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# A bowl is filled with consecutively numbered tiles from 1 to x. Joe

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Senior Manager
Joined: 22 Feb 2004
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A bowl is filled with consecutively numbered tiles from 1 to x. Joe  [#permalink]

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Updated on: 13 Jul 2015, 00:48
2
17
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Difficulty:

95% (hard)

Question Stats:

36% (02:40) correct 64% (02:43) wrong based on 280 sessions

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A bowl is filled with consecutively numbered tiles from 1 to x. Joe pulls out a tile and uses it to construct Sequence Q, which consists of 10 consecutive integers starting with the number drawn. If Joe then selects one number from Sequence Q, what is the probability that the selected number is a multiple of 3?

(1) The last number in Sequence Q is a prime number that is less than 20.
(2) x <= 10

Originally posted by crackgmat750 on 19 Jul 2004, 21:38.
Last edited by Bunuel on 13 Jul 2015, 00:48, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Senior Manager
Joined: 22 Jun 2004
Posts: 360
Location: Bangalore, India
Re: A bowl is filled with consecutively numbered tiles from 1 to x. Joe  [#permalink]

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19 Jul 2004, 22:19
1
I think it is B.

(1)If Q is less than 20 and a prime number too, then Q can be 19,17,13,11 etc. This gives us different probabilities because of multiples of 3 vary depending on the last prime number.

(2) If x <= 10, then because the sequence consists of 10 integers, it should be between 1 and 10. It has 3,6,9 as multiples of 3. The probability is C(3,1) / C(10,1) = 3/10

What is OA?

crackgmat750 wrote:
A bowl is filled with consecutively numbered tiles from 1 to x. Joe pulls out a tile and uses it to construct Sequence Q, which consists of 10 consecutive integers starting with the number drawn. If Joe then selects one number from Sequence Q, what is the probability that the selected number is a multiple of 3?

(1) The last number in Sequence Q is a prime number that is less than 20.

(2) x<10

I strongly suspect that the answer given is incorrect. I just want to confirm if iam not missing something here.

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Awaiting response,

Thnx & Rgds,
Chandra
CIO
Joined: 09 Mar 2003
Posts: 448
Re: A bowl is filled with consecutively numbered tiles from 1 to x. Joe  [#permalink]

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19 Jul 2004, 22:55
1
3

We're looking for the number of multiples of three in a list of 10 consecutive numbers. If the list starts with a multiple of three, it will end with a multiple of three, and there will be 4 multiples in the list, making the probability 4/10. If it starts with any other number, the list will have exactly 3 multiples of 3, and the probability will be 3/10. Try a few and you'll see it.

So the question is just to figure out what it starts and ends with.

1) says that the last number is a prime number less than 20. That means it's not a multiple of 3, so there can't be 4 multiples, but there must be 3 multiples. --> sufficient.

2) says the first number is less than or equal to 10. Since that can be anything, multiple of 3 or not, we cannot know --> Insufficient.
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Re: A bowl is filled with consecutively numbered tiles from 1 to x. Joe  [#permalink]

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19 Jul 2004, 23:05
Ian,

Is not D in that case?

(1)What you say is correct as for 1.

(2)If x <= 10 and the sequence consists of 10 tiles, then x = 10 because if x <10, the sequence of 10 tiles cannot be constructed. It means the probability is certain again with 3/10.

Thus both individually suffice to get the answer. Is it not D then?

ian7777 wrote:

We're looking for the number of multiples of three in a list of 10 consecutive numbers. If the list starts with a multiple of three, it will end with a multiple of three, and there will be 4 multiples in the list, making the probability 4/10. If it starts with any other number, the list will have exactly 3 multiples of 3, and the probability will be 3/10. Try a few and you'll see it.

So the question is just to figure out what it starts and ends with.

1) says that the last number is a prime number less than 20. That means it's not a multiple of 3, so there can't be 4 multiples, but there must be 3 multiples. --> sufficient.

