Probability Tricky problem

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dhonu121: Master | Next Rank: 500 Posts; Posts: 316; Joined: Sun Aug 21, 2011 6:18 am; Thanked: 16 times; Followed by:6 members

Probability Tricky problem

by dhonu121 » Thu Jun 07, 2012 12:33 am

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:A.

Why is the OA not D.
Since both A and B are able to solve the question asked.

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Source: Beat The GMAT — Data Sufficiency | Thu Jun 07, 2012 12:33 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Thu Jun 07, 2012 1:46 am

dhonu121 wrote: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.

Statement 1: This statement provides a necessary condition for a number to be a refined number. But we should note that this condition is neither sufficient nor it is a definition of refined number. There may or not be some other condition for a number to be refined number.

Not sufficient.

Statement 2: Now we know the definition of refined numbers.
Hence, we can easily calculate the number of refined numbers in the first 1000 integers and find the probability.

Sufficient.

The correct answer is B.

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dhonu121: Master | Next Rank: 500 Posts; Posts: 316; Joined: Sun Aug 21, 2011 6:18 am; Thanked: 16 times; Followed by:6 members

by dhonu121 » Thu Jun 07, 2012 3:52 am

Hi Anurag,
So will it be right to say that when an option is worded the way 1 above is, it always will be a necessary but no sufficient condition ?

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Thu Jun 07, 2012 5:42 am

dhonu121 wrote:So will it be right to say that when an option is worded the way 1 above is, it always will be a necessary but no sufficient condition ?

Yes.