Find all School-related info fast with the new School-Specific MBA Forum

It is currently 01 Aug 2015, 15:19
GMAT Club Tests

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Manager
Manager
avatar
Joined: 02 Dec 2012
Posts: 178
Followers: 3

Kudos [?]: 890 [1] , given: 0

A number of people each wrote down one of the first 30 [#permalink] New post 06 Dec 2012, 06:17
1
This post received
KUDOS
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

82% (01:38) correct 18% (01:03) wrong based on 330 sessions
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.
[Reveal] Spoiler: OA
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 28781
Followers: 4594

Kudos [?]: 47463 [0], given: 7123

Re: A number of people each wrote down one of the first 30 [#permalink] New post 06 Dec 2012, 06:23
Expert's post
1
This post was
BOOKMARKED
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.
_________________

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

PLEASE READ AND FOLLOW: 12 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 ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Manager
Manager
avatar
Joined: 22 Mar 2011
Posts: 68
Followers: 1

Kudos [?]: 3 [0], given: 10

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.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 28781
Followers: 4594

Kudos [?]: 47463 [0], given: 7123

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?
_________________

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

PLEASE READ AND FOLLOW: 12 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 ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Manager
Manager
avatar
Joined: 22 Mar 2011
Posts: 68
Followers: 1

Kudos [?]: 3 [0], given: 10

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.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 28781
Followers: 4594

Kudos [?]: 47463 [0], given: 7123

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: 12 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 ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Manager
Manager
avatar
Joined: 22 Mar 2011
Posts: 68
Followers: 1

Kudos [?]: 3 [0], given: 10

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:
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 5708
Followers: 323

Kudos [?]: 63 [0], given: 0

Premium Member
Re: A number of people each wrote down one of the first 30 [#permalink] New post 02 Aug 2014, 15:48
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Intern
Intern
avatar
Joined: 21 Jun 2014
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 1

GMAT ToolKit User
A number of people each wrote down one of the first 30 [#permalink] New post 05 Dec 2014, 15:36
This one can be confusing... I made the mistake of not reading the statements properly. The statements are giving the number of people not the sum of the amount of the number that the people wrote down.

Statement 1:
There at least 10 numbers that are written twice because 30 of the people could write down different numbers but after that the rest of the people have to reuse numbers that were already written down.

Statement 2:
The number of people could be 30 and each one writing a different number... So we don't know if there are any duplicate numbers.
Intern
Intern
avatar
Joined: 18 Apr 2015
Posts: 33
Followers: 0

Kudos [?]: 0 [0], given: 4

Re: A number of people each wrote down one of the first 30 [#permalink] New post 26 Apr 2015, 12:00
Hi,

Consider there are 3 ppl and we are asked to write down any integers from 1 to 30. I could write 2 the next one could write 10 ,the 3rd one could write 2 as well.So does the number of ppl really matter here.


By the above logic both the statements have to be correct.

Please correct me if i am wrong
Math Forum Moderator
User avatar
Joined: 06 Jul 2014
Posts: 461
Location: Ukraine
GMAT 1: 660 Q48 V33
Followers: 14

Kudos [?]: 264 [0], given: 106

GMAT ToolKit User Premium Member CAT Tests
A number of people each wrote down one of the first 30 [#permalink] New post 26 Apr 2015, 12:10
kirtivardhan wrote:
Hi,

Consider there are 3 ppl and we are asked to write down any integers from 1 to 30. I could write 2 the next one could write 10 ,the 3rd one could write 2 as well.So does the number of ppl really matter here.


By the above logic both the statements have to be correct.

Please correct me if i am wrong



In DS questions, statement will be sufficient if answer is definite. In case which you descrive two variants are possbile:
Some of this 3 persons could write the same numbers or maybe they are wrote three different numbers. For DS this is insufficient answer.
Intern
Intern
avatar
Joined: 18 Apr 2015
Posts: 33
Followers: 0

Kudos [?]: 0 [0], given: 4

Re: A number of people each wrote down one of the first 30 [#permalink] New post 26 Apr 2015, 12:48
Following the same logic,both the statements should have been insufficient right?
Math Forum Moderator
User avatar
Joined: 06 Jul 2014
Posts: 461
Location: Ukraine
GMAT 1: 660 Q48 V33
Followers: 14

Kudos [?]: 264 [0], given: 106

GMAT ToolKit User Premium Member CAT Tests
Re: A number of people each wrote down one of the first 30 [#permalink] New post 26 Apr 2015, 12:52
kirtivardhan wrote:
Following the same logic,both the statements should have been insufficient right?


No, because from first statement you know that numbers will be repeat in ANY case.
Because 40 people can't write first 30 numbers and don't repeat them.

So it's definite answer and this sufficient.
Expert Post
1 KUDOS received
EMPOWERgmat Instructor
User avatar
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 3073
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 134

Kudos [?]: 852 [1] , given: 54

Re: A number of people each wrote down one of the first 30 [#permalink] New post 27 Apr 2015, 14:17
1
This post received
KUDOS
Expert's post
Hi All,

This DS questions is a great example of how you can "rewrite" the question to find "the question behind the question."

