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# A number of people each wrote down one of the first 30 posit

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A number of people each wrote down one of the first 30 posit [#permalink]

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30 Nov 2008, 19:53
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A number of people each wrote down one of the first 30 positive integers. Were any of the integers written down by more than one of the people?

(1) The number of people who wrote down an integer was greater than 40.
(2) The number of people who wrote down an integer was less than 70.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-number-of-people-each-wrote-down-one-of-the-first-143693.html
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30 Nov 2008, 20:03
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I believe the answer is A.

This is a simple question asked in a confusing way.

The question is asking "If I have a certain number of people each choose 1 of the first positive integers, did any of the people choose the same number?" Statement 1 tells us that the number of people choosing a number was greater than 40. We know that as long as the number of people making a choice is greater than or equal to 30, then duplicates must have been chosen. So Statement 1 is sufficient.

Statement 2 only tells that the number of people making a selection is less than 70. This could be true if 5 people selected or if 65 people selected. Because we don't know for certain, Statement 2 is insufficient.

Because 1 statement is sufficient and the other is not, we do not need to discuss the statements together.

HG wrote:
A number of people each wrote down one of the first 30 positive integers. Were any of the integers written down by more than one of the people

1 - The number of people who wrote down an integer was greater than 40
2 - The number of people who wrote down an integer was less than 70

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J Allen Morris
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30 Nov 2008, 20:40
Thx that helps. I got confused with the wording
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27 Dec 2009, 22:18
Hi, thanks Jallenmorris, I agree that this is a strangely written question.

The question says: "A number of people each wrote down one of the first 30 positive integers."

The book says that statement A is sufficient: "Because the number of people was greater than 30, at least one integer had to be written down by more than one person."

Well, given the question's wording... can't you have 40+ people all writing down the same positive integer? Or, you could have several people choosing 5, and nobody choosing 29.

Did I miss something here?

You could rewrite the question like this:
"A group of people each wrote down a number. Each of the first 30 positive integers were written down by at least one person in the group. Were any of the numbers written down by more than one of the people?" That makes the question rather easy... but at least it fits the solution.

cheers,
s
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28 Dec 2009, 13:08
Answer A because there are only 30 unique integers and there are 40 people who need to choose from them.
You can imagine it as trying to fll 40 buckets with 30 integers and leaving no bucket empty.
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Re: A number of people each wrote down one of the first 30 [#permalink]

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13 Oct 2013, 00:13
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Re: A number of people each wrote down one of the first 30 posit [#permalink]

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13 Oct 2013, 03:28
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Expert's post
A number of people each wrote down one of the first 30 positive integers. Were any of the integers written down by more than one of the people?

There are 30 integers from 1 to 30, inclusive, thus the maximum number of people possible all of them to write different integers is 30. If there are more than 30 people, then at least one of the integers has to be written by more than one person.

(1) The number of people who wrote down an integer was greater than 40 --> at least one of the integers has to be written by more than one person. Sufficient.
(2) The number of people who wrote down an integer was less than 70. Not sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-number-of-people-each-wrote-down-one-of-the-first-143693.html
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Re: A number of people each wrote down one of the first 30 posit   [#permalink] 13 Oct 2013, 03:28
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# A number of people each wrote down one of the first 30 posit

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