square root. There could be other definitions or sufficient conditions for 'clean number.' Thus, there could multiple sufficient conditions. I didn't follow your explanation about inconsistency. Can you please clear that for me? Thanks in advance....



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1346

Re: What is the probability of selecting a clean number from a s [#permalink]
Show Tags
28 Sep 2012, 03:23
This question is deeply problematic, logically speaking, and you could never see a real GMAT question that resembles this one. The first reason I find it logically nonsensical is that it is not clear that we need a definition of 'clean number' at all to answer the question. If instead you were asked "What is the probability of selecting a prime number from a set of integers containing all multiples of 3 between 1 and 99, inclusive?" you obviously wouldn't need any additional information to solve. You wouldn't even need to know what a prime number was  you'd just need to know that prime numbers have some kind of definition, and that the question is therefore solvable. The same is true here. When I read this question, I think "well, I don't know what 'clean numbers' are, but as long as someone knows, the question can be answered in theory, so why do I need any statements at all?" After all, DS isn't testing if you can answer the question  it's testing if the question has only one answer. So that's the first problem: the question needs to make clear that 'clean numbers' are not something you could learn about if you read more math books, and are instead something the question has just invented on the spot. That issue is bad enough, but then as Mike pointed out, it further isn't clear whether each statement is giving a sufficient condition or only a necessary one. The wording of Statement 1, which reads "A clean number is an integer divisible by only 2 factors, one of which is greater than 2", would be true if 17 was the only clean number, and would be true if all odd primes were clean numbers. It certainly is not sufficient to define the set of clean numbers, and if the OA is A, then the question writer was very confused on this point. Of course the same issue afflicts Statement 2. So it doesn't make any sense to discuss what the answer to this question is, because the question makes no logical sense in the first place.
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com



Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4680

Re: What is the probability of selecting a clean number from a s [#permalink]
Show Tags
01 Oct 2012, 12:40
voodoochild wrote: Mike, Thanks for your help. In my opinion, both the statements are necessary conditions. How? (one uses 'must be' and the other one states a fact about any general integer). None of the conditions are sufficient. Secondly, let's assume, for our analysis, that the two conditions are sufficient. Still, a sufficient condition guarantees a specific outcome. It is not "THE sufficient condition." For instance, I could say that a 'troublesome' number is a square of 5, or a 'troublesome' number is any integer greater than 20 but less than 30 that has an integer square root. There could be other definitions or sufficient conditions for 'clean number.' Thus, there could multiple sufficient conditions. I didn't follow your explanation about inconsistency. Can you please clear that for me? Thanks in advance.... VoodooFirst of all, I heartily applaud what IanStewart says. This is a poor question, and does not merit attention in and of itself. I am responding only to answer your questions. Statement #1 equates "clean numbers" with the set of odd prime numbers  again, the whole set, or only part of the set? We don't know. Statement #2 the interpretation "if it's a clean number, then it's odd"  that's actually redundant with statement #1: if clean numbers are the set of odd primes, or some subset thereof, then of course they have to be odd. By contrast, the interpretation "if the number is odd, then it's a clean number"  that's the inconsistency of which I spoke, because then "clean numbers" would include 9, 15, 21, 27, 33, 35, etc. all kinds of odd numbers that are not prime. This would contradict statement #1, which shouldn't happen in a DS question. (Although, in a question of this poor quality, I suppose all bets are off.) Does that make sense? Mike
_________________
Mike McGarry Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)



Manager
Joined: 16 Feb 2011
Posts: 195
Schools: ABCD

Re: What is the probability of selecting a clean number from a s [#permalink]
Show Tags
01 Oct 2012, 14:33
Ian and Mike  thanks for your comments. I have deleted this example from my memory. In fact, Veritas has two such examples in their book!



Retired Moderator
Joined: 18 Sep 2014
Posts: 1199
Location: India

Re: What is the probability of selecting a clean number from a [#permalink]
Show Tags
28 Jun 2015, 10:20
GMATT73 wrote: 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. I cant really understand what is the meaning of statement 1 . I request someone to explain in detail.
_________________
The only time you can lose is when you give up. Try hard and you will suceed. Thanks = Kudos. Kudos are appreciated
http://gmatclub.com/forum/rulesforpostinginverbalgmatforum134642.html When you post a question Pls. Provide its source & TAG your questions Avoid posting from unreliable sources.
My posts http://gmatclub.com/forum/beautyofcoordinategeometry213760.html#p1649924 http://gmatclub.com/forum/callingallmarchaprilgmattakerswhowanttocross213154.html http://gmatclub.com/forum/possessivepronouns200496.html http://gmatclub.com/forum/doublenegatives206717.html http://gmatclub.com/forum/thegreatestintegerfunction223595.html#p1721773 https://gmatclub.com/forum/improvereadinghabit233410.html#p1802265



Math Expert
Joined: 02 Sep 2009
Posts: 43904

Re: What is the probability of selecting a clean number from a s [#permalink]
Show Tags
28 Jun 2015, 10:26



Retired Moderator
Joined: 06 Jul 2014
Posts: 1269
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40

What is the probability of selecting a clean number from a s [#permalink]
Show Tags
28 Jun 2015, 10:31
Mechmeera wrote: GMATT73 wrote: 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. I cant really understand what is the meaning of statement 1 . I request someone to explain in detail. Hello Mechmeera"Clean number" is name that use for some numbers with some properties. (I think that name was create by author of task) So our task is to understand what is "clear number". In first statement we see clear description of this notion: A clean number is an integer divisible by only 2 factors, one of which is greater than 2.Which integers have only two factors? This is primes, because they have as factors only themselves and 1: 2, 3, 5, 7, 11 etc. So clean numbers this is prime numbers bigger than 2: 3, 5, 7, 11 etc. Does that makes sense?
_________________
Simple way to always control time during the quant part. How to solve main idea questions without full understanding of RC. 660 (Q48, V33)  unpleasant surprise 740 (Q50, V40, IR3)  antidebrief



NonHuman User
Joined: 09 Sep 2013
Posts: 13750

Re: What is the probability of selecting a clean number from a s [#permalink]
Show Tags
21 Aug 2016, 03:56
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: What is the probability of selecting a clean number from a s
[#permalink]
21 Aug 2016, 03:56



Go to page
1 2
Next
[ 21 posts ]