We're told that an unknown number of people EACH wrote down one of the first 30 positive integers (1-30, inclusive). We're asked if ANY of the integers were written down by MORE than one person. This is a YES/NO question.

Given the 'restrictions' in this question, IF there are MORE than 30 people, then at least one of the numbers would be repeated. If there are 30 or LESS, then it's possible that a number was repeated, BUT it's also possible that NONE of the numbers were repeated. So the question is really asking...."Were there more than 30 people?"

Fact 1: The number of people....was greater than 40

This GUARANTEES that at least 1 of the numbers was written more than once, so the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

Fact 2: The number of people....was less than 70

IF....
The total number of people was greater than 30, then the answer to the question is YES.

IF...
The total number of people is 30 or LESS, then the answer to the question COULD be YES, but it COULD be NO.
Fact 2 is INSUFFICIENT.

Final Answer:
[Reveal] Spoiler:
A


GMAT assassins aren't born, they're made,
Rich
_________________

Official Guide 2016 Question Breakdown:
http://gmatclub.com/forum/empowergmat-blog-198415.html#p1527977

Rich Cohen
Rich.C@empowergmat.com
http://www.empowergmat.com

GMAT Club Verified Reviews for EMPOWERgmat & Special Discount

EMPOWERgmat Podcast - A Wild Secret About The GMAT Algorithm


Intern
Intern
avatar
Joined: 18 Apr 2015
Posts: 33
Followers: 0

Kudos [?]: 0 [0], given: 4

Re: A number of people each wrote down one of the first 30 [#permalink] New post 28 Apr 2015, 19:26
Hi Bunnel,

The thing i am not able to understand is why not 2 ppl write the same number.In that case whether the number of ppl >40 or <70 the number that they write will be repeated.

Please assist
Math Forum Moderator
User avatar
Joined: 06 Jul 2014
Posts: 461
Location: Ukraine
GMAT 1: 660 Q48 V33
Followers: 14

Kudos [?]: 264 [0], given: 106

GMAT ToolKit User Premium Member CAT Tests
Re: A number of people each wrote down one of the first 30 [#permalink] New post 28 Apr 2015, 22:35
kirtivardhan wrote:
Hi Bunnel,

The thing i am not able to understand is why not 2 ppl write the same number.In that case whether the number of ppl >40 or <70 the number that they write will be repeated.

Please assist


Hello kirtivardhan

You understand absolutely right: people from 2 statement will write the same number in any case. And we sure about this and that's why second statement Sufficient.
Intern
Intern
avatar
Joined: 18 Apr 2015
Posts: 33
Followers: 0

Kudos [?]: 0 [0], given: 4

Re: A number of people each wrote down one of the first 30 [#permalink] New post 28 Apr 2015, 22:38
If so,then the answer would have been both are sufficient
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 28781
Followers: 4594

Kudos [?]: 47463 [0], given: 7123

Re: A number of people each wrote down one of the first 30 [#permalink] New post 29 Apr 2015, 01:25
Expert's post
Expert Post
EMPOWERgmat Instructor
User avatar
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 3073
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 134

Kudos [?]: 852 [0], given: 54

Re: A number of people each wrote down one of the first 30 [#permalink] New post 29 Apr 2015, 10:03
Expert's post
kirtivardhan wrote:
Hi Bunnel,

The thing i am not able to understand is why not 2 ppl write the same number.In that case whether the number of ppl >40 or <70 the number that they write will be repeated.

Please assist


Hi kirtivardhan,

The 'tricky' part about this question is that we don't know what number each individual person wrote down.

As an example....If there were only 2 people, it's POSSIBLE that they both wrote down the SAME number, but it's ALSO POSSIBLE that they wrote down two DIFFERENT numbers.

In Fact 2, we're told that there are fewer than 70 people....so there COULD be just 2 people and the above 2 results are both possible. That's why Fact 2 is INSUFFICIENT.

GMAT assassins aren't born, they're made,
Rich
_________________

Official Guide 2016 Question Breakdown:
http://gmatclub.com/forum/empowergmat-blog-198415.html#p1527977

Rich Cohen
Rich.C@empowergmat.com
http://www.empowergmat.com

GMAT Club Verified Reviews for EMPOWERgmat & Special Discount

EMPOWERgmat Podcast - A Wild Secret About The GMAT Algorithm


Re: A number of people each wrote down one of the first 30   [#permalink] 29 Apr 2015, 10:03
    Similar topics Author Replies Last post
Similar
Topics:
11 Experts publish their posts in the topic In the sequence S of numbers, each term after the first two Bunuel 6 26 Feb 2014, 01:21
Experts publish their posts in the topic In a picnic 60% people ate two hotdogs, 30% people ate one docabuzar 4 30 Jan 2012, 11:58
2 Experts publish their posts in the topic In the sequence S of numbers, each term after the first two conan9118 5 30 May 2011, 04:54
Each of the 30 first graders in a class bought one of three banksy 2 09 Mar 2011, 14:04
1 Experts publish their posts in the topic A number of people each wrote down one of the first 30 posit HG 6 30 Nov 2008, 18:53
Display posts from previous: Sort by

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

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.