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

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A number of people each wrote down one of the first 30 [#permalink] New post 06 Dec 2012, 06:17
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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.
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Re: A number of people each wrote down one of the first 30 [#permalink] New post 06 Dec 2012, 06:23
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.

Answer: A.
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Re: A number of people each wrote down one of the first 30 [#permalink] New post 06 May 2013, 23:18
Bunuel 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?

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.

Answer: A.


How can we say that for sure? Its also possible that all the individuals wrote down 1. There is no mention that everyone has to write a unique number.
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Re: A number of people each wrote down one of the first 30 [#permalink] New post 06 May 2013, 23:22
Expert's post
melguy wrote:
Bunuel 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?

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.

Answer: A.


How can we say that for sure? Its also possible that all the individuals wrote down 1. There is no mention that everyone has to write a unique number.


Say the number of people is 41. Each should write down one of the first 30 positive integers (1, 2, 3, ..., 30). Ask yourself, can each of them write the different integer?
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COLLECTION OF QUESTIONS:
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Re: A number of people each wrote down one of the first 30 [#permalink] New post 07 May 2013, 00:56
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.

I am not sure what is stopping all 40 people from writing down number 1 on their paper? Why does it has to be a sequence.. All of the 40 can just write a single number (i.e. 1) on their paper.
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Re: A number of people each wrote down one of the first 30 [#permalink] New post 07 May 2013, 01:10
Expert's post
melguy 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.

I am not sure what is stopping all 40 people from writing down number 1 on their paper? Why does it has to be a sequence.. All of the 40 can just write a single number (i.e. 1) on their paper.


Yes, and in this case one of the integers (1) will be written down by more than one of the people. Thus the answer to the question will be YES. Does this make sense?
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Manager
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Re: A number of people each wrote down one of the first 30 [#permalink] New post 07 May 2013, 01:25
Ah....I get the problem now. Its an easy problem! Actually I was thinking exactly the opposite in my brain and wondering why am i getting the wrong answer!

Time to cut down on careless mistakes :oops:

Thanks for your patience while my brain was switched off :roll:
Re: A number of people each wrote down one of the first 30   [#permalink] 07 May 2013, 01:25
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