2) says the first number is less than or equal to 10. Since that can be anything, multiple of 3 or not, we cannot know --> Insufficient.

_________________
Awaiting response,

Thnx & Rgds,
Chandra
Senior Manager
Joined: 22 Feb 2004
Posts: 329
Re: A bowl is filled with consecutively numbered tiles from 1 to x. Joe  [#permalink]

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19 Jul 2004, 23:11
mallelac wrote:
Ian,

Is not D in that case?

(1)What you say is correct as for 1.

(2)If x <= 10 and the sequence consists of 10 tiles, then x = 10 because if x <10, the sequence of 10 tiles cannot be constructed. It means the probability is certain again with 3/10.

Thus both individually suffice to get the answer. Is it not D then?

ian7777 wrote:

We're looking for the number of multiples of three in a list of 10 consecutive numbers. If the list starts with a multiple of three, it will end with a multiple of three, and there will be 4 multiples in the list, making the probability 4/10. If it starts with any other number, the list will have exactly 3 multiples of 3, and the probability will be 3/10. Try a few and you'll see it.

So the question is just to figure out what it starts and ends with.

1) says that the last number is a prime number less than 20. That means it's not a multiple of 3, so there can't be 4 multiples, but there must be 3 multiples. --> sufficient.

2) says the first number is less than or equal to 10. Since that can be anything, multiple of 3 or not, we cannot know --> Insufficient.

Exactly..that's what I feel and think answer should be D. But the answer given is A.
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Posts: 448
Re: A bowl is filled with consecutively numbered tiles from 1 to x. Joe  [#permalink]

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19 Jul 2004, 23:14
No, it's A. You're reading the question wrong. x is the last number is the bowl that this dude is pulling his numbers out of. But once he pulls out the first number, Q is built by finding the next 9 consecutive numbers.

So if guy pulls out a 3, then Q will be 3,4,5,6,7,8,9,10,11,12. If he pulls out a 5, Q will be 5,6,7,8,9,10,11,12,13,14.

So x doesn't have to do with the number of numbers in Q, nor is it the last number in Q. It's actually the highest limit of what the first number of Q could be.

Does that make sense?
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Re: A bowl is filled with consecutively numbered tiles from 1 to x. Joe  [#permalink]

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19 Jul 2004, 23:23
1
Yes Ian, it makes sense now.

ian7777 wrote:
No, it's A. You're reading the question wrong. x is the last number is the bowl that this dude is pulling his numbers out of. But once he pulls out the first number, Q is built by finding the next 9 consecutive numbers.

So if guy pulls out a 3, then Q will be 3,4,5,6,7,8,9,10,11,12. If he pulls out a 5, Q will be 5,6,7,8,9,10,11,12,13,14.

So x doesn't have to do with the number of numbers in Q, nor is it the last number in Q. It's actually the highest limit of what the first number of Q could be.

Does that make sense?

_________________
Awaiting response,

Thnx & Rgds,
Chandra
Manager
Joined: 15 Apr 2016
Posts: 68
Re: A bowl is filled with consecutively numbered tiles from 1 to x. Joe  [#permalink]

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12 Sep 2016, 11:43
Actually for the second statement ...
(2) x <= 10

consider x =10 and i pick up 3 - 3,4,5,6,7,8,9,10,11,12 - i have 4 multiples of 3 (3,6,9,12) -prob - 4/10
Consider i pick 4 - 4,5,6,7,8,9,10,11,12,13 - i have 3 multiples of 3(6,9,12)- prob -3/10

since there are 2 results ..A is the answer
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Shri
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Re: A bowl is filled with consecutively numbered tiles from 1 to x. Joe  [#permalink]

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21 Aug 2018, 20:22
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Re: A bowl is filled with consecutively numbered tiles from 1 to x. Joe   [#permalink] 21 Aug 2018, 20:22
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