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Refined #s

by smackmartine » Wed Jun 08, 2011 9:01 pm
If a number is drawn at random from the first 1000 positive integers, what is the probability of selecting a refined number?

1) Any refined number must be divisible by 22.
2) A refined number is any even multiple of 11.

OA after some discussion.
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by cans » Wed Jun 08, 2011 9:06 pm
total possible numbers=1000
a)refined number must be divisible by 22
thus number = 22n n is an integer.
n varies from 1 to 45
(22*45=990)
thus prob = 45/1000 = 9/200
b) even multiple of 11. or multiple of 22. Thus same as a)
prob = 9/200
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by krishnasty » Wed Jun 08, 2011 9:10 pm
First 1000 positive number..from 1 to 1000

From A) we need muliples of 22 i.e. 22,44,66,88.....and so on.
get the total numbers / 1000 = ans
SUFFICIENT

From B ) its saying the same thing in different format. even multiples of 11 are 22,44,66..and so on.
SUFFICIENT

hence, IMO D
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by smackmartine » Wed Jun 08, 2011 9:27 pm
Need some more answers and explanations. Experts please comment.

OA shortly
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by Ian Stewart » Wed Jun 08, 2011 10:12 pm
This is not a realistic GMAT question. For one thing, from the stem it appears that you ought to know in advance what a 'refined number' is; the question should make clear in the stem that 'refined numbers' are an invention of the question designer. In any case, the question is really testing Critical Reasoning skills rather than Quant skills - in technical language, it's testing the distinction between necessary and sufficient conditions. If from Statement 1 we know: "Any refined number must be divisible by 22" that does *not* mean "every number which is divisible by 22 is a refined number". To give a more familiar example, if i tell you that every perfect square is non-negative, that doesn't mean that every non-negative number is a perfect square; 2 is not a perfect square, for example.

If Statement 1 is true - that any refined number is divisible by 22 - it might be that there is only one 'refined number' in the world, 22,000 say, and the probability is 0 that we pick a refined number when picking from the numbers between 0 and 1000. Or it might be that every multiple of 22 is a refined number, in which case the probability is greater than zero.

Statement 2 on the other hand tells us that refined numbers are precisely multiples of 22 from which we can find the probability, so the answer is B.
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by cans » Wed Jun 08, 2011 10:17 pm
So basically
a) provides a condition that a refined number must satisfy. There can be lots of other conditions also.
b) defines what a refined number is.
(thus providing all the conditions)
Is it correct?
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by Frankenstein » Wed Jun 08, 2011 10:27 pm
cans wrote:So basically
a) provides a condition that a refined number must satisfy. There can be lots of other conditions also.
b) defines what a refined number is.
(thus providing all the conditions)
Is it correct?
Hi,
Precisely, Yes. I believe this question is posted on the same lines of the 'Integers' question that you posted yesterday.
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by smackmartine » Wed Jun 08, 2011 10:49 pm
Great explanation by Ian.

OA is B
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by krishnasty » Thu Jun 09, 2011 12:42 am
hey guys,

i am still not able to really get a grasp of the explanation. Can someone help me out?
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by Frankenstein » Thu Jun 09, 2011 12:57 am
krishnasty wrote:hey guys,

i am still not able to really get a grasp of the explanation. Can someone help me out?
Hi,
(1)Any refined number must be divisible by 22.
Lets say the set of refined numbers are {220,440,660,880}
Any of these numbers are divisible by 22 but every number divisible by 22 need not be a refined number.

Example: Any student who got an admission to HBS, must get a GMAT score of at least 700.
This means all the students in HBS have got score>700.
But, all students getting score>700 don't get admission to HBS.
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