If a number is drawn at random from the first 1000 positive

Question

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

GMATT73 · Accepted Answer

1. Statement 1 tells us that a refined number must be a multiple of 22. This is a necessary, but not sufficient condition for a refined number. While every refined number is a multiple of 22, every multiple of 22 is not necessarily a refined number. Since we have no other info about the definition of a refined number, we cannot determine how many integers from 1-1000 fit that definition. Insuff.

2. Statement 2 provides us with a definition of a refined number- an even multiple of 11. We can find the number of even multiples of 11 in the set, so this is sufficient.

OA is (B)

HongHu · Answer

Yes I've seen this question type in the GMAT test. The trap is (1) doesn't define "refined number" and (2) does. 
For example, you can say "an even number must be an integer", this doesn't define an even number, because not every integer is an even number. Similarly with (1), every refined number must be divided by 22. But perhaps they also must be divided by 4, or something else.

believe2 · Answer

I think it should be D

1. you can find the number of numbers divisible by 22 and less than 1000 ----> sufficient

2. you can find the number of numbers divisible by 11 and less than 1000 ----> sufficient

GMATT73 · Answer

Sorry guys, OA is not D. Any other guesses?

TeHCM · Answer

B?

Somehow I think the wordings are a little tricky.........

ywilfred · Answer

Isn't (2) just a repetition of (1)?
(2) says the refined number must be an even multiple of 11. So a refined number can be 22, 44, 66, 88, 110,... etc... All these are multiples off 22, which is given in (1).

believe2 · Answer

GMATT73 I see the point.
..this question has a very good trap.

tobiastt · Answer

good question. I think it is B. I is just a condition but does not define refined numbers.

FN · Answer

what is the point?
I dont get it...(1) and (2) are saying the same thing...I would say such a twisted question will never appear on the GMAT!

christoph · Answer

the diff b/w 1) and 2) is that in 1) 22 and 44 may be refined numbers. we can calc the prob. 22 44 66 may be refinded numbers as well. the prob to the former example is different but both satisfy 1). in 2) its certain that every mutiple off 22 is a refined number. there is only one value for the prob.

Marcab · Answer

Sorry for starting this old thread, but can anyone please elaborate on this ancient problem? I am still not able to distinguish 1 and 2, apart from considering that one is definition and the other is not. Need examples for clarification.

Hiho · Answer

I would say it's more about the wording than the math.

Let's make it simple.

1. Any refined number must be divisible by 22

If refined numbers were 44n then (1) would give us wrong numbers. 44, 88, 132 = refined. But (1) doesn't tell us that 22, 44, 110 is not refined.
 
2. A refined number is any even multiple of 11.

Here we're told the actual definition of refined numbers. They're the even multiples of 11.

11*2
11*4
11*6
and so on.

This doesn't leave any blind spots or confusion.

virajgawade · Answer

Hello Guys, 
This is my first post, I hope you find it helpful.

Now in the question they have asked a no. Is drawn from first 1000 positive integers, and its probability. Def. Of refined no, is given in respective statements. Its all about wordings.

Now,
S1.) Any refined no must be divisible by 22, this include 22, 44, 242, 110, 198,.... and the list goes on, there are definite nos. and nos can be found, but the statement says ANY, which is absurd.
INSUFFICIENT.

S2.) A refined no is any even multiple of 11. This includes 22, 44, 66, 88, 286,484, 968..... and on, here also no can be found but A REFINED NO. IS MENTIONED. This makes it clear a definite no particularly even multiple of 11.
SUFFICIENT. 
BASICALLY ITS ALL ON WORDING, YOU DONT NEED TO SOLVE.

ANS B.

WHAT YOU THINK, YOU BECOME.

Nevernevergiveup · Answer

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

Well...........I thought to represent my solution in a humorous way.

The villain here in this problem(Or clever wordplay formally) is the word Any :evil:

Statement 1: Any refined number must be divisible by 22

I imagine a scenario where a top dreaded villain came to know that he can be attacked by some one.

He asks who is he?(kaun hai woh?)

Clue he gets is He is a human being.(Woh ek insaan hai :wink: )

Does that give him any proper info other than that it is not a creature or animal. Where will he search for that person? Can each and every person be that special one? No right. A bit similar scenario of Kans.......Isnt it.

So Any refined number must be divisible by 22 indicates that Refined number may include 22 and may not include 44 and still be correct.

Hence we have no idea what multiples of 22 it does include and what it doesn't and is not sufficient.

Statement 2: A refined number is any even multiple of 11............22

Here the refined number includes every multiple of 22 under 1000.

We don't have to list all of them but we know that they are finite.

Hence the statement 2 is sufficient.

one more such problem where this misguiding clue concept is used.
what-is-the-probability-of-selecting-a-clean-number-from-a-s-139647.html

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